id sid tid token lemma pos cana-1744 1 1 communications communication NOUN cana-1744 1 2 on on ADP cana-1744 1 3 applied apply VERB cana-1744 1 4 nonlinear nonlinear ADJ cana-1744 1 5 analysis analysis NOUN cana-1744 1 6 issn issn NOUN cana-1744 1 7 : : PUNCT cana-1744 1 8 1074 1074 NUM cana-1744 1 9 - - PUNCT cana-1744 1 10 133x 133x NUM cana-1744 1 11 vol vol NOUN cana-1744 1 12 32 32 NUM cana-1744 1 13 no no NOUN cana-1744 1 14 . . NOUN cana-1744 1 15 2 2 NUM cana-1744 1 16 ( ( PUNCT cana-1744 1 17 2025 2025 NUM cana-1744 1 18 ) ) PUNCT cana-1744 1 19 305 305 NUM cana-1744 1 20 https://internationalpubls.com https://internationalpubls.com X cana-1744 1 21 a a DET cana-1744 1 22 single single ADJ cana-1744 1 23 server server NOUN cana-1744 1 24 markovian markovian PROPN cana-1744 1 25 general general PROPN cana-1744 1 26 service service NOUN cana-1744 1 27 retrialencouraged retrialencourage VERB cana-1744 1 28 arrival arrival NOUN cana-1744 1 29 queuing queue VERB cana-1744 1 30 system system NOUN cana-1744 1 31 with with ADP cana-1744 1 32 persistent persistent ADJ cana-1744 1 33 retrial retrial ADJ cana-1744 1 34 technique technique NOUN cana-1744 1 35 under under ADP cana-1744 1 36 the the DET cana-1744 1 37 transitory transitory ADJ cana-1744 1 38 behaviour behaviour NOUN cana-1744 1 39 ismailkhan ismailkhan PROPN cana-1744 1 40 e1 e1 PROPN cana-1744 1 41 * * PROPN cana-1744 1 42 , , PUNCT cana-1744 1 43 s. s. PROPN cana-1744 1 44 moorthy2 moorthy2 PROPN cana-1744 1 45 , , PUNCT cana-1744 1 46 p. p. PROPN cana-1744 1 47 thangaraja3 thangaraja3 PROPN cana-1744 2 1 * * PUNCT cana-1744 2 2 , , PUNCT cana-1744 2 3 syed syed ADJ cana-1744 2 4 siddiqua siddiqua NOUN cana-1744 2 5 begum4 begum4 NOUN cana-1744 2 6 and and CCONJ cana-1744 2 7 k. k. PROPN cana-1744 2 8 rajesh5 rajesh5 PROPN cana-1744 2 9 1,3 1,3 NUM cana-1744 2 10 department department NOUN cana-1744 2 11 of of ADP cana-1744 2 12 mathematics mathematic NOUN cana-1744 2 13 , , PUNCT cana-1744 2 14 panimalar panimalar ADJ cana-1744 2 15 engineering engineering NOUN cana-1744 2 16 college college NOUN cana-1744 2 17 , , PUNCT cana-1744 2 18 chennai-600 chennai-600 NOUN cana-1744 2 19 123 123 NUM cana-1744 2 20 , , PUNCT cana-1744 2 21 tamil tamil PROPN cana-1744 2 22 nadu nadu PROPN cana-1744 2 23 , , PUNCT cana-1744 2 24 india india PROPN cana-1744 2 25 . . PROPN cana-1744 3 1 2,5 2,5 NUM cana-1744 3 2 department department NOUN cana-1744 3 3 of of ADP cana-1744 3 4 mathematics mathematic NOUN cana-1744 3 5 , , PUNCT cana-1744 3 6 government government NOUN cana-1744 3 7 arts art NOUN cana-1744 3 8 and and CCONJ cana-1744 3 9 science science NOUN cana-1744 3 10 college college PROPN cana-1744 3 11 for for ADP cana-1744 3 12 women woman NOUN cana-1744 3 13 , , PUNCT cana-1744 3 14 bargur-635104 bargur-635104 NOUN cana-1744 3 15 , , PUNCT cana-1744 3 16 tamil tamil PROPN cana-1744 3 17 nadu nadu PROPN cana-1744 3 18 , , PUNCT cana-1744 3 19 india india PROPN cana-1744 3 20 . . PROPN cana-1744 3 21 4 4 NUM cana-1744 3 22 department department NOUN cana-1744 3 23 of of ADP cana-1744 3 24 mathematics mathematic NOUN cana-1744 3 25 and and CCONJ cana-1744 3 26 actuarial actuarial ADJ cana-1744 3 27 science science NOUN cana-1744 3 28 , , PUNCT cana-1744 3 29 b.s b.s PROPN cana-1744 3 30 . . PROPN cana-1744 3 31 abdur abdur PROPN cana-1744 3 32 rahman rahman PROPN cana-1744 3 33 crescent crescent PROPN cana-1744 3 34 institute institute PROPN cana-1744 3 35 of of ADP cana-1744 3 36 science science NOUN cana-1744 3 37 and and CCONJ cana-1744 3 38 technology technology NOUN cana-1744 3 39 , , PUNCT cana-1744 3 40 vandalur vandalur NOUN cana-1744 3 41 , , PUNCT cana-1744 3 42 chennai chennai PROPN cana-1744 3 43 , , PUNCT cana-1744 3 44 tamil tamil PROPN cana-1744 3 45 nadu nadu PROPN cana-1744 3 46 , , PUNCT cana-1744 3 47 india india PROPN cana-1744 3 48 . . PUNCT cana-1744 4 1 corresponding correspond VERB cana-1744 4 2 author author NOUN cana-1744 4 3 e e NOUN cana-1744 4 4 - - NOUN cana-1744 4 5 mail mail NOUN cana-1744 4 6 : : PUNCT cana-1744 4 7 ismailkhanmubarak@gmail.com ismailkhanmubarak@gmail.com X cana-1744 4 8 , , PUNCT cana-1744 4 9 thangarajap1991@gmail.com thangarajap1991@gmail.com X cana-1744 4 10 article article NOUN cana-1744 4 11 history history NOUN cana-1744 4 12 : : PUNCT cana-1744 4 13 received receive VERB cana-1744 4 14 : : PUNCT cana-1744 4 15 01 01 NUM cana-1744 4 16 - - SYM cana-1744 4 17 08 08 NUM cana-1744 4 18 - - PUNCT cana-1744 4 19 2024 2024 NUM cana-1744 4 20 revised revise VERB cana-1744 4 21 : : PUNCT cana-1744 4 22 09 09 NUM cana-1744 4 23 - - SYM cana-1744 4 24 09 09 NUM cana-1744 4 25 - - PUNCT cana-1744 4 26 2024 2024 NUM cana-1744 4 27 accepted accept VERB cana-1744 4 28 : : PUNCT cana-1744 4 29 19 19 NUM cana-1744 4 30 - - PUNCT cana-1744 4 31 09 09 NUM cana-1744 4 32 - - PUNCT cana-1744 4 33 2024 2024 NUM cana-1744 4 34 abstract abstract NOUN cana-1744 4 35 : : PUNCT cana-1744 4 36 in in ADP cana-1744 4 37 this this DET cana-1744 4 38 paper paper NOUN cana-1744 4 39 , , PUNCT cana-1744 4 40 the the DET cana-1744 4 41 objective objective NOUN cana-1744 4 42 of of ADP cana-1744 4 43 this this DET cana-1744 4 44 research research NOUN cana-1744 4 45 is be AUX cana-1744 4 46 to to PART cana-1744 4 47 analyse analyse VERB cana-1744 4 48 the the DET cana-1744 4 49 behaviour behaviour NOUN cana-1744 4 50 and and CCONJ cana-1744 4 51 performance performance NOUN cana-1744 4 52 of of ADP cana-1744 4 53 a a DET cana-1744 4 54 single single ADJ cana-1744 4 55 server server NOUN cana-1744 4 56 retrial retrial NOUN cana-1744 4 57 - - PUNCT cana-1744 4 58 encouraged encourage VERB cana-1744 4 59 arrival arrival NOUN cana-1744 4 60 queuing queue VERB cana-1744 4 61 system system NOUN cana-1744 4 62 . . PUNCT cana-1744 5 1 specifically specifically ADV cana-1744 5 2 , , PUNCT cana-1744 5 3 it it PRON cana-1744 5 4 aims aim VERB cana-1744 5 5 to to PART cana-1744 5 6 derive derive VERB cana-1744 5 7 the the DET cana-1744 5 8 steady steady ADJ cana-1744 5 9 - - PUNCT cana-1744 5 10 state state NOUN cana-1744 5 11 distributions distribution NOUN cana-1744 5 12 for for ADP cana-1744 5 13 the the DET cana-1744 5 14 system system NOUN cana-1744 5 15 using use VERB cana-1744 5 16 the the DET cana-1744 5 17 transitory transitory ADJ cana-1744 5 18 technique technique NOUN cana-1744 5 19 . . PUNCT cana-1744 6 1 to to PART cana-1744 6 2 calculate calculate VERB cana-1744 6 3 the the DET cana-1744 6 4 performance performance NOUN cana-1744 6 5 metrics metric NOUN cana-1744 6 6 such such ADJ cana-1744 6 7 as as ADP cana-1744 6 8 the the DET cana-1744 6 9 average average ADJ cana-1744 6 10 number number NOUN cana-1744 6 11 of of ADP cana-1744 6 12 consumers consumer NOUN cana-1744 6 13 in in ADP cana-1744 6 14 the the DET cana-1744 6 15 orbit orbit NOUN cana-1744 6 16 , , PUNCT cana-1744 6 17 and and CCONJ cana-1744 6 18 probabilities probability NOUN cana-1744 6 19 of of ADP cana-1744 6 20 the the DET cana-1744 6 21 server server NOUN cana-1744 6 22 being be AUX cana-1744 6 23 busy busy ADJ cana-1744 6 24 and and CCONJ cana-1744 6 25 idle idle ADJ cana-1744 6 26 . . PUNCT cana-1744 7 1 hereafter hereafter PROPN cana-1744 7 2 conduct conduct VERB cana-1744 7 3 the the DET cana-1744 7 4 numerical numerical ADJ cana-1744 7 5 illustration illustration NOUN cana-1744 7 6 for for ADP cana-1744 7 7 various various ADJ cana-1744 7 8 service service NOUN cana-1744 7 9 time time NOUN cana-1744 7 10 distributions distribution NOUN cana-1744 7 11 like like ADP cana-1744 7 12 ( ( PUNCT cana-1744 7 13 exponential exponential NOUN cana-1744 7 14 and and CCONJ cana-1744 7 15 erlang erlang PROPN cana-1744 7 16 ) ) PUNCT cana-1744 7 17 to to PART cana-1744 7 18 understand understand VERB cana-1744 7 19 the the DET cana-1744 7 20 impact impact NOUN cana-1744 7 21 of of ADP cana-1744 7 22 different different ADJ cana-1744 7 23 system system NOUN cana-1744 7 24 performances performance NOUN cana-1744 7 25 on on ADP cana-1744 7 26 parameters parameter NOUN cana-1744 7 27 . . PUNCT cana-1744 8 1 this this DET cana-1744 8 2 research research NOUN cana-1744 8 3 helps help VERB cana-1744 8 4 in in ADP cana-1744 8 5 understanding understand VERB cana-1744 8 6 how how SCONJ cana-1744 8 7 the the DET cana-1744 8 8 system system NOUN cana-1744 8 9 performs perform VERB cana-1744 8 10 under under ADP cana-1744 8 11 different different ADJ cana-1744 8 12 conditions condition NOUN cana-1744 8 13 and and CCONJ cana-1744 8 14 can can AUX cana-1744 8 15 be be AUX cana-1744 8 16 useful useful ADJ cana-1744 8 17 for for ADP cana-1744 8 18 optimizing optimize VERB cana-1744 8 19 queue queue NOUN cana-1744 8 20 management management NOUN cana-1744 8 21 in in ADP cana-1744 8 22 different different ADJ cana-1744 8 23 applications application NOUN cana-1744 8 24 . . PUNCT cana-1744 9 1 keywords keyword NOUN cana-1744 9 2 : : PUNCT cana-1744 9 3 encouraged encouraged ADJ cana-1744 9 4 arrival arrival NOUN cana-1744 9 5 , , PUNCT cana-1744 9 6 retrial retrial ADJ cana-1744 9 7 technique technique NOUN cana-1744 9 8 , , PUNCT cana-1744 9 9 transitory transitory ADJ cana-1744 9 10 behaviour behaviour NOUN cana-1744 9 11 , , PUNCT cana-1744 9 12 exponential exponential ADJ cana-1744 9 13 distribution distribution NOUN cana-1744 9 14 , , PUNCT cana-1744 9 15 erlangian erlangian ADJ cana-1744 9 16 distribution distribution NOUN cana-1744 9 17 1 1 NUM cana-1744 9 18 . . PUNCT cana-1744 10 1 introduction introduction NOUN cana-1744 10 2 retrial retrial ADJ cana-1744 10 3 queues queue NOUN cana-1744 10 4 are be AUX cana-1744 10 5 queuing queue VERB cana-1744 10 6 systems system NOUN cana-1744 10 7 that that PRON cana-1744 10 8 allow allow VERB cana-1744 10 9 incoming incoming ADJ cana-1744 10 10 customers customer NOUN cana-1744 10 11 to to PART cana-1744 10 12 retry retry VERB cana-1744 10 13 for for ADP cana-1744 10 14 service service NOUN cana-1744 10 15 after after ADP cana-1744 10 16 a a DET cana-1744 10 17 certain certain ADJ cana-1744 10 18 amount amount NOUN cana-1744 10 19 of of ADP cana-1744 10 20 time time NOUN cana-1744 10 21 if if SCONJ cana-1744 10 22 they they PRON cana-1744 10 23 discover discover VERB cana-1744 10 24 the the DET cana-1744 10 25 server server NOUN cana-1744 10 26 and and CCONJ cana-1744 10 27 any any DET cana-1744 10 28 waiting wait VERB cana-1744 10 29 spots spot NOUN cana-1744 10 30 to to PART cana-1744 10 31 be be AUX cana-1744 10 32 occupied occupy VERB cana-1744 10 33 . . PUNCT cana-1744 11 1 an an DET cana-1744 11 2 essential essential ADJ cana-1744 11 3 component component NOUN cana-1744 11 4 of of ADP cana-1744 11 5 the the DET cana-1744 11 6 concept concept NOUN cana-1744 11 7 of of ADP cana-1744 11 8 queueing queue VERB cana-1744 11 9 is be AUX cana-1744 11 10 the the DET cana-1744 11 11 model model NOUN cana-1744 11 12 of of ADP cana-1744 11 13 retrial retrial ADJ cana-1744 11 14 queues queue NOUN cana-1744 11 15 . . PUNCT cana-1744 12 1 the the DET cana-1744 12 2 need need NOUN cana-1744 12 3 to to PART cana-1744 12 4 account account VERB cana-1744 12 5 for for ADP cana-1744 12 6 the the DET cana-1744 12 7 retry retry ADJ cana-1744 12 8 effect effect NOUN cana-1744 12 9 in in ADP cana-1744 12 10 everyday everyday ADJ cana-1744 12 11 life life NOUN cana-1744 12 12 and and CCONJ cana-1744 12 13 different different ADJ cana-1744 12 14 networking networking NOUN cana-1744 12 15 systems system NOUN cana-1744 12 16 gives give VERB cana-1744 12 17 birth birth NOUN cana-1744 12 18 to to ADP cana-1744 12 19 these these DET cana-1744 12 20 models model NOUN cana-1744 12 21 . . PUNCT cana-1744 13 1 for for ADP cana-1744 13 2 this this DET cana-1744 13 3 reason reason NOUN cana-1744 13 4 , , PUNCT cana-1744 13 5 the the DET cana-1744 13 6 study study NOUN cana-1744 13 7 of of ADP cana-1744 13 8 such such ADJ cana-1744 13 9 queue queue NOUN cana-1744 13 10 models model NOUN cana-1744 13 11 receives receive VERB cana-1744 13 12 a a DET cana-1744 13 13 lot lot NOUN cana-1744 13 14 of of ADP cana-1744 13 15 interest interest NOUN cana-1744 13 16 . . PUNCT cana-1744 14 1 several several ADJ cana-1744 14 2 communication communication NOUN cana-1744 14 3 networks network NOUN cana-1744 14 4 can can AUX cana-1744 14 5 be be AUX cana-1744 14 6 accurately accurately ADV cana-1744 14 7 described describe VERB cana-1744 14 8 by by ADP cana-1744 14 9 trial trial NOUN cana-1744 14 10 queueing queueing NOUN cana-1744 14 11 models model NOUN cana-1744 14 12 . . PUNCT cana-1744 15 1 their their PRON cana-1744 15 2 inquiry inquiry NOUN cana-1744 15 3 is be AUX cana-1744 15 4 , , PUNCT cana-1744 15 5 therefore therefore ADV cana-1744 15 6 , , PUNCT cana-1744 15 7 crucial crucial ADJ cana-1744 15 8 . . PUNCT cana-1744 16 1 in in ADP cana-1744 16 2 tele tele PROPN cana-1744 16 3 - - PUNCT cana-1744 16 4 traffic traffic NOUN cana-1744 16 5 theory theory NOUN cana-1744 16 6 and and CCONJ cana-1744 16 7 telephone telephone NOUN cana-1744 16 8 networks network NOUN cana-1744 16 9 where where SCONJ cana-1744 16 10 customers customer NOUN cana-1744 16 11 redial redial VERB cana-1744 16 12 after after ADP cana-1744 16 13 receiving receive VERB cana-1744 16 14 an an DET cana-1744 16 15 engaged engaged ADJ cana-1744 16 16 signal signal NOUN cana-1744 16 17 , , PUNCT cana-1744 16 18 retry retry ADJ cana-1744 16 19 queues queue NOUN cana-1744 16 20 have have AUX cana-1744 16 21 been be AUX cana-1744 16 22 seen see VERB cana-1744 16 23 as as ADP cana-1744 16 24 an an DET cana-1744 16 25 intriguing intriguing ADJ cana-1744 16 26 subject subject NOUN cana-1744 16 27 . . PUNCT cana-1744 17 1 a a DET cana-1744 17 2 comparative comparative ADJ cana-1744 17 3 analysis analysis NOUN cana-1744 17 4 of of ADP cana-1744 17 5 standard standard ADJ cana-1744 17 6 queuing queue VERB cana-1744 17 7 systems system NOUN cana-1744 17 8 and and CCONJ cana-1744 17 9 the the DET cana-1744 17 10 retrial retrial ADJ cana-1744 17 11 queuing queuing NOUN cana-1744 17 12 technique technique NOUN cana-1744 17 13 is be AUX cana-1744 17 14 investigated investigate VERB cana-1744 17 15 in in ADP cana-1744 17 16 [ [ X cana-1744 17 17 1 1 NUM cana-1744 17 18 ] ] PUNCT cana-1744 17 19 . . PUNCT cana-1744 18 1 a a DET cana-1744 18 2 comprehensive comprehensive ADJ cana-1744 18 3 and and CCONJ cana-1744 18 4 modern modern ADJ cana-1744 18 5 treatment treatment NOUN cana-1744 18 6 of of ADP cana-1744 18 7 retrial retrial ADJ cana-1744 18 8 queuing queuing NOUN cana-1744 18 9 systems system NOUN cana-1744 18 10 through through ADP cana-1744 18 11 computational computational ADJ cana-1744 18 12 techniques technique NOUN cana-1744 18 13 was be AUX cana-1744 18 14 studied study VERB cana-1744 18 15 in in ADP cana-1744 18 16 [ [ X cana-1744 18 17 2 2 NUM cana-1744 18 18 ] ] PUNCT cana-1744 18 19 . . PUNCT cana-1744 19 1 the the DET cana-1744 19 2 stochastic stochastic ADJ cana-1744 19 3 processes process NOUN cana-1744 19 4 arising arise VERB cana-1744 19 5 from from ADP cana-1744 19 6 these these DET cana-1744 19 7 models model NOUN cana-1744 19 8 in in ADP cana-1744 19 9 stationary stationary ADJ cana-1744 19 10 and and CCONJ cana-1744 19 11 non non ADJ cana-1744 19 12 - - ADJ cana-1744 19 13 stationary stationary ADJ cana-1744 19 14 regimes regime NOUN cana-1744 19 15 are be AUX cana-1744 19 16 investigated investigate VERB cana-1744 19 17 in in ADP cana-1744 19 18 [ [ X cana-1744 19 19 3 3 NUM cana-1744 19 20 ] ] PUNCT cana-1744 19 21 . . PUNCT cana-1744 20 1 conduct conduct VERB cana-1744 20 2 the the DET cana-1744 20 3 single single ADJ cana-1744 20 4 - - PUNCT cana-1744 20 5 server server NOUN cana-1744 20 6 queue queue NOUN cana-1744 20 7 under under ADP cana-1744 20 8 demands demand NOUN cana-1744 20 9 examined examine VERB cana-1744 20 10 in in ADP cana-1744 20 11 [ [ X cana-1744 20 12 4 4 NUM cana-1744 20 13 ] ] PUNCT cana-1744 20 14 . . PUNCT cana-1744 21 1 a a DET cana-1744 21 2 retrial retrial ADJ cana-1744 21 3 queuing queuing NOUN cana-1744 21 4 system system NOUN cana-1744 21 5 with with ADP cana-1744 21 6 results result NOUN cana-1744 21 7 was be AUX cana-1744 21 8 studied study VERB cana-1744 21 9 in in ADP cana-1744 21 10 [ [ X cana-1744 21 11 5 5 NUM cana-1744 21 12 ] ] PUNCT cana-1744 21 13 . . PUNCT cana-1744 22 1 the the DET cana-1744 22 2 primary primary ADJ cana-1744 22 3 models model NOUN cana-1744 22 4 and and CCONJ cana-1744 22 5 results result NOUN cana-1744 22 6 in in ADP cana-1744 22 7 the the DET cana-1744 22 8 field field NOUN cana-1744 22 9 of of ADP cana-1744 22 10 retrial retrial ADJ cana-1744 22 11 queues queue NOUN cana-1744 22 12 are be AUX cana-1744 22 13 investigated investigate VERB cana-1744 22 14 in in ADP cana-1744 22 15 [ [ X cana-1744 22 16 6 6 NUM cana-1744 22 17 ] ] PUNCT cana-1744 22 18 . . PUNCT cana-1744 23 1 mailto:ismailkhanmubarak@gmail.com mailto:ismailkhanmubarak@gmail.com X cana-1744 23 2 mailto:thangarajap1991@gmail.com mailto:thangarajap1991@gmail.com PROPN cana-1744 23 3 communications communication NOUN cana-1744 23 4 on on ADP cana-1744 23 5 applied apply VERB cana-1744 23 6 nonlinear nonlinear ADJ cana-1744 23 7 analysis analysis NOUN cana-1744 23 8 issn issn NOUN cana-1744 23 9 : : PUNCT cana-1744 23 10 1074 1074 NUM cana-1744 23 11 - - PUNCT cana-1744 23 12 133x 133x NUM cana-1744 23 13 vol vol NOUN cana-1744 23 14 32 32 NUM cana-1744 23 15 no no NOUN cana-1744 23 16 . . NOUN cana-1744 23 17 2 2 NUM cana-1744 23 18 ( ( PUNCT cana-1744 23 19 2025 2025 NUM cana-1744 23 20 ) ) PUNCT cana-1744 23 21 306 306 NUM cana-1744 23 22 https://internationalpubls.com https://internationalpubls.com X cana-1744 23 23 a a DET cana-1744 23 24 comprehensive comprehensive ADJ cana-1744 23 25 overview overview NOUN cana-1744 23 26 of of ADP cana-1744 23 27 the the DET cana-1744 23 28 main main ADJ cana-1744 23 29 results result NOUN cana-1744 23 30 and and CCONJ cana-1744 23 31 methods method NOUN cana-1744 23 32 in in ADP cana-1744 23 33 the the DET cana-1744 23 34 theory theory NOUN cana-1744 23 35 of of ADP cana-1744 23 36 retrial retrial ADJ cana-1744 23 37 queues queue NOUN cana-1744 23 38 studied study VERB cana-1744 23 39 in in ADP cana-1744 23 40 [ [ X cana-1744 23 41 7 7 NUM cana-1744 23 42 ] ] PUNCT cana-1744 23 43 . . PUNCT cana-1744 24 1 [ [ X cana-1744 24 2 8 8 NUM cana-1744 24 3 ] ] PUNCT cana-1744 24 4 examines examine VERB cana-1744 24 5 the the DET cana-1744 24 6 steady steady ADJ cana-1744 24 7 - - PUNCT cana-1744 24 8 state state NOUN cana-1744 24 9 behaviour behaviour NOUN cana-1744 24 10 of of ADP cana-1744 24 11 an an DET cana-1744 24 12 m m NOUN cana-1744 24 13 / / SYM cana-1744 24 14 g/1 g/1 NOUN cana-1744 24 15 queueing queue VERB cana-1744 24 16 system system NOUN cana-1744 24 17 where where SCONJ cana-1744 24 18 the the DET cana-1744 24 19 server server NOUN cana-1744 24 20 may may AUX cana-1744 24 21 provide provide VERB cana-1744 24 22 two two NUM cana-1744 24 23 phases phase NOUN cana-1744 24 24 of of ADP cana-1744 24 25 heterogeneous heterogeneous ADJ cana-1744 24 26 service service NOUN cana-1744 24 27 to to ADP cana-1744 24 28 incoming incoming ADJ cana-1744 24 29 units unit NOUN cana-1744 24 30 . . PUNCT cana-1744 25 1 [ [ X cana-1744 25 2 9 9 NUM cana-1744 25 3 ] ] PUNCT cana-1744 25 4 investigate investigate VERB cana-1744 25 5 the the DET cana-1744 25 6 steady steady ADJ cana-1744 25 7 - - PUNCT cana-1744 25 8 state state NOUN cana-1744 25 9 behaviour behaviour NOUN cana-1744 25 10 of of ADP cana-1744 25 11 an an DET cana-1744 25 12 m m NOUN cana-1744 25 13 / / SYM cana-1744 25 14 g/1 g/1 NOUN cana-1744 25 15 queueing queue VERB cana-1744 25 16 system system NOUN cana-1744 25 17 that that PRON cana-1744 25 18 incorporates incorporate VERB cana-1744 25 19 two two NUM cana-1744 25 20 phases phase NOUN cana-1744 25 21 of of ADP cana-1744 25 22 service service NOUN cana-1744 25 23 and and CCONJ cana-1744 25 24 operates operate VERB cana-1744 25 25 under under ADP cana-1744 25 26 a a DET cana-1744 25 27 d d NOUN cana-1744 25 28 - - NOUN cana-1744 25 29 policy policy NOUN cana-1744 25 30 . . PUNCT cana-1744 26 1 the the DET cana-1744 26 2 steady steady ADJ cana-1744 26 3 - - PUNCT cana-1744 26 4 state state NOUN cana-1744 26 5 behaviour behaviour NOUN cana-1744 26 6 of of ADP cana-1744 26 7 an an DET cana-1744 26 8 m m NOUN cana-1744 26 9 / / SYM cana-1744 26 10 g/1 g/1 NOUN cana-1744 26 11 queueing queue VERB cana-1744 26 12 system system NOUN cana-1744 26 13 that that PRON cana-1744 26 14 incorporates incorporate VERB cana-1744 26 15 repeated repeat VERB cana-1744 26 16 attempts attempt NOUN cana-1744 26 17 and and CCONJ cana-1744 26 18 two two NUM cana-1744 26 19 - - PUNCT cana-1744 26 20 phase phase NOUN cana-1744 26 21 service service NOUN cana-1744 26 22 was be AUX cana-1744 26 23 studied study VERB cana-1744 26 24 in in ADP cana-1744 26 25 [ [ X cana-1744 26 26 10 10 NUM cana-1744 26 27 ] ] PUNCT cana-1744 26 28 . . PUNCT cana-1744 27 1 [ [ X cana-1744 27 2 11 11 NUM cana-1744 27 3 ] ] PUNCT cana-1744 27 4 studied study VERB cana-1744 27 5 the the DET cana-1744 27 6 behaviour behaviour NOUN cana-1744 27 7 of of ADP cana-1744 27 8 an an DET cana-1744 27 9 m m NOUN cana-1744 27 10 / / SYM cana-1744 27 11 g/1 g/1 NOUN cana-1744 27 12 queuing queuing NOUN cana-1744 27 13 system system NOUN cana-1744 27 14 that that PRON cana-1744 27 15 adds add VERB cana-1744 27 16 a a DET cana-1744 27 17 second second ADJ cana-1744 27 18 optional optional ADJ cana-1744 27 19 service service NOUN cana-1744 27 20 . . PUNCT cana-1744 28 1 [ [ X cana-1744 28 2 12 12 NUM cana-1744 28 3 ] ] PUNCT cana-1744 28 4 analyzes analyze VERB cana-1744 28 5 an an PRON cana-1744 28 6 m m NOUN cana-1744 28 7 / / SYM cana-1744 28 8 g/1 g/1 NOUN cana-1744 28 9 queueing queue VERB cana-1744 28 10 system system NOUN cana-1744 28 11 that that PRON cana-1744 28 12 incorporates incorporate VERB cana-1744 28 13 a a DET cana-1744 28 14 second second ADJ cana-1744 28 15 optional optional ADJ cana-1744 28 16 service service NOUN cana-1744 28 17 and and CCONJ cana-1744 28 18 server server NOUN cana-1744 28 19 vacations vacation NOUN cana-1744 28 20 scheduled schedule VERB cana-1744 28 21 according accord VERB cana-1744 28 22 to to ADP cana-1744 28 23 a a DET cana-1744 28 24 bernoulli bernoulli NOUN cana-1744 28 25 process process NOUN cana-1744 28 26 . . PUNCT cana-1744 29 1 investigating investigate VERB cana-1744 29 2 an an DET cana-1744 29 3 m m NOUN cana-1744 29 4 / / SYM cana-1744 29 5 m/1 m/1 NOUN cana-1744 29 6 / / SYM cana-1744 29 7 n n NOUN cana-1744 29 8 system system NOUN cana-1744 29 9 with with ADP cana-1744 29 10 encouraged encouraged ADJ cana-1744 29 11 arrivals arrival NOUN cana-1744 29 12 was be AUX cana-1744 29 13 done do VERB cana-1744 29 14 in in ADP cana-1744 29 15 [ [ X cana-1744 29 16 13,14 13,14 NUM cana-1744 29 17 ] ] PUNCT cana-1744 29 18 . . PUNCT cana-1744 30 1 studying study VERB cana-1744 30 2 an an DET cana-1744 30 3 m m NOUN cana-1744 30 4 / / SYM cana-1744 30 5 m/1 m/1 NOUN cana-1744 30 6 retrial retrial ADJ cana-1744 30 7 queuing queuing NOUN cana-1744 30 8 system system NOUN cana-1744 30 9 was be AUX cana-1744 30 10 done do VERB cana-1744 30 11 in in ADP cana-1744 30 12 [ [ X cana-1744 30 13 15 15 NUM cana-1744 30 14 ] ] SYM cana-1744 30 15 2 2 NUM cana-1744 30 16 . . PUNCT cana-1744 30 17 model model NOUN cana-1744 30 18 assumptions assumption NOUN cana-1744 30 19 : : PUNCT cana-1744 30 20 the the DET cana-1744 30 21 following follow VERB cana-1744 30 22 presumptions presumption NOUN cana-1744 30 23 form form VERB cana-1744 30 24 the the DET cana-1744 30 25 basis basis NOUN cana-1744 30 26 of of ADP cana-1744 30 27 this this DET cana-1744 30 28 model model NOUN cana-1744 30 29 's 's PART cana-1744 30 30 analysis analysis NOUN cana-1744 30 31 . . PUNCT cana-1744 31 1 • • NUM cana-1744 31 2 patron patron NOUN cana-1744 31 3 entry entry NOUN cana-1744 31 4 follows follow VERB cana-1744 31 5 an an DET cana-1744 31 6 encouraged encouraged ADJ cana-1744 31 7 arrival arrival NOUN cana-1744 31 8 with with ADP cana-1744 31 9 rate rate NOUN cana-1744 31 10 λ λ X cana-1744 31 11 × × NOUN cana-1744 31 12 ( ( PUNCT cana-1744 31 13 1 1 NUM cana-1744 31 14 + + CCONJ cana-1744 31 15 δ δ PROPN cana-1744 31 16 ) ) PUNCT cana-1744 31 17 . . PUNCT cana-1744 32 1 δ δ PROPN cana-1744 32 2 represents represent VERB cana-1744 32 3 the the DET cana-1744 32 4 discount discount NOUN cana-1744 32 5 values value NOUN cana-1744 32 6 are be AUX cana-1744 32 7 10 10 NUM cana-1744 32 8 % % NOUN cana-1744 32 9 i.e i.e ADP cana-1744 32 10 the the DET cana-1744 32 11 interval interval NOUN cana-1744 32 12 between between ADP cana-1744 32 13 the the DET cana-1744 32 14 encouraged encouraged ADJ cana-1744 32 15 arrival arrival NOUN cana-1744 32 16 is be AUX cana-1744 32 17 an an DET cana-1744 32 18 identical identical ADJ cana-1744 32 19 distribution distribution NOUN cana-1744 32 20 under under ADP cana-1744 32 21 an an DET cana-1744 32 22 average average ADJ cana-1744 32 23 rate rate NOUN cana-1744 32 24 of of ADP cana-1744 32 25 1 1 NUM cana-1744 32 26 λ×(1+δ λ×(1+δ NOUN cana-1744 32 27 ) ) PUNCT cana-1744 32 28 . . PUNCT cana-1744 33 1 the the DET cana-1744 33 2 service service NOUN cana-1744 33 3 time time NOUN cana-1744 33 4 adheres adhere VERB cana-1744 33 5 to to ADP cana-1744 33 6 a a DET cana-1744 33 7 general general ADJ cana-1744 33 8 distribution distribution NOUN cana-1744 33 9 under under ADP cana-1744 33 10 a a DET cana-1744 33 11 conditional conditional ADJ cana-1744 33 12 probability probability NOUN cana-1744 33 13 density density NOUN cana-1744 33 14 of of ADP cana-1744 33 15 service service NOUN cana-1744 33 16 via via ADP cana-1744 33 17 the the DET cana-1744 33 18 interval interval NOUN cana-1744 33 19 ( ( PUNCT cana-1744 33 20 𝑦 𝑦 NOUN cana-1744 33 21 , , PUNCT cana-1744 33 22 𝑦 𝑦 NOUN cana-1744 33 23 + + X cana-1744 33 24 δ δ PROPN cana-1744 33 25 ∗ ∗ NOUN cana-1744 33 26 𝑦 𝑦 NOUN cana-1744 33 27 ) ) PUNCT cana-1744 33 28 to to PART cana-1744 33 29 obtain obtain VERB cana-1744 33 30 the the DET cana-1744 33 31 expected expect VERB cana-1744 33 32 service service NOUN cana-1744 33 33 time time NOUN cana-1744 33 34 𝑦 𝑦 X cana-1744 33 35 , , PUNCT cana-1744 33 36 we we PRON cana-1744 33 37 have have VERB cana-1744 33 38 𝜇(𝑦 𝜇(𝑦 NOUN cana-1744 33 39 ) ) PUNCT cana-1744 33 40 = = SYM cana-1744 33 41 𝑎(𝑦 𝑎(𝑦 NOUN cana-1744 33 42 ) ) PUNCT cana-1744 33 43 1 1 NUM cana-1744 33 44 − − NOUN cana-1744 33 45 𝐴(𝑦 𝐴(𝑦 NOUN cana-1744 33 46 ) ) PUNCT cana-1744 33 47 ( ( PUNCT cana-1744 33 48 1 1 X cana-1744 33 49 ) ) PUNCT cana-1744 33 50 where where SCONJ cana-1744 33 51 𝑎(𝑦 𝑎(𝑦 NOUN cana-1744 33 52 ) ) PUNCT cana-1744 33 53 = = SYM cana-1744 33 54 𝜇(𝑦)𝑒−∫ 𝜇(𝑦)𝑒−∫ NOUN cana-1744 33 55     SPACE cana-1744 33 56 𝑦 𝑦 NOUN cana-1744 33 57 0 0 NUM cana-1744 33 58     SPACE cana-1744 33 59 𝜇(𝑇)𝑑𝑇 𝜇(𝑇)𝑑𝑇 NOUN cana-1744 33 60 ( ( PUNCT cana-1744 33 61 2 2 NUM cana-1744 33 62 ) ) PUNCT cana-1744 33 63 • • NUM cana-1744 33 64 patron patron NOUN cana-1744 33 65 follows follow VERB cana-1744 33 66 fcfs fcfs ADJ cana-1744 33 67 discipline discipline NOUN cana-1744 33 68 • • ADP cana-1744 33 69 the the DET cana-1744 33 70 extend extend NOUN cana-1744 33 71 of of ADP cana-1744 33 72 the the DET cana-1744 33 73 patron patron NOUN cana-1744 33 74 and and CCONJ cana-1744 33 75 group group NOUN cana-1744 33 76 is be AUX cana-1744 33 77 infinite infinite ADJ cana-1744 33 78 , , PUNCT cana-1744 33 79 beginning begin VERB cana-1744 33 80 with with ADP cana-1744 33 81 arrival arrival NOUN cana-1744 33 82 via via ADP cana-1744 33 83 the the DET cana-1744 33 84 inter inter NOUN cana-1744 33 85 of of ADP cana-1744 33 86 time time NOUN cana-1744 33 87 is be AUX cana-1744 33 88 ( ( PUNCT cana-1744 33 89 𝑇 𝑇 PROPN cana-1744 33 90 , , PUNCT cana-1744 33 91 𝑇 𝑇 PROPN cana-1744 33 92 + + CCONJ cana-1744 33 93 δ δ PROPN cana-1744 33 94 ∗ ∗ NOUN cana-1744 33 95 𝑇 𝑇 PROPN cana-1744 33 96 ) ) PUNCT cana-1744 33 97 is be AUX cana-1744 33 98 λ λ X cana-1744 33 99 × × NOUN cana-1744 33 100 ( ( PUNCT cana-1744 33 101 1 1 NUM cana-1744 33 102 + + NUM cana-1744 33 103 δ)δ𝑇 δ)δ𝑇 PROPN cana-1744 33 104 + + NUM cana-1744 33 105 𝑧(δ 𝑧(δ PROPN cana-1744 33 106 ∗ ∗ NOUN cana-1744 33 107 𝑇 𝑇 PROPN cana-1744 33 108 ) ) PUNCT cana-1744 33 109 . . PUNCT cana-1744 34 1 hereafter hereafter ADV cana-1744 34 2 , , PUNCT cana-1744 34 3 retry retry ADJ cana-1744 34 4 attempts attempt NOUN cana-1744 34 5 via via ADP cana-1744 34 6 the the DET cana-1744 34 7 time time NOUN cana-1744 34 8 of of ADP cana-1744 34 9 interval interval NOUN cana-1744 34 10 is be AUX cana-1744 34 11 ( ( PUNCT cana-1744 34 12 𝑇 𝑇 PROPN cana-1744 34 13 , , PUNCT cana-1744 34 14 𝑇 𝑇 PROPN cana-1744 34 15 + + CCONJ cana-1744 34 16 δ δ PROPN cana-1744 34 17 ∗ ∗ NOUN cana-1744 34 18 𝑇 𝑇 PROPN cana-1744 34 19 ) ) PUNCT cana-1744 34 20 is be AUX cana-1744 34 21 obtained obtain VERB cana-1744 34 22 that that SCONJ cana-1744 34 23 𝜒δ 𝜒δ NOUN cana-1744 34 24 ∗ ∗ NOUN cana-1744 34 25 t t PROPN cana-1744 34 26 + + CCONJ cana-1744 34 27 z(δ z(δ PROPN cana-1744 34 28 ∗ ∗ NOUN cana-1744 34 29 t t PROPN cana-1744 34 30 ) ) PUNCT cana-1744 34 31 . . PUNCT cana-1744 35 1 multiple multiple ADJ cana-1744 35 2 departures departure NOUN cana-1744 35 3 within within ADP cana-1744 35 4 the the DET cana-1744 35 5 given give VERB cana-1744 35 6 time time NOUN cana-1744 35 7 interval interval NOUN cana-1744 35 8 ( ( PUNCT cana-1744 35 9 𝑇 𝑇 PROPN cana-1744 35 10 , , PUNCT cana-1744 35 11 𝑇 𝑇 PROPN cana-1744 35 12 + + CCONJ cana-1744 35 13 δ δ PROPN cana-1744 35 14 ∗ ∗ NOUN cana-1744 35 15 𝑇 𝑇 PROPN cana-1744 35 16 ) ) PUNCT cana-1744 35 17 are be AUX cana-1744 35 18 0 0 NUM cana-1744 35 19 . . NOUN cana-1744 35 20 • • NOUN cana-1744 36 1 the the DET cana-1744 36 2 retrial retrial ADJ cana-1744 36 3 rate rate NOUN cana-1744 36 4 is be AUX cana-1744 36 5 ( ( PUNCT cana-1744 36 6 1 1 NUM cana-1744 36 7 − − PROPN cana-1744 36 8 𝜓zm)𝜒 𝜓zm)𝜒 PROPN cana-1744 36 9 , , PUNCT cana-1744 36 10 where where SCONJ cana-1744 36 11 𝜓zm 𝜓zm PROPN cana-1744 36 12 denotes denote NOUN cana-1744 36 13 kronecker kronecker NOUN cana-1744 36 14 's 's PART cana-1744 36 15 delta delta NOUN cana-1744 36 16 . . PUNCT cana-1744 37 1 • • NUM cana-1744 37 2 the the DET cana-1744 37 3 transitory transitory ADJ cana-1744 37 4 behaviour behaviour NOUN cana-1744 37 5 of of ADP cana-1744 37 6 this this DET cana-1744 37 7 model model NOUN cana-1744 37 8 is be AUX cana-1744 37 9 developed develop VERB cana-1744 37 10 by by ADP cana-1744 37 11 the the DET cana-1744 37 12 supplementary supplementary ADJ cana-1744 37 13 variable variable ADJ cana-1744 37 14 technique technique NOUN cana-1744 37 15 . . PUNCT cana-1744 38 1 • • NUM cana-1744 38 2 steady steady ADJ cana-1744 38 3 - - PUNCT cana-1744 38 4 state state NOUN cana-1744 38 5 of of ADP cana-1744 38 6 the the DET cana-1744 38 7 probability probability NOUN cana-1744 38 8 distributions distribution NOUN cana-1744 38 9 derived derive VERB cana-1744 38 10 for for ADP cana-1744 38 11 different different ADJ cana-1744 38 12 service service NOUN cana-1744 38 13 - - PUNCT cana-1744 38 14 time time NOUN cana-1744 38 15 distributions distribution NOUN cana-1744 38 16 ( ( PUNCT cana-1744 38 17 exponential exponential NOUN cana-1744 38 18 and and CCONJ cana-1744 38 19 erlang erlang PROPN cana-1744 38 20 ) ) PUNCT cana-1744 38 21 . . PUNCT cana-1744 39 1 the the DET cana-1744 39 2 probability probability NOUN cana-1744 39 3 of of ADP cana-1744 39 4 the the DET cana-1744 39 5 system system NOUN cana-1744 39 6 - - PUNCT cana-1744 39 7 server server NOUN cana-1744 39 8 being being NOUN cana-1744 39 9 idle idle ADJ cana-1744 39 10 engages engage VERB cana-1744 39 11 for for ADP cana-1744 39 12 different different ADJ cana-1744 39 13 parameters parameter NOUN cana-1744 39 14 . . PUNCT cana-1744 40 1 3 3 X cana-1744 40 2 . . X cana-1744 40 3 to to PART cana-1744 40 4 derive derive VERB cana-1744 40 5 the the DET cana-1744 40 6 set set NOUN cana-1744 40 7 of of ADP cana-1744 40 8 differential differential ADJ cana-1744 40 9 - - PUNCT cana-1744 40 10 difference difference NOUN cana-1744 40 11 equations equation NOUN cana-1744 40 12 of of ADP cana-1744 40 13 the the DET cana-1744 40 14 model model NOUN cana-1744 40 15 we we PRON cana-1744 40 16 write write VERB cana-1744 40 17 the the DET cana-1744 40 18 basic basic ADJ cana-1744 40 19 equations equation NOUN cana-1744 40 20 and and CCONJ cana-1744 40 21 derive derive VERB cana-1744 40 22 the the DET cana-1744 40 23 governing govern VERB cana-1744 40 24 equations equation NOUN cana-1744 40 25 are be AUX cana-1744 40 26 described describe VERB cana-1744 40 27 as as SCONJ cana-1744 40 28 follows follow VERB cana-1744 40 29 𝑃𝑚1 𝑃𝑚1 NOUN cana-1744 41 1 ′ ′ NUM cana-1744 42 1 ( ( PUNCT cana-1744 42 2 𝑦 𝑦 NOUN cana-1744 42 3 , , PUNCT cana-1744 42 4 𝑇 𝑇 PROPN cana-1744 42 5 ) ) PUNCT cana-1744 42 6 + + NUM cana-1744 42 7 ∂ ∂ NUM cana-1744 42 8 ∂𝑇 ∂𝑇 X cana-1744 42 9 𝑃𝑚1(𝑦 𝑃𝑚1(𝑦 X cana-1744 42 10 , , PUNCT cana-1744 42 11 𝑇 𝑇 PROPN cana-1744 42 12 ) ) PUNCT cana-1744 43 1 + + CCONJ cana-1744 43 2 ( ( PUNCT cana-1744 43 3 λ λ INTJ cana-1744 43 4 × × NOUN cana-1744 43 5 ( ( PUNCT cana-1744 43 6 1 1 NUM cana-1744 43 7 + + CCONJ cana-1744 43 8 δ δ NOUN cana-1744 43 9 ) ) PUNCT cana-1744 44 1 + + NUM cana-1744 44 2 𝜇(𝑦))𝑃𝑚1(𝑦 𝜇(𝑦))𝑃𝑚1(𝑦 NOUN cana-1744 44 3 , , PUNCT cana-1744 44 4 𝑇 𝑇 PROPN cana-1744 44 5 ) ) PUNCT cana-1744 44 6 = = PUNCT cana-1744 45 1 λ λ X cana-1744 45 2 × × NOUN cana-1744 45 3 ( ( PUNCT cana-1744 45 4 1 1 NUM cana-1744 45 5 + + NUM cana-1744 45 6 δ)𝑃𝑚−11(𝑦 δ)𝑃𝑚−11(𝑦 PROPN cana-1744 45 7 , , PUNCT cana-1744 45 8 𝑇 𝑇 PROPN cana-1744 45 9 ) ) PUNCT cana-1744 45 10 ( ( PUNCT cana-1744 45 11 3 3 X cana-1744 45 12 ) ) PUNCT cana-1744 45 13 𝑃01 𝑃01 NOUN cana-1744 45 14 ′ ′ NUM cana-1744 45 15 ( ( PUNCT cana-1744 45 16 𝑦 𝑦 NOUN cana-1744 45 17 , , PUNCT cana-1744 45 18 𝑇 𝑇 PROPN cana-1744 45 19 ) ) PUNCT cana-1744 45 20 + + NUM cana-1744 45 21 ∂ ∂ NUM cana-1744 45 22 ∂𝑇 ∂𝑇 PROPN cana-1744 45 23 𝑃01(𝑦 𝑃01(𝑦 PROPN cana-1744 45 24 , , PUNCT cana-1744 45 25 𝑇 𝑇 PROPN cana-1744 45 26 ) ) PUNCT cana-1744 45 27 + + CCONJ cana-1744 45 28 ( ( PUNCT cana-1744 45 29 λ λ INTJ cana-1744 45 30 × × NOUN cana-1744 45 31 ( ( PUNCT cana-1744 45 32 1 1 NUM cana-1744 45 33 + + CCONJ cana-1744 45 34 δ δ X cana-1744 45 35 ) ) PUNCT cana-1744 46 1 + + NUM cana-1744 46 2 𝜇(𝑦))𝑃01(𝑦 𝜇(𝑦))𝑃01(𝑦 PROPN cana-1744 46 3 , , PUNCT cana-1744 46 4 𝑇 𝑇 PROPN cana-1744 46 5 ) ) PUNCT cana-1744 46 6 = = SYM cana-1744 46 7 0 0 NUM cana-1744 46 8 ( ( PUNCT cana-1744 46 9 4 4 X cana-1744 46 10 ) ) PUNCT cana-1744 46 11 communications communication NOUN cana-1744 46 12 on on ADP cana-1744 46 13 applied apply VERB cana-1744 46 14 nonlinear nonlinear ADJ cana-1744 46 15 analysis analysis NOUN cana-1744 46 16 issn issn NOUN cana-1744 46 17 : : PUNCT cana-1744 46 18 1074 1074 NUM cana-1744 46 19 - - PUNCT cana-1744 46 20 133x 133x NUM cana-1744 46 21 vol vol NOUN cana-1744 46 22 32 32 NUM cana-1744 46 23 no no NOUN cana-1744 46 24 . . NOUN cana-1744 46 25 2 2 NUM cana-1744 46 26 ( ( PUNCT cana-1744 46 27 2025 2025 NUM cana-1744 46 28 ) ) PUNCT cana-1744 46 29 307 307 NUM cana-1744 46 30 https://internationalpubls.com https://internationalpubls.com X cana-1744 46 31 𝑃𝑚0 𝑃𝑚0 NOUN cana-1744 47 1 ′ ′ NUM cana-1744 47 2 ( ( PUNCT cana-1744 47 3 𝑇 𝑇 PROPN cana-1744 47 4 ) ) PUNCT cana-1744 47 5 + + CCONJ cana-1744 47 6 ( ( PUNCT cana-1744 47 7 λ λ INTJ cana-1744 47 8 × × NOUN cana-1744 47 9 ( ( PUNCT cana-1744 47 10 1 1 NUM cana-1744 47 11 + + CCONJ cana-1744 47 12 δ δ NOUN cana-1744 47 13 ) ) PUNCT cana-1744 48 1 + + NUM cana-1744 48 2 𝜎)𝑃𝑚0(𝑇 𝜎)𝑃𝑚0(𝑇 NOUN cana-1744 48 3 ) ) PUNCT cana-1744 48 4 = = SYM cana-1744 48 5 ∫ ∫ PROPN cana-1744 48 6 0 0 NUM cana-1744 48 7 ∞ ∞ NUM cana-1744 48 8     SPACE cana-1744 48 9 𝑃𝑚1(𝑦 𝑃𝑚1(𝑦 NOUN cana-1744 48 10 , , PUNCT cana-1744 48 11 𝑇)𝜇(𝑦)𝑑𝑦 𝑇)𝜇(𝑦)𝑑𝑦 VERB cana-1744 48 12 forn forn PROPN cana-1744 48 13 = = SYM cana-1744 48 14 1,2,3 1,2,3 NUM cana-1744 48 15 , , PUNCT cana-1744 48 16 … … PUNCT cana-1744 48 17 ( ( PUNCT cana-1744 48 18 5 5 X cana-1744 48 19 ) ) PUNCT cana-1744 48 20 𝑃00 𝑃00 PROPN cana-1744 48 21 ′ ′ NUM cana-1744 48 22 ( ( PUNCT cana-1744 48 23 𝑇 𝑇 PROPN cana-1744 48 24 ) ) PUNCT cana-1744 48 25 + + NOUN cana-1744 48 26 λ λ X cana-1744 48 27 × × NOUN cana-1744 48 28 ( ( PUNCT cana-1744 48 29 1 1 NUM cana-1744 48 30 + + NUM cana-1744 48 31 δ)𝑃00(𝑇 δ)𝑃00(𝑇 NOUN cana-1744 48 32 ) ) PUNCT cana-1744 48 33 = = SYM cana-1744 48 34 ∫0 ∫0 ADP cana-1744 48 35 ∞ ∞ PROPN cana-1744 48 36     SPACE cana-1744 48 37 𝑃01(𝑦 𝑃01(𝑦 PROPN cana-1744 48 38 , , PUNCT cana-1744 49 1 𝑇)𝜇(𝑦)𝑑𝑦 𝑇)𝜇(𝑦)𝑑𝑦 PROPN cana-1744 49 2 = = PRON cana-1744 49 3 ∫0 ∫0 ADP cana-1744 49 4 ∞ ∞ PROPN cana-1744 49 5     SPACE cana-1744 49 6 𝑃01(𝑦 𝑃01(𝑦 PROPN cana-1744 49 7 , , PUNCT cana-1744 49 8 𝑇)𝜇(𝑦)𝑑𝑦 𝑇)𝜇(𝑦)𝑑𝑦 PROPN cana-1744 49 9 ( ( PUNCT cana-1744 49 10 6 6 NUM cana-1744 49 11 ) ) PUNCT cana-1744 49 12 the the DET cana-1744 49 13 subsequent subsequent ADJ cana-1744 49 14 boundary boundary ADJ cana-1744 49 15 conditions condition NOUN cana-1744 49 16 apply apply VERB cana-1744 49 17 while while SCONJ cana-1744 49 18 solving solve VERB cana-1744 49 19 the the DET cana-1744 49 20 aforementioned aforementioned ADJ cana-1744 49 21 equations equation NOUN cana-1744 49 22 ( ( PUNCT cana-1744 49 23 3 3 NUM cana-1744 49 24 ) ) PUNCT cana-1744 49 25 through through ADP cana-1744 49 26 ( ( PUNCT cana-1744 49 27 6 6 NUM cana-1744 49 28 ) ) PUNCT cana-1744 49 29 𝑃𝑚1(0 𝑃𝑚1(0 NOUN cana-1744 49 30 , , PUNCT cana-1744 49 31 𝑇 𝑇 PROPN cana-1744 49 32 ) ) PUNCT cana-1744 49 33 = = PUNCT cana-1744 50 1 λ λ X cana-1744 50 2 × × NOUN cana-1744 50 3 ( ( PUNCT cana-1744 50 4 1 1 NUM cana-1744 50 5 + + CCONJ cana-1744 50 6 δ)𝑃𝑚0(𝑇 δ)𝑃𝑚0(𝑇 NOUN cana-1744 50 7 ) ) PUNCT cana-1744 50 8 + + NUM cana-1744 50 9 𝜎𝑃𝑚+10(𝑇 𝜎𝑃𝑚+10(𝑇 NUM cana-1744 50 10 ) ) PUNCT cana-1744 50 11 ( ( PUNCT cana-1744 50 12 7 7 X cana-1744 50 13 ) ) PUNCT cana-1744 50 14 𝑃01(0 𝑃01(0 PROPN cana-1744 50 15 , , PUNCT cana-1744 50 16 𝑇 𝑇 PROPN cana-1744 50 17 ) ) PUNCT cana-1744 50 18 = = PUNCT cana-1744 51 1 λ λ X cana-1744 51 2 × × NOUN cana-1744 51 3 ( ( PUNCT cana-1744 51 4 1 1 NUM cana-1744 51 5 + + NUM cana-1744 51 6 δ)𝑃00(𝑇 δ)𝑃00(𝑇 NOUN cana-1744 51 7 ) ) PUNCT cana-1744 51 8 + + NUM cana-1744 51 9 𝜎𝑃10(𝑇 𝜎𝑃10(𝑇 NOUN cana-1744 51 10 ) ) PUNCT cana-1744 51 11 ( ( PUNCT cana-1744 51 12 8) 8) NUM cana-1744 51 13 primary primary ADJ cana-1744 51 14 condition condition NOUN cana-1744 51 15 is be AUX cana-1744 51 16 𝑃00(0 𝑃00(0 NOUN cana-1744 51 17 ) ) PUNCT cana-1744 51 18 = = SYM cana-1744 51 19 1 1 NUM cana-1744 51 20 ( ( PUNCT cana-1744 51 21 9 9 NUM cana-1744 51 22 ) ) PUNCT cana-1744 51 23 for for ADP cana-1744 51 24 the the DET cana-1744 51 25 server server NOUN cana-1744 51 26 that that PRON cana-1744 51 27 is be AUX cana-1744 51 28 engaged engage VERB cana-1744 51 29 or or CCONJ cana-1744 51 30 unoccupied unoccupied ADJ cana-1744 51 31 in in ADP cana-1744 51 32 the the DET cana-1744 51 33 transitory transitory ADJ cana-1744 51 34 state state NOUN cana-1744 51 35 , , PUNCT cana-1744 51 36 we we PRON cana-1744 51 37 create create VERB cana-1744 51 38 the the DET cana-1744 51 39 subsequent subsequent ADJ cana-1744 51 40 probability probability NOUN cana-1744 51 41 - - PUNCT cana-1744 51 42 generating generate VERB cana-1744 51 43 functions function NOUN cana-1744 51 44 𝑃0(𝑇 𝑃0(𝑇 PROPN cana-1744 51 45 , , PUNCT cana-1744 51 46 𝑍 𝑍 PROPN cana-1744 51 47 ) ) PUNCT cana-1744 51 48 = = SYM cana-1744 51 49 ∑ ∑ PUNCT cana-1744 51 50 𝑚=0 𝑚=0 SYM cana-1744 51 51 ∞ ∞ NUM cana-1744 51 52     SPACE cana-1744 51 53 𝑃𝑚0(𝑇)𝑍 𝑃𝑚0(𝑇)𝑍 PROPN cana-1744 51 54 𝑚and𝑃1(𝑇 𝑚and𝑃1(𝑇 X cana-1744 51 55 , , PUNCT cana-1744 51 56 𝑍 𝑍 PROPN cana-1744 51 57 ) ) PUNCT cana-1744 51 58 = = SYM cana-1744 51 59 ∑𝑚=0 ∑𝑚=0 PROPN cana-1744 51 60 ∞ ∞ PROPN cana-1744 51 61     SPACE cana-1744 51 62 𝑃𝑚1(𝑇)𝑍 𝑃𝑚1(𝑇)𝑍 PROPN cana-1744 51 63 𝑚 𝑚 X cana-1744 51 64 ( ( PUNCT cana-1744 51 65 10 10 NUM cana-1744 51 66 ) ) PUNCT cana-1744 51 67 the the DET cana-1744 51 68 lt lt NOUN cana-1744 51 69 of of ADP cana-1744 51 70 𝑔(𝑇 𝑔(𝑇 NUM cana-1744 51 71 ) ) PUNCT cana-1744 51 72 is be AUX cana-1744 51 73 described describe VERB cana-1744 51 74 by by ADP cana-1744 51 75 𝑔∗(𝑐 𝑔∗(𝑐 PROPN cana-1744 51 76 ) ) PUNCT cana-1744 51 77 = = SYM cana-1744 52 1 ∫ ∫ PROPN cana-1744 52 2 0 0 NUM cana-1744 53 1 ∞ ∞ NUM cana-1744 53 2     SPACE cana-1744 53 3 𝑒−𝑐𝑇𝑔(𝑇)𝑑𝑇 𝑒−𝑐𝑇𝑔(𝑇)𝑑𝑇 NOUN cana-1744 53 4 ( ( PUNCT cana-1744 53 5 11 11 NUM cana-1744 53 6 ) ) PUNCT cana-1744 53 7 apply apply VERB cana-1744 53 8 lt lt DET cana-1744 53 9 equations equation NOUN cana-1744 53 10 ( ( PUNCT cana-1744 53 11 3 3 X cana-1744 53 12 ) ) PUNCT cana-1744 53 13 to to ADP cana-1744 53 14 ( ( PUNCT cana-1744 53 15 10 10 NUM cana-1744 53 16 ) ) PUNCT cana-1744 53 17 , , PUNCT cana-1744 53 18 we we PRON cana-1744 53 19 obtain obtain VERB cana-1744 53 20 𝑃′𝑚1 𝑃′𝑚1 ADJ cana-1744 53 21 ∗ ∗ NOUN cana-1744 53 22 ( ( PUNCT cana-1744 53 23 𝑦 𝑦 NOUN cana-1744 53 24 , , PUNCT cana-1744 53 25 𝑐 𝑐 NOUN cana-1744 53 26 ) ) PUNCT cana-1744 54 1 + + CCONJ cana-1744 54 2 ( ( PUNCT cana-1744 54 3 𝑐 𝑐 PROPN cana-1744 54 4 + + NOUN cana-1744 54 5 λ λ PROPN cana-1744 54 6 × × NOUN cana-1744 54 7 ( ( PUNCT cana-1744 54 8 1 1 NUM cana-1744 54 9 + + CCONJ cana-1744 54 10 δ δ NOUN cana-1744 54 11 ) ) PUNCT cana-1744 55 1 + + CCONJ cana-1744 56 1 𝜇(𝑦))𝑃𝑚1 𝜇(𝑦))𝑃𝑚1 PROPN cana-1744 56 2 ′∗ ′∗ NUM cana-1744 56 3 ( ( PUNCT cana-1744 56 4 𝑦 𝑦 NOUN cana-1744 56 5 , , PUNCT cana-1744 56 6 𝑐 𝑐 NOUN cana-1744 56 7 ) ) PUNCT cana-1744 56 8 = = PUNCT cana-1744 57 1 λ λ X cana-1744 57 2 × × NOUN cana-1744 57 3 ( ( PUNCT cana-1744 57 4 1 1 NUM cana-1744 57 5 + + NUM cana-1744 57 6 δ)𝑃′𝑚−11 δ)𝑃′𝑚−11 VERB cana-1744 57 7 ∗ ∗ NOUN cana-1744 57 8 ( ( PUNCT cana-1744 57 9 𝑦 𝑦 NOUN cana-1744 57 10 , , PUNCT cana-1744 57 11 𝑐 𝑐 NOUN cana-1744 57 12 ) ) PUNCT cana-1744 57 13 for for ADP cana-1744 57 14 m m NOUN cana-1744 57 15 = = NOUN cana-1744 57 16 1,2,3 1,2,3 NUM cana-1744 57 17 , , PUNCT cana-1744 57 18 … … PUNCT cana-1744 57 19 ( ( PUNCT cana-1744 57 20 12 12 NUM cana-1744 57 21 ) ) PUNCT cana-1744 58 1 𝑃′01 𝑃′01 NOUN cana-1744 58 2 ∗ ∗ NOUN cana-1744 58 3 ( ( PUNCT cana-1744 58 4 𝑦 𝑦 NOUN cana-1744 58 5 , , PUNCT cana-1744 58 6 𝑐 𝑐 NOUN cana-1744 58 7 ) ) PUNCT cana-1744 58 8 + + CCONJ cana-1744 58 9 ( ( PUNCT cana-1744 58 10 𝑐 𝑐 PROPN cana-1744 58 11 + + NOUN cana-1744 58 12 λ λ PROPN cana-1744 58 13 × × NOUN cana-1744 58 14 ( ( PUNCT cana-1744 58 15 1 1 NUM cana-1744 58 16 + + CCONJ cana-1744 58 17 δ δ NOUN cana-1744 58 18 ) ) PUNCT cana-1744 59 1 + + CCONJ cana-1744 59 2 𝜇(𝑦))𝑃′01 𝜇(𝑦))𝑃′01 NOUN cana-1744 59 3 ∗ ∗ NOUN cana-1744 59 4 ( ( PUNCT cana-1744 59 5 𝑦 𝑦 NOUN cana-1744 59 6 , , PUNCT cana-1744 59 7 𝑐 𝑐 NOUN cana-1744 59 8 ) ) PUNCT cana-1744 59 9 = = SYM cana-1744 59 10 0 0 NUM cana-1744 59 11 ( ( PUNCT cana-1744 59 12 13 13 NUM cana-1744 59 13 ) ) PUNCT cana-1744 59 14 ( ( PUNCT cana-1744 59 15 𝑐 𝑐 PROPN cana-1744 59 16 + + NOUN cana-1744 59 17 λ λ PROPN cana-1744 59 18 × × NOUN cana-1744 59 19 ( ( PUNCT cana-1744 59 20 1 1 NUM cana-1744 59 21 + + CCONJ cana-1744 59 22 δ δ NOUN cana-1744 59 23 ) ) PUNCT cana-1744 59 24 + + NUM cana-1744 59 25 𝜎)𝑃𝑚0 𝜎)𝑃𝑚0 PROPN cana-1744 59 26 ∗(𝑇 ∗(𝑇 PROPN cana-1744 59 27 ) ) PUNCT cana-1744 59 28 = = SYM cana-1744 60 1 ∫ ∫ PROPN cana-1744 60 2 0 0 NUM cana-1744 61 1 ∞ ∞ NUM cana-1744 61 2     SPACE cana-1744 61 3 𝑃𝑚1 𝑃𝑚1 NOUN cana-1744 61 4 ∗(𝑦 ∗(𝑦 NOUN cana-1744 61 5 , , PUNCT cana-1744 61 6 𝑐)𝜇(𝑦)𝑑𝑦 𝑐)𝜇(𝑦)𝑑𝑦 NOUN cana-1744 61 7 for for ADP cana-1744 61 8 m m PROPN cana-1744 61 9 = = NOUN cana-1744 61 10 1,2,3 1,2,3 NUM cana-1744 61 11 , , PUNCT cana-1744 61 12 … … PUNCT cana-1744 61 13 ( ( PUNCT cana-1744 61 14 14 14 NUM cana-1744 61 15 ) ) PUNCT cana-1744 61 16 ( ( PUNCT cana-1744 61 17 λ λ INTJ cana-1744 61 18 × × NOUN cana-1744 61 19 ( ( PUNCT cana-1744 61 20 1 1 NUM cana-1744 61 21 + + CCONJ cana-1744 61 22 δ δ X cana-1744 61 23 ) ) PUNCT cana-1744 62 1 + + CCONJ cana-1744 62 2 𝑐)𝑃00 𝑐)𝑃00 ADP cana-1744 62 3 ∗(𝑐 ∗(𝑐 NOUN cana-1744 62 4 ) ) PUNCT cana-1744 62 5 = = SYM cana-1744 62 6 1 1 NUM cana-1744 62 7 + + NUM cana-1744 62 8 ∫ ∫ PROPN cana-1744 62 9 0 0 NUM cana-1744 63 1 ∞ ∞ NUM cana-1744 63 2     SPACE cana-1744 63 3 𝑃01 𝑃01 PROPN cana-1744 63 4 ∗(𝑦 ∗(𝑦 NOUN cana-1744 63 5 , , PUNCT cana-1744 63 6 𝑐)𝜇(𝑦)𝑑𝑦 𝑐)𝜇(𝑦)𝑑𝑦 NOUN cana-1744 63 7 ( ( PUNCT cana-1744 63 8 15 15 NUM cana-1744 63 9 ) ) PUNCT cana-1744 63 10 the the DET cana-1744 63 11 subsequent subsequent ADJ cana-1744 63 12 equations equation NOUN cana-1744 63 13 ( ( PUNCT cana-1744 63 14 12 12 NUM cana-1744 63 15 ) ) PUNCT cana-1744 63 16 to to ADP cana-1744 63 17 ( ( PUNCT cana-1744 63 18 15 15 NUM cana-1744 63 19 ) ) PUNCT cana-1744 63 20 are be AUX cana-1744 63 21 derived derive VERB cana-1744 63 22 from from ADP cana-1744 63 23 the the DET cana-1744 63 24 boundary boundary ADJ cana-1744 63 25 values value NOUN cana-1744 63 26 𝑃𝑚1 𝑃𝑚1 VERB cana-1744 63 27 ∗(0 ∗(0 PROPN cana-1744 63 28 , , PUNCT cana-1744 63 29 𝑐 𝑐 NOUN cana-1744 63 30 ) ) PUNCT cana-1744 63 31 = = PUNCT cana-1744 64 1 λ λ X cana-1744 64 2 × × NOUN cana-1744 64 3 ( ( PUNCT cana-1744 64 4 1 1 NUM cana-1744 64 5 + + NUM cana-1744 64 6 δ)𝑃𝑚0 δ)𝑃𝑚0 NOUN cana-1744 64 7 ∗(𝑐 ∗(𝑐 NOUN cana-1744 64 8 ) ) PUNCT cana-1744 65 1 + + CCONJ cana-1744 65 2 𝜒 𝜒 X cana-1744 65 3 ′∗(𝑐 ′∗(𝑐 PROPN cana-1744 65 4 ) ) PUNCT cana-1744 65 5 ( ( PUNCT cana-1744 65 6 16 16 X cana-1744 65 7 ) ) PUNCT cana-1744 65 8 𝑃01 𝑃01 PROPN cana-1744 65 9 ∗(0 ∗(0 ADJ cana-1744 65 10 , , PUNCT cana-1744 65 11 𝑐 𝑐 NOUN cana-1744 65 12 ) ) PUNCT cana-1744 65 13 = = PUNCT cana-1744 66 1 λ λ X cana-1744 66 2 × × NOUN cana-1744 66 3 ( ( PUNCT cana-1744 66 4 1 1 NUM cana-1744 66 5 + + CCONJ cana-1744 66 6 δ)𝑃00 δ)𝑃00 ADP cana-1744 66 7 ∗(𝑐 ∗(𝑐 PROPN cana-1744 66 8 ) ) PUNCT cana-1744 67 1 + + CCONJ cana-1744 67 2 𝜒𝑃10 𝜒𝑃10 PROPN cana-1744 67 3 ∗(𝑐 ∗(𝑐 PROPN cana-1744 67 4 ) ) PUNCT cana-1744 67 5 ( ( PUNCT cana-1744 67 6 17 17 NUM cana-1744 67 7 ) ) PUNCT cana-1744 67 8 theorem theorem NOUN cana-1744 67 9 1 1 NUM cana-1744 67 10 : : PUNCT cana-1744 67 11 for for SCONJ cana-1744 67 12 the the DET cana-1744 67 13 single single ADJ cana-1744 67 14 server server NOUN cana-1744 67 15 markovian markovian PROPN cana-1744 67 16 general general PROPN cana-1744 67 17 service service NOUN cana-1744 67 18 retrial retrial NOUN cana-1744 67 19 encouraged encourage VERB cana-1744 67 20 arrival arrival NOUN cana-1744 67 21 queuing queue VERB cana-1744 67 22 system system NOUN cana-1744 67 23 under under ADP cana-1744 67 24 the the DET cana-1744 67 25 persistent persistent ADJ cana-1744 67 26 retrial retrial ADJ cana-1744 67 27 technique technique NOUN cana-1744 67 28 , , PUNCT cana-1744 67 29 a. a. NOUN cana-1744 67 30 the the DET cana-1744 67 31 transitory transitory ADJ cana-1744 67 32 result result NOUN cana-1744 67 33 of of ADP cana-1744 67 34 the the DET cana-1744 67 35 patrons patron NOUN cana-1744 67 36 in in ADP cana-1744 67 37 the the DET cana-1744 67 38 group group NOUN cana-1744 67 39 , , PUNCT cana-1744 67 40 when when SCONJ cana-1744 67 41 the the DET cana-1744 67 42 systemserver systemserver NOUN cana-1744 67 43 is be AUX cana-1744 67 44 free free ADJ cana-1744 67 45 in in ADP cana-1744 67 46 the the DET cana-1744 67 47 system system NOUN cana-1744 67 48 , , PUNCT cana-1744 67 49 is be AUX cana-1744 67 50 provided provide VERB cana-1744 67 51 by by ADP cana-1744 67 52 𝑃0 𝑃0 NOUN cana-1744 67 53 ∗(𝑐 ∗(𝑐 PROPN cana-1744 67 54 , , PUNCT cana-1744 67 55 𝑍 𝑍 PROPN cana-1744 67 56 ) ) PUNCT cana-1744 67 57 = = SYM cana-1744 67 58 1 1 NUM cana-1744 67 59 + + NUM cana-1744 67 60 𝜒𝑃00 𝜒𝑃00 NOUN cana-1744 67 61 ∗ ∗ NOUN cana-1744 67 62 ( ( PUNCT cana-1744 67 63 𝑐 𝑐 NOUN cana-1744 67 64 ) ) PUNCT cana-1744 67 65 − − NOUN cana-1744 67 66 𝜒 𝜒 SYM cana-1744 67 67 𝑍 𝑍 PROPN cana-1744 67 68 𝑃00 𝑃00 PROPN cana-1744 67 69 ∗ ∗ NOUN cana-1744 67 70 ( ( PUNCT cana-1744 67 71 𝑐)𝑎‾(𝑐 𝑐)𝑎‾(𝑐 NOUN cana-1744 67 72 + + CCONJ cana-1744 67 73 λ λ X cana-1744 67 74 × × NOUN cana-1744 67 75 ( ( PUNCT cana-1744 67 76 1 1 NUM cana-1744 67 77 + + CCONJ cana-1744 67 78 δ δ NOUN cana-1744 67 79 ) ) PUNCT cana-1744 67 80 − − PROPN cana-1744 68 1 λ λ INTJ cana-1744 68 2 × × NOUN cana-1744 68 3 ( ( PUNCT cana-1744 68 4 1 1 NUM cana-1744 68 5 + + CCONJ cana-1744 68 6 δ δ PROPN cana-1744 68 7 ) ) PUNCT cana-1744 68 8 ∗ ∗ NOUN cana-1744 68 9 𝑍 𝑍 PROPN cana-1744 68 10 ) ) PUNCT cana-1744 68 11 ( ( PUNCT cana-1744 68 12 𝑐 𝑐 PROPN cana-1744 68 13 + + NOUN cana-1744 68 14 λ λ PROPN cana-1744 68 15 × × NOUN cana-1744 68 16 ( ( PUNCT cana-1744 68 17 1 1 NUM cana-1744 68 18 + + CCONJ cana-1744 68 19 δ δ NOUN cana-1744 68 20 ) ) PUNCT cana-1744 69 1 + + SYM cana-1744 69 2 𝜎 𝜎 X cana-1744 69 3 ) ) PUNCT cana-1744 69 4 − − PROPN cana-1744 70 1 ( ( PUNCT cana-1744 70 2 λ λ INTJ cana-1744 70 3 × × NOUN cana-1744 70 4 ( ( PUNCT cana-1744 70 5 1 1 NUM cana-1744 70 6 + + CCONJ cana-1744 70 7 δ δ X cana-1744 70 8 ) ) PUNCT cana-1744 71 1 + + CCONJ cana-1744 71 2 𝜎 𝜎 ADJ cana-1744 71 3 𝑍)𝑎‾(𝑐 𝑍)𝑎‾(𝑐 NOUN cana-1744 71 4 + + NUM cana-1744 71 5 λ λ X cana-1744 71 6 × × NOUN cana-1744 71 7 ( ( PUNCT cana-1744 71 8 1 1 NUM cana-1744 71 9 + + CCONJ cana-1744 71 10 δ δ NOUN cana-1744 71 11 ) ) PUNCT cana-1744 71 12 − − PROPN cana-1744 72 1 λ λ INTJ cana-1744 72 2 × × NOUN cana-1744 72 3 ( ( PUNCT cana-1744 72 4 1 1 NUM cana-1744 72 5 + + CCONJ cana-1744 72 6 δ δ PROPN cana-1744 72 7 ) ) PUNCT cana-1744 72 8 ∗ ∗ NOUN cana-1744 72 9 𝑍 𝑍 PROPN cana-1744 72 10 ) ) PUNCT cana-1744 72 11 b. b. NOUN cana-1744 73 1 the the DET cana-1744 73 2 transitory transitory ADJ cana-1744 73 3 result result NOUN cana-1744 73 4 of of ADP cana-1744 73 5 the the DET cana-1744 73 6 patrons patron NOUN cana-1744 73 7 in in ADP cana-1744 73 8 the the DET cana-1744 73 9 group group NOUN cana-1744 73 10 , , PUNCT cana-1744 73 11 when when SCONJ cana-1744 73 12 the the DET cana-1744 73 13 systemserver systemserver NOUN cana-1744 73 14 is be AUX cana-1744 73 15 engaged engage VERB cana-1744 73 16 in in ADP cana-1744 73 17 the the DET cana-1744 73 18 system system NOUN cana-1744 73 19 , , PUNCT cana-1744 73 20 is be AUX cana-1744 73 21 provided provide VERB cana-1744 73 22 by by ADP cana-1744 73 23 communications communication NOUN cana-1744 73 24 on on ADP cana-1744 73 25 applied apply VERB cana-1744 73 26 nonlinear nonlinear ADJ cana-1744 73 27 analysis analysis NOUN cana-1744 73 28 issn issn NOUN cana-1744 73 29 : : PUNCT cana-1744 73 30 1074 1074 NUM cana-1744 73 31 - - PUNCT cana-1744 73 32 133x 133x NUM cana-1744 73 33 vol vol NOUN cana-1744 73 34 32 32 NUM cana-1744 73 35 no no NOUN cana-1744 73 36 . . NOUN cana-1744 73 37 2 2 NUM cana-1744 73 38 ( ( PUNCT cana-1744 73 39 2025 2025 NUM cana-1744 73 40 ) ) PUNCT cana-1744 73 41 308 308 NUM cana-1744 73 42 https://internationalpubls.com https://internationalpubls.com X cana-1744 73 43 𝑃1 𝑃1 NOUN cana-1744 73 44 ∗(𝑐 ∗(𝑐 PROPN cana-1744 73 45 , , PUNCT cana-1744 73 46 𝑍 𝑍 PROPN cana-1744 73 47 ) ) PUNCT cana-1744 73 48 = = SYM cana-1744 73 49 ( ( PUNCT cana-1744 73 50 λ λ INTJ cana-1744 73 51 × × NOUN cana-1744 73 52 ( ( PUNCT cana-1744 73 53 1 1 NUM cana-1744 73 54 + + CCONJ cana-1744 73 55 δ δ NOUN cana-1744 73 56 ) ) PUNCT cana-1744 74 1 + + CCONJ cana-1744 74 2 𝜎 𝜎 ADJ cana-1744 74 3 𝑍 𝑍 NOUN cana-1744 74 4 ) ) PUNCT cana-1744 74 5 ( ( PUNCT cana-1744 74 6 1 1 NUM cana-1744 74 7 + + NUM cana-1744 74 8 𝜒𝑃00 𝜒𝑃00 NOUN cana-1744 74 9 ∗ ∗ NOUN cana-1744 74 10 ( ( PUNCT cana-1744 74 11 𝑐 𝑐 NOUN cana-1744 74 12 ) ) PUNCT cana-1744 74 13 − − NOUN cana-1744 74 14 𝜒 𝜒 SYM cana-1744 74 15 𝑍 𝑍 PROPN cana-1744 74 16 𝑃00 𝑃00 PROPN cana-1744 74 17 ∗ ∗ NOUN cana-1744 74 18 ( ( PUNCT cana-1744 74 19 𝑐)𝑎‾(𝑐 𝑐)𝑎‾(𝑐 NOUN cana-1744 74 20 + + CCONJ cana-1744 74 21 λ λ X cana-1744 74 22 × × NOUN cana-1744 74 23 ( ( PUNCT cana-1744 74 24 1 1 NUM cana-1744 74 25 + + CCONJ cana-1744 74 26 δ δ NOUN cana-1744 74 27 ) ) PUNCT cana-1744 74 28 − − PROPN cana-1744 75 1 λ λ INTJ cana-1744 75 2 × × NOUN cana-1744 75 3 ( ( PUNCT cana-1744 75 4 1 1 NUM cana-1744 75 5 + + CCONJ cana-1744 75 6 δ δ PROPN cana-1744 75 7 ) ) PUNCT cana-1744 75 8 ∗ ∗ NOUN cana-1744 75 9 𝑍 𝑍 PROPN cana-1744 75 10 ) ) PUNCT cana-1744 75 11 ( ( PUNCT cana-1744 75 12 𝑐 𝑐 PROPN cana-1744 75 13 + + NOUN cana-1744 75 14 λ λ PROPN cana-1744 75 15 × × NOUN cana-1744 75 16 ( ( PUNCT cana-1744 75 17 1 1 NUM cana-1744 75 18 + + CCONJ cana-1744 75 19 δ δ NOUN cana-1744 75 20 ) ) PUNCT cana-1744 75 21 + + SYM cana-1744 75 22 𝜒 𝜒 X cana-1744 75 23 ) ) PUNCT cana-1744 75 24 − − PROPN cana-1744 75 25 ( ( PUNCT cana-1744 75 26 λ λ INTJ cana-1744 75 27 × × NOUN cana-1744 75 28 ( ( PUNCT cana-1744 75 29 1 1 NUM cana-1744 75 30 + + CCONJ cana-1744 75 31 δ δ NOUN cana-1744 75 32 ) ) PUNCT cana-1744 76 1 + + CCONJ cana-1744 76 2 𝜒 𝜒 PART cana-1744 76 3 𝑧 𝑧 NOUN cana-1744 76 4 ) ) PUNCT cana-1744 77 1 𝑎‾(𝑐 𝑎‾(𝑐 NOUN cana-1744 77 2 + + NOUN cana-1744 77 3 λ λ X cana-1744 77 4 × × NOUN cana-1744 77 5 ( ( PUNCT cana-1744 77 6 1 1 NUM cana-1744 77 7 + + CCONJ cana-1744 77 8 δ δ NOUN cana-1744 77 9 ) ) PUNCT cana-1744 77 10 − − PROPN cana-1744 78 1 λ λ INTJ cana-1744 78 2 × × NOUN cana-1744 78 3 ( ( PUNCT cana-1744 78 4 1 1 NUM cana-1744 78 5 + + CCONJ cana-1744 78 6 δ δ PROPN cana-1744 78 7 ) ) PUNCT cana-1744 78 8 ∗ ∗ NOUN cana-1744 78 9 𝑍 𝑍 PROPN cana-1744 78 10 ) ) PUNCT cana-1744 78 11 ) ) PUNCT cana-1744 79 1 − − PROPN cana-1744 80 1 𝜎 𝜎 PRON cana-1744 80 2 𝑧 𝑧 PRON cana-1744 80 3 𝑃00 𝑃00 PROPN cana-1744 80 4 ∗ ∗ NOUN cana-1744 80 5 𝑐 𝑐 PROPN cana-1744 81 1 + + CCONJ cana-1744 81 2 λ λ X cana-1744 81 3 × × NOUN cana-1744 81 4 ( ( PUNCT cana-1744 81 5 1 1 NUM cana-1744 81 6 + + CCONJ cana-1744 81 7 δ δ NOUN cana-1744 81 8 ) ) PUNCT cana-1744 81 9 − − PROPN cana-1744 82 1 λ λ INTJ cana-1744 82 2 × × NOUN cana-1744 82 3 ( ( PUNCT cana-1744 82 4 1 1 NUM cana-1744 82 5 + + CCONJ cana-1744 82 6 δ δ PROPN cana-1744 82 7 ) ) PUNCT cana-1744 82 8 ∗ ∗ NOUN cana-1744 82 9 𝑍 𝑍 NOUN cana-1744 82 10 ( ( PUNCT cana-1744 82 11 1 1 NUM cana-1744 82 12 − − NOUN cana-1744 82 13 𝑎‾(𝑐 𝑎‾(𝑐 NOUN cana-1744 82 14 + + NOUN cana-1744 82 15 λ λ X cana-1744 82 16 × × NOUN cana-1744 82 17 ( ( PUNCT cana-1744 82 18 1 1 NUM cana-1744 82 19 + + CCONJ cana-1744 82 20 δ δ NOUN cana-1744 82 21 ) ) PUNCT cana-1744 82 22 − − PROPN cana-1744 83 1 λ λ INTJ cana-1744 83 2 × × NOUN cana-1744 83 3 ( ( PUNCT cana-1744 83 4 1 1 NUM cana-1744 83 5 + + CCONJ cana-1744 83 6 δ δ PROPN cana-1744 83 7 ) ) PUNCT cana-1744 83 8 ∗ ∗ NOUN cana-1744 83 9 𝑍 𝑍 PROPN cana-1744 83 10 ) ) PUNCT cana-1744 83 11 ) ) PUNCT cana-1744 83 12 c. c. NOUN cana-1744 83 13 the the DET cana-1744 83 14 steady steady ADJ cana-1744 83 15 - - PUNCT cana-1744 83 16 state state NOUN cana-1744 83 17 result result NOUN cana-1744 83 18 of of ADP cana-1744 83 19 patrons patron NOUN cana-1744 83 20 in in ADP cana-1744 83 21 the the DET cana-1744 83 22 group group NOUN cana-1744 83 23 when when SCONJ cana-1744 83 24 the the DET cana-1744 83 25 server server NOUN cana-1744 83 26 is be AUX cana-1744 83 27 free free ADJ cana-1744 83 28 in in ADP cana-1744 83 29 the the DET cana-1744 83 30 service service NOUN cana-1744 83 31 system system NOUN cana-1744 83 32 is be AUX cana-1744 83 33 provided provide VERB cana-1744 83 34 by by ADP cana-1744 83 35 𝑃0(𝑍 𝑃0(𝑍 NOUN cana-1744 83 36 ) ) PUNCT cana-1744 83 37 = = SYM cana-1744 83 38 𝑝00 𝑝00 VERB cana-1744 83 39 1 1 NUM cana-1744 83 40 − − PROPN cana-1744 83 41 ( ( PUNCT cana-1744 83 42 λ λ INTJ cana-1744 83 43 × × NOUN cana-1744 83 44 ( ( PUNCT cana-1744 83 45 1 1 NUM cana-1744 83 46 + + CCONJ cana-1744 83 47 δ δ PROPN cana-1744 83 48 ) ) PUNCT cana-1744 83 49 ∗ ∗ NOUN cana-1744 83 50 𝑍 𝑍 PROPN cana-1744 83 51 𝜒 𝜒 NOUN cana-1744 83 52 ) ) PUNCT cana-1744 83 53 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 83 54 ) ) PUNCT cana-1744 83 55 where where SCONJ cana-1744 83 56 𝛿(𝑍 𝛿(𝑍 NOUN cana-1744 83 57 ) ) PUNCT cana-1744 84 1 = = SYM cana-1744 84 2 1 1 NUM cana-1744 84 3 − − NOUN cana-1744 84 4 𝑎‾ 𝑎‾ ADV cana-1744 84 5 𝑎‾ 𝑎‾ NOUN cana-1744 84 6 − − PROPN cana-1744 84 7 𝑍 𝑍 PROPN cana-1744 84 8 , , PUNCT cana-1744 84 9 𝑃00 𝑃00 X cana-1744 84 10 = = SYM cana-1744 85 1 1 1 NUM cana-1744 85 2 − − NUM cana-1744 85 3 𝜌1 𝜌1 NOUN cana-1744 85 4 and and CCONJ cana-1744 85 5 𝜌1 𝜌1 NOUN cana-1744 85 6 = = PUNCT cana-1744 86 1 λ λ X cana-1744 86 2 × × NOUN cana-1744 86 3 ( ( PUNCT cana-1744 86 4 1 1 NUM cana-1744 86 5 + + CCONJ cana-1744 86 6 δ)(λ δ)(λ ADJ cana-1744 86 7 × × NOUN cana-1744 86 8 ( ( PUNCT cana-1744 86 9 1 1 NUM cana-1744 86 10 + + CCONJ cana-1744 86 11 δ δ NOUN cana-1744 86 12 ) ) PUNCT cana-1744 86 13 + + SYM cana-1744 86 14 𝜒 𝜒 X cana-1744 86 15 ) ) PUNCT cana-1744 86 16 𝜒 𝜒 NOUN cana-1744 86 17 𝐸(𝑌 𝐸(𝑌 PROPN cana-1744 86 18 ) ) PUNCT cana-1744 86 19 d. d. NOUN cana-1744 86 20 the the DET cana-1744 86 21 steady steady ADJ cana-1744 86 22 - - PUNCT cana-1744 86 23 state state NOUN cana-1744 86 24 result result NOUN cana-1744 86 25 of of ADP cana-1744 86 26 patrons patron NOUN cana-1744 86 27 in in ADP cana-1744 86 28 the the DET cana-1744 86 29 group group NOUN cana-1744 86 30 when when SCONJ cana-1744 86 31 the the DET cana-1744 86 32 server server NOUN cana-1744 86 33 is be AUX cana-1744 86 34 engaged engage VERB cana-1744 86 35 in in ADP cana-1744 86 36 the the DET cana-1744 86 37 service service NOUN cana-1744 86 38 system system NOUN cana-1744 86 39 is be AUX cana-1744 86 40 provided provide VERB cana-1744 86 41 by by ADP cana-1744 86 42 𝑷𝟏(𝒁 𝑷𝟏(𝒁 NUM cana-1744 86 43 ) ) PUNCT cana-1744 87 1 = = SYM cana-1744 87 2 𝑷𝟎𝟎 𝑷𝟎𝟎 PROPN cana-1744 87 3 ( ( PUNCT cana-1744 87 4 𝜹(𝒁 𝜹(𝒁 X cana-1744 87 5 ) ) PUNCT cana-1744 87 6 𝟏 𝟏 NUM cana-1744 87 7 − − NOUN cana-1744 87 8 ( ( PUNCT cana-1744 87 9 𝚲 𝚲 NOUN cana-1744 87 10 × × NOUN cana-1744 87 11 ( ( PUNCT cana-1744 87 12 𝟏 𝟏 NUM cana-1744 87 13 + + NUM cana-1744 87 14 𝛅)𝒁 𝛅)𝒁 ADJ cana-1744 87 15 𝝌 𝝌 NOUN cana-1744 87 16 ) ) PUNCT cana-1744 87 17 𝜹(𝒁 𝜹(𝒁 X cana-1744 87 18 ) ) PUNCT cana-1744 87 19 ) ) PUNCT cana-1744 88 1 proof proof NOUN cana-1744 88 2 : : PUNCT cana-1744 88 3 we we PRON cana-1744 88 4 determine determine VERB cana-1744 88 5 the the DET cana-1744 88 6 probability probability NOUN cana-1744 88 7 - - PUNCT cana-1744 88 8 generating generate VERB cana-1744 88 9 functions function NOUN cana-1744 88 10 𝜔(𝑦 𝜔(𝑦 NOUN cana-1744 88 11 , , PUNCT cana-1744 88 12 𝑇 𝑇 PROPN cana-1744 88 13 , , PUNCT cana-1744 88 14 𝑍 𝑍 PROPN cana-1744 88 15 ) ) PUNCT cana-1744 88 16 = = PUNCT cana-1744 88 17 ∑ ∑ PUNCT cana-1744 88 18     SPACE cana-1744 88 19 ∞ ∞ NUM cana-1744 88 20 𝑚=0 𝑚=0 PUNCT cana-1744 88 21     SPACE cana-1744 88 22 𝑃𝑚1(𝑦 𝑃𝑚1(𝑦 PROPN cana-1744 88 23 , , PUNCT cana-1744 88 24 𝑇)𝑍 𝑇)𝑍 VERB cana-1744 88 25 𝑚 𝑚 PROPN cana-1744 88 26 ( ( PUNCT cana-1744 88 27 18 18 NUM cana-1744 88 28 ) ) PUNCT cana-1744 88 29 𝑃0(𝑇 𝑃0(𝑇 PROPN cana-1744 88 30 , , PUNCT cana-1744 88 31 𝑍 𝑍 PROPN cana-1744 88 32 ) ) PUNCT cana-1744 88 33 = = PUNCT cana-1744 88 34 ∑ ∑ PUNCT cana-1744 88 35     SPACE cana-1744 88 36 ∞ ∞ NUM cana-1744 88 37 𝑚=0 𝑚=0 PUNCT cana-1744 88 38     SPACE cana-1744 88 39 𝑃𝑚0(𝑇)𝑍 𝑃𝑚0(𝑇)𝑍 PROPN cana-1744 88 40 𝑚 𝑚 X cana-1744 88 41 ( ( PUNCT cana-1744 88 42 19 19 NUM cana-1744 88 43 ) ) PUNCT cana-1744 88 44 using use VERB cana-1744 88 45 the the DET cana-1744 88 46 lt lt NOUN cana-1744 88 47 to to ADP cana-1744 88 48 the the DET cana-1744 88 49 equations equation NOUN cana-1744 88 50 ( ( PUNCT cana-1744 88 51 18 18 NUM cana-1744 88 52 ) ) PUNCT cana-1744 88 53 and and CCONJ cana-1744 88 54 ( ( PUNCT cana-1744 88 55 19 19 NUM cana-1744 88 56 ) ) PUNCT cana-1744 88 57 , , PUNCT cana-1744 88 58 we we PRON cana-1744 88 59 obtain obtain VERB cana-1744 88 60 𝜔∗(𝑦 𝜔∗(𝑦 NOUN cana-1744 88 61 , , PUNCT cana-1744 88 62 𝑐 𝑐 NOUN cana-1744 88 63 , , PUNCT cana-1744 88 64 𝑍 𝑍 PROPN cana-1744 88 65 ) ) PUNCT cana-1744 88 66 = = SYM cana-1744 88 67 ∑𝑚=0 ∑𝑚=0 PROPN cana-1744 88 68 ∞ ∞ PROPN cana-1744 88 69     SPACE cana-1744 88 70 𝑃𝑚1 𝑃𝑚1 NOUN cana-1744 88 71 ∗ ∗ NOUN cana-1744 88 72 ( ( PUNCT cana-1744 88 73 𝑦 𝑦 NOUN cana-1744 88 74 , , PUNCT cana-1744 88 75 𝑐)𝑍𝑚 𝑐)𝑍𝑚 NOUN cana-1744 88 76 ( ( PUNCT cana-1744 88 77 20 20 NUM cana-1744 88 78 ) ) PUNCT cana-1744 88 79 𝑃0 𝑃0 NOUN cana-1744 88 80 ∗(𝑐 ∗(𝑐 PROPN cana-1744 88 81 , , PUNCT cana-1744 88 82 𝑍 𝑍 PROPN cana-1744 88 83 ) ) PUNCT cana-1744 88 84 = = SYM cana-1744 88 85 ∑𝑚=0 ∑𝑚=0 PROPN cana-1744 88 86 ∞ ∞ PROPN cana-1744 88 87     SPACE cana-1744 88 88 𝑃∗ 𝑃∗ ADJ cana-1744 88 89 𝑚0(𝑐)𝑍 𝑚0(𝑐)𝑍 PROPN cana-1744 88 90 𝑚 𝑚 X cana-1744 88 91 ( ( PUNCT cana-1744 88 92 21 21 NUM cana-1744 88 93 ) ) PUNCT cana-1744 88 94 partly partly ADV cana-1744 88 95 differentiate differentiate VERB cana-1744 88 96 ( ( PUNCT cana-1744 88 97 20 20 NUM cana-1744 88 98 ) ) PUNCT cana-1744 88 99 concerning concern VERB cana-1744 88 100 𝑦 𝑦 PROPN cana-1744 88 101 𝜔′∗(𝑦 𝜔′∗(𝑦 NOUN cana-1744 88 102 , , PUNCT cana-1744 88 103 𝑐 𝑐 NOUN cana-1744 88 104 , , PUNCT cana-1744 88 105 𝑍 𝑍 PROPN cana-1744 88 106 ) ) PUNCT cana-1744 88 107 = = SYM cana-1744 88 108 ∑𝑚=0 ∑𝑚=0 PROPN cana-1744 88 109 ∞ ∞ PROPN cana-1744 88 110     SPACE cana-1744 89 1 𝑃′𝑚1 𝑃′𝑚1 PROPN cana-1744 89 2 ∗ ∗ NOUN cana-1744 89 3 ( ( PUNCT cana-1744 89 4 𝑦 𝑦 NOUN cana-1744 89 5 , , PUNCT cana-1744 89 6 𝑐)𝑍𝑚 𝑐)𝑍𝑚 NOUN cana-1744 89 7 ( ( PUNCT cana-1744 89 8 22 22 NUM cana-1744 89 9 ) ) PUNCT cana-1744 89 10 substitute substitute NOUN cana-1744 89 11 ( ( PUNCT cana-1744 89 12 12 12 NUM cana-1744 89 13 ) ) PUNCT cana-1744 89 14 and and CCONJ cana-1744 89 15 ( ( PUNCT cana-1744 89 16 13 13 NUM cana-1744 89 17 ) ) PUNCT cana-1744 89 18 in in ADP cana-1744 89 19 ( ( PUNCT cana-1744 89 20 20 20 NUM cana-1744 89 21 ) ) PUNCT cana-1744 89 22 , , PUNCT cana-1744 89 23 we we PRON cana-1744 89 24 have have VERB cana-1744 89 25 𝜔′∗(𝑦 𝜔′∗(𝑦 NOUN cana-1744 89 26 , , PUNCT cana-1744 89 27 𝑐 𝑐 NOUN cana-1744 89 28 , , PUNCT cana-1744 89 29 𝑍 𝑍 PROPN cana-1744 89 30 ) ) PUNCT cana-1744 89 31 + + CCONJ cana-1744 90 1 ( ( PUNCT cana-1744 90 2 𝑐 𝑐 PROPN cana-1744 90 3 + + NOUN cana-1744 90 4 λ λ PROPN cana-1744 90 5 × × NOUN cana-1744 90 6 ( ( PUNCT cana-1744 90 7 1 1 NUM cana-1744 90 8 + + CCONJ cana-1744 90 9 δ δ NOUN cana-1744 90 10 ) ) PUNCT cana-1744 90 11 − − PROPN cana-1744 91 1 λ λ INTJ cana-1744 91 2 × × NOUN cana-1744 91 3 ( ( PUNCT cana-1744 91 4 1 1 NUM cana-1744 91 5 + + CCONJ cana-1744 91 6 δ δ PROPN cana-1744 91 7 ) ) PUNCT cana-1744 91 8 ∗ ∗ NOUN cana-1744 91 9 𝑍 𝑍 PROPN cana-1744 91 10 + + CCONJ cana-1744 91 11 𝜇(𝑦))𝜔∗(𝑦 𝜇(𝑦))𝜔∗(𝑦 PROPN cana-1744 91 12 , , PUNCT cana-1744 91 13 𝑐 𝑐 NOUN cana-1744 91 14 , , PUNCT cana-1744 91 15 𝑍 𝑍 PROPN cana-1744 91 16 ) ) PUNCT cana-1744 91 17 = = SYM cana-1744 91 18 0 0 NUM cana-1744 91 19 ( ( PUNCT cana-1744 91 20 23 23 NUM cana-1744 91 21 ) ) PUNCT cana-1744 91 22 when when SCONJ cana-1744 91 23 we we PRON cana-1744 91 24 solve solve VERB cana-1744 91 25 the the DET cana-1744 91 26 differential differential ADJ cana-1744 91 27 equation equation NOUN cana-1744 91 28 above above ADV cana-1744 91 29 , , PUNCT cana-1744 91 30 we we PRON cana-1744 91 31 obtain obtain VERB cana-1744 91 32 𝜔∗(𝑦 𝜔∗(𝑦 NOUN cana-1744 91 33 , , PUNCT cana-1744 91 34 𝑐 𝑐 NOUN cana-1744 91 35 , , PUNCT cana-1744 91 36 𝑍 𝑍 PROPN cana-1744 91 37 ) ) PUNCT cana-1744 91 38 = = SYM cana-1744 91 39 𝜔∗(0 𝜔∗(0 NOUN cana-1744 91 40 , , PUNCT cana-1744 91 41 𝑐 𝑐 X cana-1744 91 42 , , PUNCT cana-1744 91 43 𝑍)𝑒−(𝑐+λ×(1+δ)−λ×(1+δ)∗𝑍)𝑦𝑒−∫ 𝑍)𝑒−(𝑐+λ×(1+δ)−λ×(1+δ)∗𝑍)𝑦𝑒−∫ PRON cana-1744 91 44     SPACE cana-1744 91 45 𝑦 𝑦 NOUN cana-1744 91 46 0 0 NUM cana-1744 91 47     SPACE cana-1744 91 48 𝜇(𝑦)𝑑𝑦 𝜇(𝑦)𝑑𝑦 PROPN cana-1744 91 49 ( ( PUNCT cana-1744 91 50 24 24 NUM cana-1744 91 51 ) ) PUNCT cana-1744 91 52 where where SCONJ cana-1744 91 53 communications communication NOUN cana-1744 91 54 on on ADP cana-1744 91 55 applied apply VERB cana-1744 91 56 nonlinear nonlinear ADJ cana-1744 91 57 analysis analysis NOUN cana-1744 91 58 issn issn NOUN cana-1744 91 59 : : PUNCT cana-1744 91 60 1074 1074 NUM cana-1744 91 61 - - PUNCT cana-1744 91 62 133x 133x NUM cana-1744 91 63 vol vol NOUN cana-1744 91 64 32 32 NUM cana-1744 91 65 no no NOUN cana-1744 91 66 . . NOUN cana-1744 91 67 2 2 NUM cana-1744 91 68 ( ( PUNCT cana-1744 91 69 2025 2025 NUM cana-1744 91 70 ) ) PUNCT cana-1744 91 71 309 309 NUM cana-1744 91 72 https://internationalpubls.com https://internationalpubls.com X cana-1744 91 73 𝜔∗(0 𝜔∗(0 NOUN cana-1744 91 74 , , PUNCT cana-1744 91 75 𝑐 𝑐 NOUN cana-1744 91 76 , , PUNCT cana-1744 91 77 𝑍 𝑍 PROPN cana-1744 91 78 ) ) PUNCT cana-1744 91 79 = = PUNCT cana-1744 91 80 ∑ ∑ PUNCT cana-1744 91 81     SPACE cana-1744 91 82 ∞ ∞ NUM cana-1744 91 83 𝑚=0 𝑚=0 PUNCT cana-1744 91 84     SPACE cana-1744 91 85 𝑃𝑚1 𝑃𝑚1 NOUN cana-1744 91 86 ∗ ∗ NOUN cana-1744 91 87 ( ( PUNCT cana-1744 91 88 0 0 NUM cana-1744 91 89 , , PUNCT cana-1744 91 90 𝑐)𝑍𝑚 𝑐)𝑍𝑚 NOUN cana-1744 91 91 ( ( PUNCT cana-1744 91 92 25 25 NUM cana-1744 91 93 ) ) PUNCT cana-1744 91 94 substituting substituting NOUN cana-1744 91 95 ( ( PUNCT cana-1744 91 96 16 16 NUM cana-1744 91 97 ) ) PUNCT cana-1744 91 98 and and CCONJ cana-1744 91 99 ( ( PUNCT cana-1744 91 100 17 17 NUM cana-1744 91 101 ) ) PUNCT cana-1744 91 102 in in ADP cana-1744 91 103 ( ( PUNCT cana-1744 91 104 25 25 NUM cana-1744 91 105 ) ) PUNCT cana-1744 91 106 , , PUNCT cana-1744 91 107 we we PRON cana-1744 91 108 obtain obtain VERB cana-1744 91 109 𝜔∗(0 𝜔∗(0 NOUN cana-1744 91 110 , , PUNCT cana-1744 91 111 𝑐 𝑐 NOUN cana-1744 91 112 , , PUNCT cana-1744 91 113 𝑍 𝑍 PROPN cana-1744 91 114 ) ) PUNCT cana-1744 91 115 = = SYM cana-1744 91 116 ( ( PUNCT cana-1744 91 117 λ λ INTJ cana-1744 91 118 × × NOUN cana-1744 91 119 ( ( PUNCT cana-1744 91 120 1 1 NUM cana-1744 91 121 + + CCONJ cana-1744 91 122 δ δ NOUN cana-1744 91 123 ) ) PUNCT cana-1744 92 1 + + CCONJ cana-1744 92 2 𝜒 𝜒 NUM cana-1744 92 3 𝑍 𝑍 NOUN cana-1744 92 4 ) ) PUNCT cana-1744 92 5 𝑃0 𝑃0 NOUN cana-1744 92 6 ∗(𝑐 ∗(𝑐 PROPN cana-1744 92 7 , , PUNCT cana-1744 92 8 𝑍 𝑍 PROPN cana-1744 92 9 ) ) PUNCT cana-1744 92 10 − − NOUN cana-1744 92 11 𝜒 𝜒 SYM cana-1744 92 12 𝑍 𝑍 PROPN cana-1744 92 13 𝑃00 𝑃00 PROPN cana-1744 92 14 ∗ ∗ NOUN cana-1744 92 15 ( ( PUNCT cana-1744 92 16 26 26 NUM cana-1744 92 17 ) ) PUNCT cana-1744 92 18 multiply multiply ADP cana-1744 92 19 the the DET cana-1744 92 20 equation equation NOUN cana-1744 92 21 ( ( PUNCT cana-1744 92 22 24 24 NUM cana-1744 92 23 ) ) PUNCT cana-1744 92 24 by by ADP cana-1744 92 25 𝜇(𝑦 𝜇(𝑦 NOUN cana-1744 92 26 ) ) PUNCT cana-1744 92 27 ∫ ∫ PROPN cana-1744 93 1 𝑖𝑛𝑔 𝑖𝑛𝑔 INTJ cana-1744 93 2 with with ADP cana-1744 93 3 respect respect NOUN cana-1744 93 4 x x PUNCT cana-1744 93 5 between between ADP cana-1744 93 6 0 0 NUM cana-1744 93 7 and and CCONJ cana-1744 93 8 ∞ ∞ NUM cana-1744 93 9 ∫ ∫ PROPN cana-1744 93 10     SPACE cana-1744 93 11 ∞ ∞ PROPN cana-1744 93 12 0 0 NUM cana-1744 93 13     SPACE cana-1744 93 14 𝜔∗(𝑦 𝜔∗(𝑦 PROPN cana-1744 93 15 , , PUNCT cana-1744 93 16 𝑐 𝑐 NOUN cana-1744 93 17 , , PUNCT cana-1744 93 18 𝑍)𝜇(𝑦)𝑑𝑦 𝑍)𝜇(𝑦)𝑑𝑦 NOUN cana-1744 93 19 = = PUNCT cana-1744 93 20 𝜔∗(0 𝜔∗(0 NOUN cana-1744 93 21 , , PUNCT cana-1744 93 22 𝑐 𝑐 PRON cana-1744 93 23 , , PUNCT cana-1744 93 24 𝑍)∫ 𝑍)∫ NOUN cana-1744 93 25     SPACE cana-1744 93 26 ∞ ∞ PROPN cana-1744 93 27 0 0 NUM cana-1744 93 28     SPACE cana-1744 93 29 𝑒−(𝑐+λ×(1+δ)−λ×(1+δ)∗𝑍)𝑦𝑒−∫ 𝑒−(𝑐+λ×(1+δ)−λ×(1+δ)∗𝑍)𝑦𝑒−∫ VERB cana-1744 93 30     SPACE cana-1744 93 31 𝑦 𝑦 NOUN cana-1744 93 32 0 0 NUM cana-1744 93 33     SPACE cana-1744 93 34 𝜇(𝑦)𝑑𝑦𝜇(𝑦)𝑑𝑦 𝜇(𝑦)𝑑𝑦𝜇(𝑦)𝑑𝑦 X cana-1744 93 35 ( ( PUNCT cana-1744 93 36 27 27 NUM cana-1744 93 37 ) ) PUNCT cana-1744 93 38 ∫ ∫ PROPN cana-1744 93 39     SPACE cana-1744 93 40 ∞ ∞ PROPN cana-1744 93 41 0 0 NUM cana-1744 93 42     SPACE cana-1744 93 43 𝜔∗(𝑦 𝜔∗(𝑦 PROPN cana-1744 93 44 , , PUNCT cana-1744 93 45 𝑐 𝑐 NOUN cana-1744 93 46 , , PUNCT cana-1744 93 47 𝑍)𝜇(𝑦)𝑑𝑦 𝑍)𝜇(𝑦)𝑑𝑦 NOUN cana-1744 93 48 = = PUNCT cana-1744 93 49 𝜔∗(0 𝜔∗(0 NOUN cana-1744 93 50 , , PUNCT cana-1744 93 51 𝑐 𝑐 PRON cana-1744 93 52 , , PUNCT cana-1744 93 53 𝑍)∫ 𝑍)∫ NOUN cana-1744 93 54     SPACE cana-1744 93 55 ∞ ∞ PROPN cana-1744 93 56 0 0 NUM cana-1744 93 57     SPACE cana-1744 93 58 𝑒−(𝑐+λ×(1+δ)−λ×(1+δ)∗𝑍)𝑦𝑎(𝑦)𝑑𝑦 𝑒−(𝑐+λ×(1+δ)−λ×(1+δ)∗𝑍)𝑦𝑎(𝑦)𝑑𝑦 PROPN cana-1744 93 59 ( ( PUNCT cana-1744 93 60 28 28 NUM cana-1744 93 61 ) ) PUNCT cana-1744 93 62 ∫ ∫ PROPN cana-1744 93 63     SPACE cana-1744 94 1 ∞ ∞ PROPN cana-1744 94 2 0 0 NUM cana-1744 94 3     SPACE cana-1744 94 4 𝜔∗(𝑦 𝜔∗(𝑦 PROPN cana-1744 94 5 , , PUNCT cana-1744 94 6 𝑐 𝑐 NOUN cana-1744 94 7 , , PUNCT cana-1744 94 8 𝑍)𝜇(𝑦)𝑑𝑦 𝑍)𝜇(𝑦)𝑑𝑦 NOUN cana-1744 94 9 = = PUNCT cana-1744 94 10 𝜔∗(0 𝜔∗(0 NOUN cana-1744 94 11 , , PUNCT cana-1744 94 12 𝑐 𝑐 NOUN cana-1744 94 13 , , PUNCT cana-1744 94 14 𝑍)𝑎‾(𝑐 𝑍)𝑎‾(𝑐 NOUN cana-1744 94 15 + + X cana-1744 94 16 λ λ X cana-1744 94 17 × × NOUN cana-1744 94 18 ( ( PUNCT cana-1744 94 19 1 1 NUM cana-1744 94 20 + + CCONJ cana-1744 94 21 δ δ NOUN cana-1744 94 22 ) ) PUNCT cana-1744 94 23 − − PROPN cana-1744 95 1 λ λ INTJ cana-1744 95 2 × × NOUN cana-1744 95 3 ( ( PUNCT cana-1744 95 4 1 1 NUM cana-1744 95 5 + + CCONJ cana-1744 95 6 δ δ PROPN cana-1744 95 7 ) ) PUNCT cana-1744 95 8 ∗ ∗ NOUN cana-1744 95 9 𝑍 𝑍 PROPN cana-1744 95 10 ) ) PUNCT cana-1744 95 11 ( ( PUNCT cana-1744 95 12 29 29 NUM cana-1744 95 13 ) ) PUNCT cana-1744 95 14 where where SCONJ cana-1744 95 15 𝑎‾(𝑐 𝑎‾(𝑐 NOUN cana-1744 95 16 ) ) PUNCT cana-1744 95 17 = = SYM cana-1744 96 1 ∫ ∫ PROPN cana-1744 96 2 0 0 NUM cana-1744 97 1 ∞ ∞ NUM cana-1744 97 2     SPACE cana-1744 97 3 𝑒−𝑐𝑦𝑎(𝑦)𝑑𝑦 𝑒−𝑐𝑦𝑎(𝑦)𝑑𝑦 PROPN cana-1744 97 4 is be AUX cana-1744 97 5 the the DET cana-1744 97 6 lt lt NOUN cana-1744 97 7 of of ADP cana-1744 97 8 the the DET cana-1744 97 9 service service NOUN cana-1744 97 10 - - PUNCT cana-1744 97 11 system system NOUN cana-1744 97 12 time time NOUN cana-1744 97 13 distribution distribution NOUN cana-1744 97 14 ∫ ∫ PROPN cana-1744 97 15 𝑖𝑛𝑔 𝑖𝑛𝑔 INTJ cana-1744 98 1 the the DET cana-1744 98 2 equation equation NOUN cana-1744 98 3 ( ( PUNCT cana-1744 98 4 24 24 NUM cana-1744 98 5 ) ) PUNCT cana-1744 98 6 with with ADP cana-1744 98 7 respect respect NOUN cana-1744 98 8 to to ADP cana-1744 98 9 𝑦 𝑦 PRON cana-1744 98 10 via via ADP cana-1744 98 11 0 0 NUM cana-1744 98 12 and and CCONJ cana-1744 98 13 ∞ ∞ NUM cana-1744 98 14 , , PUNCT cana-1744 98 15 we we PRON cana-1744 98 16 have have VERB cana-1744 98 17 𝑃1 𝑃1 NOUN cana-1744 98 18 ∗(𝑐 ∗(𝑐 PROPN cana-1744 98 19 , , PUNCT cana-1744 98 20 𝑍 𝑍 PROPN cana-1744 98 21 ) ) PUNCT cana-1744 98 22 = = SYM cana-1744 98 23 𝜔∗(0 𝜔∗(0 NOUN cana-1744 98 24 , , PUNCT cana-1744 98 25 𝑐 𝑐 NOUN cana-1744 98 26 , , PUNCT cana-1744 98 27 𝑍 𝑍 PROPN cana-1744 98 28 ) ) PUNCT cana-1744 98 29 𝑐 𝑐 NOUN cana-1744 99 1 + + NOUN cana-1744 99 2 λ λ PROPN cana-1744 99 3 × × NOUN cana-1744 99 4 ( ( PUNCT cana-1744 99 5 1 1 NUM cana-1744 99 6 + + CCONJ cana-1744 99 7 δ δ NOUN cana-1744 99 8 ) ) PUNCT cana-1744 99 9 − − PROPN cana-1744 100 1 λ λ INTJ cana-1744 100 2 × × NOUN cana-1744 100 3 ( ( PUNCT cana-1744 100 4 1 1 NUM cana-1744 100 5 + + CCONJ cana-1744 100 6 δ δ PROPN cana-1744 100 7 ) ) PUNCT cana-1744 100 8 ∗ ∗ NOUN cana-1744 100 9 𝑍 𝑍 NOUN cana-1744 100 10 ( ( PUNCT cana-1744 100 11 1 1 NUM cana-1744 100 12 − − NOUN cana-1744 100 13 𝑎‾(𝑐 𝑎‾(𝑐 NOUN cana-1744 100 14 + + NOUN cana-1744 100 15 λ λ X cana-1744 100 16 × × NOUN cana-1744 100 17 ( ( PUNCT cana-1744 100 18 1 1 NUM cana-1744 100 19 + + CCONJ cana-1744 100 20 δ δ NOUN cana-1744 100 21 ) ) PUNCT cana-1744 100 22 − − PROPN cana-1744 101 1 λ λ INTJ cana-1744 101 2 × × NOUN cana-1744 101 3 ( ( PUNCT cana-1744 101 4 1 1 NUM cana-1744 101 5 + + CCONJ cana-1744 101 6 δ δ PROPN cana-1744 101 7 ) ) PUNCT cana-1744 101 8 ∗ ∗ NOUN cana-1744 101 9 𝑍 𝑍 PROPN cana-1744 101 10 ) ) PUNCT cana-1744 101 11 ) ) PUNCT cana-1744 101 12 ( ( PUNCT cana-1744 101 13 30 30 X cana-1744 101 14 ) ) PUNCT cana-1744 101 15 substitute substitute NOUN cana-1744 101 16 the the DET cana-1744 101 17 above above ADJ cana-1744 101 18 equation equation NOUN cana-1744 101 19 ( ( PUNCT cana-1744 101 20 26 26 NUM cana-1744 101 21 ) ) PUNCT cana-1744 101 22 in in ADP cana-1744 101 23 ( ( PUNCT cana-1744 101 24 30 30 NUM cana-1744 101 25 ) ) PUNCT cana-1744 101 26 , , PUNCT cana-1744 101 27 we we PRON cana-1744 101 28 obtain obtain VERB cana-1744 101 29 𝑃1 𝑃1 NOUN cana-1744 101 30 ∗(𝑐 ∗(𝑐 PROPN cana-1744 101 31 , , PUNCT cana-1744 101 32 𝑍 𝑍 PROPN cana-1744 101 33 ) ) PUNCT cana-1744 101 34 = = SYM cana-1744 101 35 ( ( PUNCT cana-1744 101 36 λ λ INTJ cana-1744 101 37 × × NOUN cana-1744 101 38 ( ( PUNCT cana-1744 101 39 1 1 NUM cana-1744 101 40 + + CCONJ cana-1744 101 41 δ δ NOUN cana-1744 101 42 ) ) PUNCT cana-1744 102 1 + + NUM cana-1744 102 2 𝜒 𝜒 X cana-1744 102 3 𝑍)𝑃0 𝑍)𝑃0 ADJ cana-1744 102 4 ∗(𝑐 ∗(𝑐 NOUN cana-1744 102 5 , , PUNCT cana-1744 102 6 𝑍 𝑍 PROPN cana-1744 102 7 ) ) PUNCT cana-1744 102 8 − − NOUN cana-1744 102 9 𝜒 𝜒 SYM cana-1744 102 10 𝑍 𝑍 PROPN cana-1744 102 11 𝑃00 𝑃00 PROPN cana-1744 102 12 ∗ ∗ NOUN cana-1744 102 13 𝑐 𝑐 PROPN cana-1744 103 1 + + CCONJ cana-1744 103 2 λ λ X cana-1744 103 3 × × NOUN cana-1744 103 4 ( ( PUNCT cana-1744 103 5 1 1 NUM cana-1744 103 6 + + CCONJ cana-1744 103 7 δ δ NOUN cana-1744 103 8 ) ) PUNCT cana-1744 103 9 − − PROPN cana-1744 104 1 λ λ INTJ cana-1744 104 2 × × NOUN cana-1744 104 3 ( ( PUNCT cana-1744 104 4 1 1 NUM cana-1744 104 5 + + CCONJ cana-1744 104 6 δ δ PROPN cana-1744 104 7 ) ) PUNCT cana-1744 104 8 ∗ ∗ NOUN cana-1744 104 9 𝑍 𝑍 NOUN cana-1744 104 10 ( ( PUNCT cana-1744 104 11 1 1 NUM cana-1744 104 12 − − NOUN cana-1744 104 13 𝑎‾(𝑐 𝑎‾(𝑐 NOUN cana-1744 104 14 + + NOUN cana-1744 104 15 λ λ X cana-1744 104 16 × × NOUN cana-1744 104 17 ( ( PUNCT cana-1744 104 18 1 1 NUM cana-1744 104 19 + + CCONJ cana-1744 104 20 δ δ NOUN cana-1744 104 21 ) ) PUNCT cana-1744 104 22 − − PROPN cana-1744 105 1 λ λ INTJ cana-1744 105 2 × × NOUN cana-1744 105 3 ( ( PUNCT cana-1744 105 4 1 1 NUM cana-1744 105 5 + + CCONJ cana-1744 105 6 δ δ PROPN cana-1744 105 7 ) ) PUNCT cana-1744 105 8 ∗ ∗ NOUN cana-1744 105 9 𝑍 𝑍 PROPN cana-1744 105 10 ) ) PUNCT cana-1744 105 11 ) ) PUNCT cana-1744 105 12 ( ( PUNCT cana-1744 105 13 31 31 NUM cana-1744 105 14 ) ) PUNCT cana-1744 105 15 multiply multiply ADP cana-1744 105 16 the the DET cana-1744 105 17 above above ADJ cana-1744 105 18 equation equation NOUN cana-1744 105 19 ( ( PUNCT cana-1744 105 20 14 14 NUM cana-1744 105 21 ) ) PUNCT cana-1744 105 22 by by ADP cana-1744 105 23 𝑍𝑚 𝑍𝑚 PROPN cana-1744 105 24 on on ADP cana-1744 105 25 symmetry symmetry NOUN cana-1744 105 26 sides side NOUN cana-1744 105 27 and and CCONJ cana-1744 105 28 add add VERB cana-1744 105 29 over over ADP cana-1744 105 30 𝑚 𝑚 NOUN cana-1744 105 31 = = SYM cana-1744 105 32 1 1 NUM cana-1744 105 33 to to ADP cana-1744 105 34 ∞ ∞ NUM cana-1744 105 35 , , PUNCT cana-1744 105 36 we we PRON cana-1744 105 37 obtain obtain VERB cana-1744 105 38 ( ( PUNCT cana-1744 105 39 𝑐 𝑐 NOUN cana-1744 105 40 + + NOUN cana-1744 105 41 λ λ PROPN cana-1744 105 42 × × NOUN cana-1744 105 43 ( ( PUNCT cana-1744 105 44 1 1 NUM cana-1744 105 45 + + CCONJ cana-1744 105 46 δ δ NOUN cana-1744 105 47 ) ) PUNCT cana-1744 105 48 + + NUM cana-1744 105 49 𝜒)∑1 𝜒)∑1 NUM cana-1744 106 1 ∞ ∞ NUM cana-1744 106 2     SPACE cana-1744 106 3 𝑃𝑚0 𝑃𝑚0 NOUN cana-1744 106 4 ∗(𝑇)𝑍𝑚 ∗(𝑇)𝑍𝑚 PROPN cana-1744 106 5 = = SYM cana-1744 106 6 ∫ ∫ PROPN cana-1744 106 7 0 0 NUM cana-1744 107 1 ∞ ∞ NUM cana-1744 107 2     SPACE cana-1744 107 3 ( ( PUNCT cana-1744 107 4 ∑1 ∑1 NOUN cana-1744 107 5 ∞ ∞ NUM cana-1744 107 6     SPACE cana-1744 107 7 𝑃𝑚1 𝑃𝑚1 NOUN cana-1744 107 8 ∗(𝑦 ∗(𝑦 NOUN cana-1744 107 9 , , PUNCT cana-1744 107 10 𝑐)𝑍𝑚)𝜇(𝑦)𝑑𝑦 𝑐)𝑍𝑚)𝜇(𝑦)𝑑𝑦 X cana-1744 107 11 ( ( PUNCT cana-1744 107 12 32 32 NUM cana-1744 107 13 ) ) PUNCT cana-1744 107 14 ( ( PUNCT cana-1744 107 15 𝑐 𝑐 NOUN cana-1744 107 16 + + NOUN cana-1744 107 17 λ λ PROPN cana-1744 107 18 × × NOUN cana-1744 107 19 ( ( PUNCT cana-1744 107 20 1 1 NUM cana-1744 107 21 + + CCONJ cana-1744 107 22 δ δ NOUN cana-1744 107 23 ) ) PUNCT cana-1744 108 1 + + CCONJ cana-1744 108 2 𝜒)(𝑃0 𝜒)(𝑃0 ADJ cana-1744 108 3 ∗(𝑐 ∗(𝑐 PROPN cana-1744 108 4 , , PUNCT cana-1744 108 5 𝑍 𝑍 PROPN cana-1744 108 6 ) ) PUNCT cana-1744 108 7 − − PROPN cana-1744 108 8 𝑃00 𝑃00 PROPN cana-1744 108 9 ∗ ∗ NOUN cana-1744 108 10 ( ( PUNCT cana-1744 108 11 𝑐 𝑐 NOUN cana-1744 108 12 ) ) PUNCT cana-1744 108 13 ) ) PUNCT cana-1744 109 1 = = SYM cana-1744 109 2 ∫ ∫ PROPN cana-1744 109 3 0 0 NUM cana-1744 110 1 ∞ ∞ NUM cana-1744 110 2     SPACE cana-1744 110 3 ( ( PUNCT cana-1744 110 4 𝜔∗(𝑦 𝜔∗(𝑦 PROPN cana-1744 110 5 , , PUNCT cana-1744 110 6 𝑐 𝑐 NOUN cana-1744 110 7 , , PUNCT cana-1744 110 8 𝑍 𝑍 PROPN cana-1744 110 9 ) ) PUNCT cana-1744 110 10 − − PROPN cana-1744 110 11 𝑃01 𝑃01 PROPN cana-1744 110 12 ∗ ∗ X cana-1744 110 13 ( ( PUNCT cana-1744 110 14 𝑦 𝑦 NOUN cana-1744 110 15 , , PUNCT cana-1744 110 16 𝑐))𝜇(𝑦)𝑑𝑦 𝑐))𝜇(𝑦)𝑑𝑦 NOUN cana-1744 110 17 ( ( PUNCT cana-1744 110 18 33 33 NUM cana-1744 110 19 ) ) PUNCT cana-1744 110 20 substitute substitute NOUN cana-1744 110 21 the the DET cana-1744 110 22 above above ADJ cana-1744 110 23 equations equation NOUN cana-1744 110 24 ( ( PUNCT cana-1744 110 25 15 15 NUM cana-1744 110 26 ) ) PUNCT cana-1744 110 27 and and CCONJ cana-1744 110 28 ( ( PUNCT cana-1744 110 29 29 29 NUM cana-1744 110 30 ) ) PUNCT cana-1744 110 31 in in ADP cana-1744 110 32 ( ( PUNCT cana-1744 110 33 33 33 NUM cana-1744 110 34 ) ) PUNCT cana-1744 110 35 , , PUNCT cana-1744 110 36 we we PRON cana-1744 110 37 obtain obtain VERB cana-1744 110 38 ( ( PUNCT cana-1744 110 39 𝑐 𝑐 NOUN cana-1744 110 40 + + NOUN cana-1744 110 41 λ λ PROPN cana-1744 110 42 × × NOUN cana-1744 110 43 ( ( PUNCT cana-1744 110 44 1 1 NUM cana-1744 110 45 + + CCONJ cana-1744 110 46 δ δ X cana-1744 110 47 ) ) PUNCT cana-1744 111 1 + + NUM cana-1744 111 2 𝜒)𝑃0 𝜒)𝑃0 NOUN cana-1744 111 3 ∗(𝑐 ∗(𝑐 PROPN cana-1744 111 4 , , PUNCT cana-1744 111 5 𝑍 𝑍 PROPN cana-1744 111 6 ) ) PUNCT cana-1744 111 7 = = SYM cana-1744 111 8 1 1 NUM cana-1744 111 9 + + NUM cana-1744 111 10 𝜎𝑃00 𝜎𝑃00 ADP cana-1744 111 11 ∗ ∗ NOUN cana-1744 111 12 ( ( PUNCT cana-1744 111 13 𝑐 𝑐 NOUN cana-1744 111 14 ) ) PUNCT cana-1744 111 15 + + NUM cana-1744 111 16 𝜔∗(0 𝜔∗(0 NOUN cana-1744 111 17 , , PUNCT cana-1744 111 18 𝑐 𝑐 NOUN cana-1744 111 19 , , PUNCT cana-1744 111 20 𝑍)𝑏‾(𝑐 𝑍)𝑏‾(𝑐 NOUN cana-1744 111 21 + + PUNCT cana-1744 111 22 λ λ X cana-1744 111 23 × × NOUN cana-1744 111 24 ( ( PUNCT cana-1744 111 25 1 1 NUM cana-1744 111 26 + + CCONJ cana-1744 111 27 δ δ NOUN cana-1744 111 28 ) ) PUNCT cana-1744 111 29 − − PROPN cana-1744 112 1 λ λ INTJ cana-1744 112 2 × × NOUN cana-1744 112 3 ( ( PUNCT cana-1744 112 4 1 1 NUM cana-1744 112 5 + + CCONJ cana-1744 112 6 δ δ PROPN cana-1744 112 7 ) ) PUNCT cana-1744 112 8 ∗ ∗ NOUN cana-1744 112 9 𝑍 𝑍 PROPN cana-1744 112 10 ) ) PUNCT cana-1744 112 11 ( ( PUNCT cana-1744 112 12 34 34 NUM cana-1744 112 13 ) ) PUNCT cana-1744 112 14 substitute substitute NOUN cana-1744 112 15 the the DET cana-1744 112 16 above above ADJ cana-1744 112 17 equation equation NOUN cana-1744 112 18 ( ( PUNCT cana-1744 112 19 26 26 NUM cana-1744 112 20 ) ) PUNCT cana-1744 112 21 in in ADP cana-1744 112 22 ( ( PUNCT cana-1744 112 23 34 34 NUM cana-1744 112 24 ) ) PUNCT cana-1744 112 25 , , PUNCT cana-1744 112 26 we we PRON cana-1744 112 27 have have VERB cana-1744 112 28 ( ( PUNCT cana-1744 112 29 𝑐 𝑐 NOUN cana-1744 112 30 + + NOUN cana-1744 112 31 λ λ PROPN cana-1744 112 32 × × NOUN cana-1744 112 33 ( ( PUNCT cana-1744 112 34 1 1 NUM cana-1744 112 35 + + CCONJ cana-1744 112 36 δ δ X cana-1744 112 37 ) ) PUNCT cana-1744 113 1 + + NUM cana-1744 113 2 𝜒)𝑃0 𝜒)𝑃0 NOUN cana-1744 113 3 ∗(𝑐 ∗(𝑐 PROPN cana-1744 113 4 , , PUNCT cana-1744 113 5 𝑍 𝑍 PROPN cana-1744 113 6 ) ) PUNCT cana-1744 113 7 = = SYM cana-1744 113 8 1 1 NUM cana-1744 113 9 + + NUM cana-1744 113 10 𝜒𝑃00 𝜒𝑃00 NOUN cana-1744 113 11 ∗ ∗ NOUN cana-1744 113 12 ( ( PUNCT cana-1744 113 13 𝑐 𝑐 NOUN cana-1744 113 14 ) ) PUNCT cana-1744 113 15 + + CCONJ cana-1744 114 1 [ [ X cana-1744 114 2 ( ( PUNCT cana-1744 114 3 λ λ INTJ cana-1744 114 4 × × NOUN cana-1744 114 5 ( ( PUNCT cana-1744 114 6 1 1 NUM cana-1744 114 7 + + CCONJ cana-1744 114 8 δ δ NOUN cana-1744 114 9 ) ) PUNCT cana-1744 115 1 + + CCONJ cana-1744 115 2 𝜎 𝜎 ADJ cana-1744 115 3 𝑍 𝑍 PROPN cana-1744 115 4 ) ) PUNCT cana-1744 115 5 𝑃0 𝑃0 NOUN cana-1744 115 6 ∗(𝑐 ∗(𝑐 PROPN cana-1744 115 7 , , PUNCT cana-1744 115 8 𝑍 𝑍 PROPN cana-1744 115 9 ) ) PUNCT cana-1744 115 10 − − NOUN cana-1744 115 11 𝜎 𝜎 PROPN cana-1744 115 12 𝑍 𝑍 PROPN cana-1744 115 13 𝑃00 𝑃00 PROPN cana-1744 115 14 ∗ ∗ NOUN cana-1744 115 15 ( ( PUNCT cana-1744 115 16 𝑐 𝑐 NOUN cana-1744 115 17 ) ) PUNCT cana-1744 115 18 ] ] PUNCT cana-1744 116 1 𝑎‾ 𝑎‾ PROPN cana-1744 116 2 + + PUNCT cana-1744 116 3 λ λ X cana-1744 116 4 × × NOUN cana-1744 116 5 ( ( PUNCT cana-1744 116 6 1 1 NUM cana-1744 116 7 + + CCONJ cana-1744 116 8 δ δ NOUN cana-1744 116 9 ) ) PUNCT cana-1744 117 1 − − PROPN cana-1744 118 1 λ λ INTJ cana-1744 118 2 × × NOUN cana-1744 118 3 ( ( PUNCT cana-1744 118 4 1 1 NUM cana-1744 118 5 + + CCONJ cana-1744 118 6 δ δ PROPN cana-1744 118 7 ) ) PUNCT cana-1744 118 8 ∗ ∗ NOUN cana-1744 118 9 𝑍 𝑍 PROPN cana-1744 118 10 ) ) PUNCT cana-1744 118 11 ( ( PUNCT cana-1744 118 12 35 35 NUM cana-1744 118 13 ) ) PUNCT cana-1744 118 14 𝑃0 𝑃0 NOUN cana-1744 118 15 ∗(𝑐 ∗(𝑐 PROPN cana-1744 118 16 , , PUNCT cana-1744 118 17 𝑍 𝑍 PROPN cana-1744 118 18 ) ) PUNCT cana-1744 118 19 = = SYM cana-1744 118 20 1 1 NUM cana-1744 118 21 + + NUM cana-1744 118 22 𝜒𝑃00 𝜒𝑃00 NOUN cana-1744 118 23 ∗ ∗ NOUN cana-1744 118 24 ( ( PUNCT cana-1744 118 25 𝑐 𝑐 NOUN cana-1744 118 26 ) ) PUNCT cana-1744 118 27 − − NOUN cana-1744 118 28 𝜒 𝜒 SYM cana-1744 118 29 𝑍 𝑍 PROPN cana-1744 118 30 𝑃00 𝑃00 PROPN cana-1744 118 31 ∗ ∗ NOUN cana-1744 118 32 ( ( PUNCT cana-1744 118 33 𝑐)𝑎‾(𝑐 𝑐)𝑎‾(𝑐 NOUN cana-1744 118 34 + + CCONJ cana-1744 118 35 λ λ X cana-1744 118 36 × × NOUN cana-1744 118 37 ( ( PUNCT cana-1744 118 38 1 1 NUM cana-1744 118 39 + + CCONJ cana-1744 118 40 δ δ NOUN cana-1744 118 41 ) ) PUNCT cana-1744 118 42 − − PROPN cana-1744 119 1 λ λ INTJ cana-1744 119 2 × × NOUN cana-1744 119 3 ( ( PUNCT cana-1744 119 4 1 1 NUM cana-1744 119 5 + + CCONJ cana-1744 119 6 δ δ PROPN cana-1744 119 7 ) ) PUNCT cana-1744 119 8 ∗ ∗ NOUN cana-1744 119 9 𝑍 𝑍 PROPN cana-1744 119 10 ) ) PUNCT cana-1744 119 11 ( ( PUNCT cana-1744 119 12 𝑐 𝑐 PROPN cana-1744 119 13 + + NOUN cana-1744 119 14 λ λ PROPN cana-1744 119 15 × × NOUN cana-1744 119 16 ( ( PUNCT cana-1744 119 17 1 1 NUM cana-1744 119 18 + + CCONJ cana-1744 119 19 δ δ NOUN cana-1744 119 20 ) ) PUNCT cana-1744 119 21 + + SYM cana-1744 119 22 𝜒 𝜒 X cana-1744 119 23 ) ) PUNCT cana-1744 119 24 − − PROPN cana-1744 119 25 ( ( PUNCT cana-1744 119 26 λ λ INTJ cana-1744 119 27 × × NOUN cana-1744 119 28 ( ( PUNCT cana-1744 119 29 1 1 NUM cana-1744 119 30 + + CCONJ cana-1744 119 31 δ δ NOUN cana-1744 119 32 ) ) PUNCT cana-1744 120 1 + + CCONJ cana-1744 121 1 𝜒 𝜒 X cana-1744 121 2 𝑍)𝑎‾(𝑐 𝑍)𝑎‾(𝑐 NOUN cana-1744 121 3 + + NUM cana-1744 121 4 λ λ X cana-1744 121 5 × × NOUN cana-1744 121 6 ( ( PUNCT cana-1744 121 7 1 1 NUM cana-1744 121 8 + + CCONJ cana-1744 121 9 δ δ NOUN cana-1744 121 10 ) ) PUNCT cana-1744 121 11 − − PROPN cana-1744 122 1 λ λ INTJ cana-1744 122 2 × × NOUN cana-1744 122 3 ( ( PUNCT cana-1744 122 4 1 1 NUM cana-1744 122 5 + + CCONJ cana-1744 122 6 δ δ PROPN cana-1744 122 7 ) ) PUNCT cana-1744 122 8 ∗ ∗ NOUN cana-1744 122 9 𝑍 𝑍 PROPN cana-1744 122 10 ) ) PUNCT cana-1744 122 11 ( ( PUNCT cana-1744 122 12 36 36 NUM cana-1744 122 13 ) ) PUNCT cana-1744 122 14 communications communication NOUN cana-1744 122 15 on on ADP cana-1744 122 16 applied apply VERB cana-1744 122 17 nonlinear nonlinear ADJ cana-1744 122 18 analysis analysis NOUN cana-1744 122 19 issn issn NOUN cana-1744 122 20 : : PUNCT cana-1744 122 21 1074 1074 NUM cana-1744 122 22 - - PUNCT cana-1744 122 23 133x 133x NUM cana-1744 122 24 vol vol NOUN cana-1744 122 25 32 32 NUM cana-1744 122 26 no no NOUN cana-1744 122 27 . . NOUN cana-1744 122 28 2 2 NUM cana-1744 122 29 ( ( PUNCT cana-1744 122 30 2025 2025 NUM cana-1744 122 31 ) ) PUNCT cana-1744 122 32 310 310 NUM cana-1744 122 33 https://internationalpubls.com https://internationalpubls.com X cana-1744 122 34 in in ADP cana-1744 122 35 equation equation NOUN cana-1744 122 36 ( ( PUNCT cana-1744 122 37 36 36 NUM cana-1744 122 38 ) ) PUNCT cana-1744 122 39 means mean VERB cana-1744 122 40 transitory transitory ADJ cana-1744 122 41 results result NOUN cana-1744 122 42 of of ADP cana-1744 122 43 the the DET cana-1744 122 44 patrons patron NOUN cana-1744 122 45 in in ADP cana-1744 122 46 the the DET cana-1744 122 47 group group NOUN cana-1744 122 48 when when SCONJ cana-1744 122 49 the the DET cana-1744 122 50 server server NOUN cana-1744 122 51 is be AUX cana-1744 122 52 free free ADJ cana-1744 122 53 in in ADP cana-1744 122 54 the the DET cana-1744 122 55 system system NOUN cana-1744 122 56 . . PUNCT cana-1744 123 1 𝑃1 𝑃1 NOUN cana-1744 123 2 ∗(𝑐 ∗(𝑐 PROPN cana-1744 123 3 , , PUNCT cana-1744 123 4 𝑍 𝑍 PROPN cana-1744 123 5 ) ) PUNCT cana-1744 123 6 = = SYM cana-1744 123 7 ( ( PUNCT cana-1744 123 8 λ λ INTJ cana-1744 123 9 × × NOUN cana-1744 123 10 ( ( PUNCT cana-1744 123 11 1 1 NUM cana-1744 123 12 + + CCONJ cana-1744 123 13 δ δ NOUN cana-1744 123 14 ) ) PUNCT cana-1744 124 1 + + CCONJ cana-1744 124 2 𝜎 𝜎 ADJ cana-1744 124 3 𝑍 𝑍 NOUN cana-1744 124 4 ) ) PUNCT cana-1744 124 5 ( ( PUNCT cana-1744 124 6 1 1 NUM cana-1744 124 7 + + NUM cana-1744 124 8 𝜒𝑃00 𝜒𝑃00 NOUN cana-1744 124 9 ∗ ∗ NOUN cana-1744 124 10 ( ( PUNCT cana-1744 124 11 𝑐 𝑐 NOUN cana-1744 124 12 ) ) PUNCT cana-1744 124 13 − − NOUN cana-1744 124 14 𝜒 𝜒 SYM cana-1744 124 15 𝑍 𝑍 PROPN cana-1744 124 16 𝑃00 𝑃00 PROPN cana-1744 124 17 ∗ ∗ NOUN cana-1744 124 18 ( ( PUNCT cana-1744 124 19 𝑐)𝑎‾(𝑐 𝑐)𝑎‾(𝑐 NOUN cana-1744 124 20 + + CCONJ cana-1744 124 21 λ λ X cana-1744 124 22 × × NOUN cana-1744 124 23 ( ( PUNCT cana-1744 124 24 1 1 NUM cana-1744 124 25 + + CCONJ cana-1744 124 26 δ δ NOUN cana-1744 124 27 ) ) PUNCT cana-1744 124 28 − − PROPN cana-1744 125 1 λ λ INTJ cana-1744 125 2 × × NOUN cana-1744 125 3 ( ( PUNCT cana-1744 125 4 1 1 NUM cana-1744 125 5 + + CCONJ cana-1744 125 6 δ δ PROPN cana-1744 125 7 ) ) PUNCT cana-1744 125 8 ∗ ∗ NOUN cana-1744 125 9 𝑍 𝑍 PROPN cana-1744 125 10 ) ) PUNCT cana-1744 125 11 ( ( PUNCT cana-1744 125 12 𝑐 𝑐 PROPN cana-1744 125 13 + + NOUN cana-1744 125 14 λ λ PROPN cana-1744 125 15 × × NOUN cana-1744 125 16 ( ( PUNCT cana-1744 125 17 1 1 NUM cana-1744 125 18 + + CCONJ cana-1744 125 19 δ δ NOUN cana-1744 125 20 ) ) PUNCT cana-1744 125 21 + + SYM cana-1744 125 22 𝜒 𝜒 X cana-1744 125 23 ) ) PUNCT cana-1744 125 24 − − PROPN cana-1744 125 25 ( ( PUNCT cana-1744 125 26 λ λ INTJ cana-1744 125 27 × × NOUN cana-1744 125 28 ( ( PUNCT cana-1744 125 29 1 1 NUM cana-1744 125 30 + + CCONJ cana-1744 125 31 δ δ NOUN cana-1744 125 32 ) ) PUNCT cana-1744 126 1 + + CCONJ cana-1744 126 2 𝜒 𝜒 NUM cana-1744 126 3 𝑍 𝑍 NOUN cana-1744 126 4 ) ) PUNCT cana-1744 126 5 𝑎‾(𝑐 𝑎‾(𝑐 NOUN cana-1744 126 6 + + NOUN cana-1744 126 7 λ λ X cana-1744 126 8 × × NOUN cana-1744 126 9 ( ( PUNCT cana-1744 126 10 1 1 NUM cana-1744 126 11 + + CCONJ cana-1744 126 12 δ δ NOUN cana-1744 126 13 ) ) PUNCT cana-1744 126 14 − − PROPN cana-1744 127 1 λ λ INTJ cana-1744 127 2 × × NOUN cana-1744 127 3 ( ( PUNCT cana-1744 127 4 1 1 NUM cana-1744 127 5 + + CCONJ cana-1744 127 6 δ δ PROPN cana-1744 127 7 ) ) PUNCT cana-1744 127 8 ∗ ∗ NOUN cana-1744 127 9 𝑍 𝑍 PROPN cana-1744 127 10 ) ) PUNCT cana-1744 127 11 ) ) PUNCT cana-1744 128 1 − − PROPN cana-1744 129 1 𝜎 𝜎 PROPN cana-1744 129 2 𝑍 𝑍 PROPN cana-1744 129 3 𝑃00 𝑃00 PROPN cana-1744 129 4 ∗ ∗ NOUN cana-1744 129 5 𝑐 𝑐 PROPN cana-1744 130 1 + + CCONJ cana-1744 130 2 λ λ X cana-1744 130 3 × × NOUN cana-1744 130 4 ( ( PUNCT cana-1744 130 5 1 1 NUM cana-1744 130 6 + + CCONJ cana-1744 130 7 δ δ NOUN cana-1744 130 8 ) ) PUNCT cana-1744 130 9 − − PROPN cana-1744 131 1 λ λ INTJ cana-1744 131 2 × × NOUN cana-1744 131 3 ( ( PUNCT cana-1744 131 4 1 1 NUM cana-1744 131 5 + + CCONJ cana-1744 131 6 δ δ PROPN cana-1744 131 7 ) ) PUNCT cana-1744 131 8 ∗ ∗ NOUN cana-1744 131 9 𝑍 𝑍 PROPN cana-1744 131 10 ( ( PUNCT cana-1744 131 11 −𝑎‾(𝑐 −𝑎‾(𝑐 NOUN cana-1744 131 12 + + CCONJ cana-1744 131 13 λ λ X cana-1744 131 14 × × NOUN cana-1744 131 15 ( ( PUNCT cana-1744 131 16 1 1 NUM cana-1744 131 17 + + CCONJ cana-1744 131 18 δ δ NOUN cana-1744 131 19 ) ) PUNCT cana-1744 131 20 − − PROPN cana-1744 132 1 λ λ INTJ cana-1744 132 2 × × NOUN cana-1744 132 3 ( ( PUNCT cana-1744 132 4 1 1 NUM cana-1744 132 5 + + CCONJ cana-1744 132 6 δ δ PROPN cana-1744 132 7 ) ) PUNCT cana-1744 132 8 ∗ ∗ NOUN cana-1744 132 9 𝑍 𝑍 PROPN cana-1744 132 10 ) ) PUNCT cana-1744 132 11 ) ) PUNCT cana-1744 132 12 ( ( PUNCT cana-1744 132 13 37 37 NUM cana-1744 132 14 ) ) PUNCT cana-1744 132 15 in in ADP cana-1744 132 16 equation equation NOUN cana-1744 132 17 ( ( PUNCT cana-1744 132 18 37 37 NUM cana-1744 132 19 ) ) PUNCT cana-1744 132 20 means mean VERB cana-1744 132 21 transitory transitory ADJ cana-1744 132 22 results result NOUN cana-1744 132 23 of of ADP cana-1744 132 24 the the DET cana-1744 132 25 patrons patron NOUN cana-1744 132 26 in in ADP cana-1744 132 27 the the DET cana-1744 132 28 group group NOUN cana-1744 132 29 when when SCONJ cana-1744 132 30 the the DET cana-1744 132 31 server server NOUN cana-1744 132 32 is be AUX cana-1744 132 33 engaged engage VERB cana-1744 132 34 in in ADP cana-1744 132 35 the the DET cana-1744 132 36 system system NOUN cana-1744 132 37 . . PUNCT cana-1744 133 1 using use VERB cana-1744 133 2 the the DET cana-1744 133 3 tauberian tauberian ADJ cana-1744 133 4 theorem theorem NOUN cana-1744 133 5 with with ADP cana-1744 133 6 lt lt DET cana-1744 133 7 equation equation NOUN cana-1744 133 8 ( ( PUNCT cana-1744 133 9 35 35 NUM cana-1744 133 10 ) ) PUNCT cana-1744 133 11 , , PUNCT cana-1744 133 12 we we PRON cana-1744 133 13 obtain obtain VERB cana-1744 133 14 ( ( PUNCT cana-1744 133 15 λ λ INTJ cana-1744 133 16 × × NOUN cana-1744 133 17 ( ( PUNCT cana-1744 133 18 1 1 NUM cana-1744 133 19 + + CCONJ cana-1744 133 20 δ δ NOUN cana-1744 133 21 ) ) PUNCT cana-1744 134 1 + + CCONJ cana-1744 134 2 𝜒)𝑃0(𝑍 𝜒)𝑃0(𝑍 ADV cana-1744 134 3 ) ) PUNCT cana-1744 134 4 = = PUNCT cana-1744 135 1 𝜎𝑃00 𝜎𝑃00 ADP cana-1744 135 2 + + PUNCT cana-1744 136 1 [ [ X cana-1744 136 2 ( ( PUNCT cana-1744 136 3 λ λ INTJ cana-1744 136 4 × × NOUN cana-1744 136 5 ( ( PUNCT cana-1744 136 6 1 1 NUM cana-1744 136 7 + + CCONJ cana-1744 136 8 δ δ NOUN cana-1744 136 9 ) ) PUNCT cana-1744 137 1 + + CCONJ cana-1744 137 2 𝜒 𝜒 NUM cana-1744 137 3 𝑍 𝑍 NOUN cana-1744 137 4 ) ) PUNCT cana-1744 137 5 𝑃0(𝑍 𝑃0(𝑍 NOUN cana-1744 137 6 ) ) PUNCT cana-1744 137 7 − − ADP cana-1744 137 8 𝜒 𝜒 SYM cana-1744 137 9 𝑍 𝑍 PROPN cana-1744 137 10 𝑃00 𝑃00 NOUN cana-1744 137 11 ] ] PUNCT cana-1744 137 12 𝑎‾(λ 𝑎‾(λ PROPN cana-1744 137 13 × × NOUN cana-1744 137 14 ( ( PUNCT cana-1744 137 15 1 1 NUM cana-1744 137 16 + + NUM cana-1744 137 17 δ δ NOUN cana-1744 137 18 ) ) PUNCT cana-1744 137 19 − − PROPN cana-1744 138 1 λ λ INTJ cana-1744 138 2 × × NOUN cana-1744 138 3 ( ( PUNCT cana-1744 138 4 1 1 NUM cana-1744 138 5 + + CCONJ cana-1744 138 6 δ δ PROPN cana-1744 138 7 ) ) PUNCT cana-1744 138 8 ∗ ∗ NOUN cana-1744 138 9 𝑍 𝑍 PROPN cana-1744 138 10 ) ) PUNCT cana-1744 138 11 ( ( PUNCT cana-1744 138 12 38 38 NUM cana-1744 138 13 ) ) PUNCT cana-1744 138 14 solving solve VERB cana-1744 138 15 the the DET cana-1744 138 16 equation equation NOUN cana-1744 138 17 ( ( PUNCT cana-1744 138 18 38 38 NUM cana-1744 138 19 ) ) PUNCT cana-1744 138 20 , , PUNCT cana-1744 138 21 we we PRON cana-1744 138 22 obtain obtain VERB cana-1744 138 23 𝑃0(𝑍 𝑃0(𝑍 PRON cana-1744 138 24 ) ) PUNCT cana-1744 138 25 = = SYM cana-1744 138 26 𝜒𝑝00(𝑍−𝑎‾ 𝜒𝑝00(𝑍−𝑎‾ PROPN cana-1744 138 27 ) ) PUNCT cana-1744 138 28 𝑍(λ×(1+δ)+𝜒)−(𝜒+λ×(1+δ)𝑍)𝑎‾ 𝑍(λ×(1+δ)+𝜒)−(𝜒+λ×(1+δ)𝑍)𝑎‾ PROPN cana-1744 138 29 ( ( PUNCT cana-1744 138 30 39 39 NUM cana-1744 138 31 ) ) PUNCT cana-1744 138 32 𝑃0(𝑍 𝑃0(𝑍 NOUN cana-1744 138 33 ) ) PUNCT cana-1744 138 34 = = VERB cana-1744 138 35 𝑝00 𝑝00 NOUN cana-1744 138 36 1− 1− NUM cana-1744 138 37 ( ( PUNCT cana-1744 138 38 λ×(1+δ)𝑍 λ×(1+δ)𝑍 NUM cana-1744 138 39 𝜒 𝜒 X cana-1744 138 40 ) ) PUNCT cana-1744 138 41 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 138 42 ) ) PUNCT cana-1744 138 43 where where SCONJ cana-1744 138 44 𝛿(𝑍 𝛿(𝑍 NOUN cana-1744 138 45 ) ) PUNCT cana-1744 139 1 = = PRON cana-1744 139 2 1−𝑎‾ 1−𝑎‾ NUM cana-1744 139 3 𝑎−𝑍̅̅ 𝑎−𝑍̅̅ PRON cana-1744 139 4 ̅̅ ̅̅ PROPN cana-1744 139 5 ̅̅ ̅̅ PROPN cana-1744 139 6 ( ( PUNCT cana-1744 139 7 40 40 NUM cana-1744 139 8 ) ) PUNCT cana-1744 139 9 in in ADP cana-1744 139 10 equation equation NOUN cana-1744 139 11 ( ( PUNCT cana-1744 139 12 40 40 NUM cana-1744 139 13 ) ) PUNCT cana-1744 139 14 means mean VERB cana-1744 139 15 steady steady ADJ cana-1744 139 16 - - PUNCT cana-1744 139 17 state state NOUN cana-1744 139 18 probability probability NOUN cana-1744 139 19 of of ADP cana-1744 139 20 patrons patron NOUN cana-1744 139 21 in in ADP cana-1744 139 22 the the DET cana-1744 139 23 group group NOUN cana-1744 139 24 when when SCONJ cana-1744 139 25 the the DET cana-1744 139 26 system system NOUN cana-1744 139 27 server server NOUN cana-1744 139 28 is be AUX cana-1744 139 29 free free ADJ cana-1744 139 30 . . PUNCT cana-1744 140 1 using use VERB cana-1744 140 2 the the DET cana-1744 140 3 tauberian tauberian ADJ cana-1744 140 4 theorem theorem NOUN cana-1744 140 5 with with ADP cana-1744 140 6 lt lt DET cana-1744 140 7 equation equation NOUN cana-1744 140 8 ( ( PUNCT cana-1744 140 9 31 31 NUM cana-1744 140 10 ) ) PUNCT cana-1744 140 11 , , PUNCT cana-1744 140 12 we we PRON cana-1744 140 13 obtain obtain VERB cana-1744 140 14 𝑃1(𝑍 𝑃1(𝑍 PROPN cana-1744 140 15 ) ) PUNCT cana-1744 140 16 = = PUNCT cana-1744 141 1 ( ( PUNCT cana-1744 141 2 λ λ INTJ cana-1744 141 3 × × NOUN cana-1744 141 4 ( ( PUNCT cana-1744 141 5 1 1 NUM cana-1744 141 6 + + CCONJ cana-1744 141 7 δ δ NOUN cana-1744 141 8 ) ) PUNCT cana-1744 142 1 + + NUM cana-1744 142 2 𝜒 𝜒 X cana-1744 142 3 𝑍)𝑃0 𝑍)𝑃0 NUM cana-1744 142 4 ( ( PUNCT cana-1744 142 5 𝑍 𝑍 PROPN cana-1744 142 6 ) ) PUNCT cana-1744 142 7 − − NOUN cana-1744 142 8 𝜒 𝜒 SYM cana-1744 142 9 𝑍 𝑍 PROPN cana-1744 142 10 𝑃00 𝑃00 PROPN cana-1744 142 11 λ λ PROPN cana-1744 142 12 × × NOUN cana-1744 142 13 ( ( PUNCT cana-1744 142 14 1 1 NUM cana-1744 142 15 + + CCONJ cana-1744 142 16 δ δ NOUN cana-1744 142 17 ) ) PUNCT cana-1744 142 18 − − PROPN cana-1744 143 1 λ λ INTJ cana-1744 143 2 × × NOUN cana-1744 143 3 ( ( PUNCT cana-1744 143 4 1 1 NUM cana-1744 143 5 + + CCONJ cana-1744 143 6 δ δ PROPN cana-1744 143 7 ) ) PUNCT cana-1744 143 8 ∗ ∗ NOUN cana-1744 143 9 𝑍 𝑍 NOUN cana-1744 143 10 ( ( PUNCT cana-1744 143 11 1 1 NUM cana-1744 143 12 − − NOUN cana-1744 143 13 𝑎‾(λ 𝑎‾(λ PROPN cana-1744 143 14 × × NOUN cana-1744 143 15 ( ( PUNCT cana-1744 143 16 1 1 NUM cana-1744 143 17 + + NUM cana-1744 143 18 δ δ NOUN cana-1744 143 19 ) ) PUNCT cana-1744 143 20 − − PROPN cana-1744 144 1 λ λ INTJ cana-1744 144 2 × × NOUN cana-1744 144 3 ( ( PUNCT cana-1744 144 4 1 1 NUM cana-1744 144 5 + + CCONJ cana-1744 144 6 δ δ PROPN cana-1744 144 7 ) ) PUNCT cana-1744 144 8 ∗ ∗ NOUN cana-1744 144 9 𝑍 𝑍 PROPN cana-1744 144 10 ) ) PUNCT cana-1744 144 11 ) ) PUNCT cana-1744 145 1 ( ( PUNCT cana-1744 145 2 41 41 NUM cana-1744 145 3 ) ) PUNCT cana-1744 145 4 substitute substitute NOUN cana-1744 145 5 the the DET cana-1744 145 6 equation equation NOUN cana-1744 145 7 ( ( PUNCT cana-1744 145 8 40 40 NUM cana-1744 145 9 ) ) PUNCT cana-1744 145 10 in in ADP cana-1744 145 11 ( ( PUNCT cana-1744 145 12 41 41 NUM cana-1744 145 13 ) ) PUNCT cana-1744 145 14 , , PUNCT cana-1744 145 15 we we PRON cana-1744 145 16 obtain obtain VERB cana-1744 145 17 𝑃1(𝑍 𝑃1(𝑍 PROPN cana-1744 145 18 ) ) PUNCT cana-1744 145 19 = = SYM cana-1744 145 20 𝑃00 𝑃00 PROPN cana-1744 145 21 ( ( PUNCT cana-1744 145 22 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 145 23 ) ) PUNCT cana-1744 145 24 1 1 NUM cana-1744 145 25 − − PROPN cana-1744 145 26 ( ( PUNCT cana-1744 145 27 λ λ INTJ cana-1744 145 28 × × NOUN cana-1744 145 29 ( ( PUNCT cana-1744 145 30 1 1 NUM cana-1744 145 31 + + CCONJ cana-1744 145 32 δ)𝑍 δ)𝑍 VERB cana-1744 145 33 𝜒 𝜒 X cana-1744 145 34 ) ) PUNCT cana-1744 145 35 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 145 36 ) ) PUNCT cana-1744 145 37 ) ) PUNCT cana-1744 145 38 ( ( PUNCT cana-1744 145 39 42 42 NUM cana-1744 145 40 ) ) PUNCT cana-1744 145 41 in in ADP cana-1744 145 42 equation equation NOUN cana-1744 145 43 ( ( PUNCT cana-1744 145 44 42 42 NUM cana-1744 145 45 ) ) PUNCT cana-1744 145 46 means mean VERB cana-1744 145 47 steady steady ADJ cana-1744 145 48 - - PUNCT cana-1744 145 49 state state NOUN cana-1744 145 50 probability probability NOUN cana-1744 145 51 of of ADP cana-1744 145 52 patrons patron NOUN cana-1744 145 53 in in ADP cana-1744 145 54 the the DET cana-1744 145 55 group group NOUN cana-1744 145 56 when when SCONJ cana-1744 145 57 the the DET cana-1744 145 58 system system NOUN cana-1744 145 59 server server NOUN cana-1744 145 60 is be AUX cana-1744 145 61 free free ADJ cana-1744 145 62 . . PUNCT cana-1744 146 1 the the DET cana-1744 146 2 normalized normalize VERB cana-1744 146 3 state state NOUN cana-1744 146 4 is be AUX cana-1744 146 5 𝑃0(1 𝑃0(1 NUM cana-1744 146 6 ) ) PUNCT cana-1744 147 1 + + CCONJ cana-1744 147 2 𝑃1(1 𝑃1(1 X cana-1744 147 3 ) ) PUNCT cana-1744 147 4 = = SYM cana-1744 147 5 1 1 NUM cana-1744 147 6 ( ( PUNCT cana-1744 147 7 43 43 NUM cana-1744 147 8 ) ) PUNCT cana-1744 147 9 𝛿(1 𝛿(1 PROPN cana-1744 147 10 ) ) PUNCT cana-1744 147 11 = = SYM cana-1744 147 12 λ×(1+δ)𝐸(𝑌 λ×(1+δ)𝐸(𝑌 PROPN cana-1744 147 13 ) ) PUNCT cana-1744 147 14 1−λ×(1+δ)𝐸(𝑌 1−λ×(1+δ)𝐸(𝑌 NUM cana-1744 147 15 ) ) PUNCT cana-1744 147 16 = = PUNCT cana-1744 148 1 𝜌 𝜌 X cana-1744 148 2 1−𝜌 1−𝜌 NUM cana-1744 148 3 where where SCONJ cana-1744 148 4 λ×(1+δ λ×(1+δ NOUN cana-1744 148 5 ) ) PUNCT cana-1744 148 6 𝜇 𝜇 ADP cana-1744 148 7 = = X cana-1744 148 8 λ λ X cana-1744 148 9 × × NOUN cana-1744 148 10 ( ( PUNCT cana-1744 148 11 1 1 NUM cana-1744 148 12 + + NUM cana-1744 148 13 δ)𝐸(𝑌 δ)𝐸(𝑌 NOUN cana-1744 148 14 ) ) PUNCT cana-1744 148 15 ( ( PUNCT cana-1744 148 16 44 44 X cana-1744 148 17 ) ) PUNCT cana-1744 148 18 communications communication NOUN cana-1744 148 19 on on ADP cana-1744 148 20 applied apply VERB cana-1744 148 21 nonlinear nonlinear ADJ cana-1744 148 22 analysis analysis NOUN cana-1744 148 23 issn issn NOUN cana-1744 148 24 : : PUNCT cana-1744 148 25 1074 1074 NUM cana-1744 148 26 - - PUNCT cana-1744 148 27 133x 133x NUM cana-1744 148 28 vol vol NOUN cana-1744 148 29 32 32 NUM cana-1744 148 30 no no NOUN cana-1744 148 31 . . NOUN cana-1744 148 32 2 2 NUM cana-1744 148 33 ( ( PUNCT cana-1744 148 34 2025 2025 NUM cana-1744 148 35 ) ) PUNCT cana-1744 148 36 311 311 NUM cana-1744 148 37 https://internationalpubls.com https://internationalpubls.com X cana-1744 148 38 𝛿(1 𝛿(1 PROPN cana-1744 148 39 ) ) PUNCT cana-1744 149 1 = = PUNCT cana-1744 149 2 ( ( PUNCT cana-1744 149 3 λ λ INTJ cana-1744 149 4 × × NOUN cana-1744 149 5 ( ( PUNCT cana-1744 149 6 1 1 NUM cana-1744 149 7 + + NUM cana-1744 149 8 δ))2𝐸(𝑌2 δ))2𝐸(𝑌2 NUM cana-1744 149 9 ) ) PUNCT cana-1744 149 10 2(1 2(1 NUM cana-1744 149 11 − − NOUN cana-1744 150 1 𝜌)2 𝜌)2 NOUN cana-1744 150 2 ( ( PUNCT cana-1744 150 3 45 45 NUM cana-1744 150 4 ) ) PUNCT cana-1744 150 5 𝑃0(1 𝑃0(1 NOUN cana-1744 150 6 ) ) PUNCT cana-1744 151 1 = = SYM cana-1744 151 2 lim𝑍→1 lim𝑍→1 PROPN cana-1744 151 3     SPACE cana-1744 151 4 𝑃0(𝑍 𝑃0(𝑍 PROPN cana-1744 151 5 ) ) PUNCT cana-1744 152 1 = = SYM cana-1744 152 2 lim𝑍→1 lim𝑍→1 PROPN cana-1744 152 3     SPACE cana-1744 152 4 𝑝00 𝑝00 VERB cana-1744 152 5 1 1 NUM cana-1744 152 6 − − PROPN cana-1744 152 7 ( ( PUNCT cana-1744 152 8 λ λ INTJ cana-1744 152 9 × × NOUN cana-1744 152 10 ( ( PUNCT cana-1744 152 11 1 1 NUM cana-1744 152 12 + + CCONJ cana-1744 152 13 δ)𝑍 δ)𝑍 VERB cana-1744 152 14 𝜒 𝜒 X cana-1744 152 15 ) ) PUNCT cana-1744 152 16 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 152 17 ) ) PUNCT cana-1744 153 1 = = SYM cana-1744 153 2 𝑃00 𝑃00 PROPN cana-1744 153 3 ( ( PUNCT cana-1744 153 4 1 1 NUM cana-1744 153 5 − − PROPN cana-1744 153 6 λ λ INTJ cana-1744 153 7 × × NOUN cana-1744 153 8 ( ( PUNCT cana-1744 153 9 1 1 NUM cana-1744 153 10 + + CCONJ cana-1744 153 11 δ)𝑍 δ)𝑍 VERB cana-1744 153 12 𝜒 𝜒 SYM cana-1744 153 13 1 1 NUM cana-1744 153 14 − − NOUN cana-1744 153 15 ( ( PUNCT cana-1744 153 16 λ λ INTJ cana-1744 153 17 × × NOUN cana-1744 153 18 ( ( PUNCT cana-1744 153 19 1 1 NUM cana-1744 153 20 + + CCONJ cana-1744 153 21 δ)𝑍 δ)𝑍 NOUN cana-1744 153 22 𝜒 𝜒 X cana-1744 153 23 ) ) PUNCT cana-1744 153 24 1 1 NUM cana-1744 153 25 ) ) PUNCT cana-1744 153 26 ( ( PUNCT cana-1744 153 27 46 46 NUM cana-1744 153 28 ) ) PUNCT cana-1744 153 29 𝑃1(1 𝑃1(1 ADJ cana-1744 153 30 ) ) PUNCT cana-1744 153 31 = = SYM cana-1744 153 32 lim𝑧→1 lim𝑧→1 PROPN cana-1744 153 33     SPACE cana-1744 153 34 𝑃1(𝑍 𝑃1(𝑍 PROPN cana-1744 153 35 ) ) PUNCT cana-1744 153 36 = = PUNCT cana-1744 153 37 lim𝑧→1 lim𝑧→1 PROPN cana-1744 153 38     SPACE cana-1744 153 39 𝑃00 𝑃00 PROPN cana-1744 153 40 ( ( PUNCT cana-1744 153 41 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 153 42 ) ) PUNCT cana-1744 153 43 1 1 NUM cana-1744 153 44 − − PROPN cana-1744 153 45 ( ( PUNCT cana-1744 153 46 λ λ INTJ cana-1744 153 47 × × NOUN cana-1744 153 48 ( ( PUNCT cana-1744 153 49 1 1 NUM cana-1744 153 50 + + CCONJ cana-1744 153 51 δ)𝑍 δ)𝑍 VERB cana-1744 153 52 𝜒 𝜒 X cana-1744 153 53 ) ) PUNCT cana-1744 153 54 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 153 55 ) ) PUNCT cana-1744 153 56 ) ) PUNCT cana-1744 154 1 = = SYM cana-1744 154 2 𝑃00 𝑃00 PROPN cana-1744 154 3 ( ( PUNCT cana-1744 154 4 λ λ PROPN cana-1744 154 5 × × NOUN cana-1744 154 6 ( ( PUNCT cana-1744 154 7 1 1 NUM cana-1744 154 8 + + CCONJ cana-1744 154 9 δ)𝑍 δ)𝑍 VERB cana-1744 154 10 𝜒 𝜒 SYM cana-1744 154 11 1 1 NUM cana-1744 154 12 − − PROPN cana-1744 154 13 𝜌1 𝜌1 NOUN cana-1744 154 14 ) ) PUNCT cana-1744 154 15 ( ( PUNCT cana-1744 154 16 47 47 NUM cana-1744 154 17 ) ) PUNCT cana-1744 154 18 substitute substitute VERB cana-1744 154 19 the the DET cana-1744 154 20 equations equation NOUN cana-1744 154 21 ( ( PUNCT cana-1744 154 22 46 46 NUM cana-1744 154 23 ) ) PUNCT cana-1744 154 24 and and CCONJ cana-1744 154 25 ( ( PUNCT cana-1744 154 26 47 47 NUM cana-1744 154 27 ) ) PUNCT cana-1744 154 28 in in ADP cana-1744 154 29 ( ( PUNCT cana-1744 154 30 43 43 NUM cana-1744 154 31 ) ) PUNCT cana-1744 154 32 , , PUNCT cana-1744 154 33 we we PRON cana-1744 154 34 obtain obtain VERB cana-1744 154 35 𝑃00 𝑃00 X cana-1744 154 36 = = SYM cana-1744 154 37 1 1 NUM cana-1744 154 38 − − PROPN cana-1744 154 39 ( ( PUNCT cana-1744 154 40 λ×(1+δ)𝑍 λ×(1+δ)𝑍 NUM cana-1744 154 41 𝜒 𝜒 X cana-1744 154 42 ) ) PUNCT cana-1744 154 43 1 1 NUM cana-1744 154 44 ( ( PUNCT cana-1744 154 45 48 48 NUM cana-1744 154 46 ) ) PUNCT cana-1744 154 47 theorem theorem NOUN cana-1744 154 48 2 2 NUM cana-1744 154 49 : : PUNCT cana-1744 154 50 the the DET cana-1744 154 51 performance performance NOUN cana-1744 154 52 metrics metric NOUN cana-1744 154 53 of of ADP cana-1744 154 54 the the DET cana-1744 154 55 single single ADJ cana-1744 154 56 server server NOUN cana-1744 154 57 markovian markovian PROPN cana-1744 154 58 general general PROPN cana-1744 154 59 encouraged encourage VERB cana-1744 154 60 arrival arrival NOUN cana-1744 154 61 retrial retrial ADJ cana-1744 154 62 queuing queuing NOUN cana-1744 154 63 system system NOUN cana-1744 154 64 under under ADP cana-1744 154 65 persistent persistent ADJ cana-1744 154 66 retrial retrial ADJ cana-1744 154 67 policy policy NOUN cana-1744 154 68 are be AUX cana-1744 154 69 provided provide VERB cana-1744 154 70 below below ADP cana-1744 154 71 a. a. NOUN cana-1744 154 72 the the DET cana-1744 154 73 probability probability NOUN cana-1744 154 74 of of ADP cana-1744 154 75 the the DET cana-1744 154 76 system system NOUN cana-1744 154 77 's 's PART cana-1744 154 78 server server NOUN cana-1744 154 79 being be AUX cana-1744 154 80 free free ADJ cana-1744 154 81 = = NOUN cana-1744 154 82 𝑃0 𝑃0 NOUN cana-1744 154 83 = = NOUN cana-1744 154 84 1 1 NUM cana-1744 154 85 − − PROPN cana-1744 155 1 λ λ INTJ cana-1744 155 2 × × NOUN cana-1744 155 3 ( ( PUNCT cana-1744 155 4 1 1 NUM cana-1744 155 5 + + CCONJ cana-1744 155 6 δ δ PROPN cana-1744 155 7 ) ) PUNCT cana-1744 155 8 µ µ X cana-1744 155 9 b. b. NOUN cana-1744 155 10 the the DET cana-1744 155 11 probability probability NOUN cana-1744 155 12 of of ADP cana-1744 155 13 the the DET cana-1744 155 14 system system NOUN cana-1744 155 15 's 's PART cana-1744 155 16 server server NOUN cana-1744 155 17 being be AUX cana-1744 155 18 engaged engage VERB cana-1744 155 19 = = VERB cana-1744 155 20 𝑃1 𝑃1 NOUN cana-1744 155 21 = = PUNCT cana-1744 155 22 λ λ X cana-1744 155 23 × × NOUN cana-1744 155 24 ( ( PUNCT cana-1744 155 25 1 1 NUM cana-1744 155 26 + + CCONJ cana-1744 155 27 δ δ PROPN cana-1744 155 28 ) ) PUNCT cana-1744 155 29 µ µ PROPN cana-1744 155 30 c. c. NOUN cana-1744 155 31 mean mean NOUN cana-1744 155 32 number number NOUN cana-1744 155 33 of of ADP cana-1744 155 34 patrons patron NOUN cana-1744 155 35 in in ADP cana-1744 155 36 the the DET cana-1744 155 37 group group NOUN cana-1744 155 38 l𝑞 l𝑞 VERB cana-1744 155 39 = = SYM cana-1744 155 40 1 1 NUM cana-1744 155 41 ( ( PUNCT cana-1744 155 42 1 1 NUM cana-1744 155 43 − − PROPN cana-1744 155 44 ( ( PUNCT cana-1744 155 45 λ λ INTJ cana-1744 155 46 × × NOUN cana-1744 155 47 ( ( PUNCT cana-1744 155 48 1 1 NUM cana-1744 155 49 + + CCONJ cana-1744 155 50 δ δ PROPN cana-1744 155 51 ) ) PUNCT cana-1744 155 52 µ µ X cana-1744 155 53 ) ) PUNCT cana-1744 155 54 1 1 NUM cana-1744 155 55 ) ) PUNCT cana-1744 155 56 ( ( PUNCT cana-1744 155 57 ( ( PUNCT cana-1744 155 58 λ λ INTJ cana-1744 155 59 × × NOUN cana-1744 155 60 ( ( PUNCT cana-1744 155 61 1 1 NUM cana-1744 155 62 + + NUM cana-1744 155 63 δ))2𝐸(𝑌2 δ))2𝐸(𝑌2 ADJ cana-1744 155 64 ) ) PUNCT cana-1744 155 65 2 2 NUM cana-1744 155 66 ( ( PUNCT cana-1744 155 67 1 1 NUM cana-1744 155 68 + + NUM cana-1744 155 69 λ λ PROPN cana-1744 155 70 × × NOUN cana-1744 155 71 ( ( PUNCT cana-1744 155 72 1 1 NUM cana-1744 155 73 + + CCONJ cana-1744 155 74 δ δ PROPN cana-1744 155 75 ) ) PUNCT cana-1744 155 76 𝜒 𝜒 NOUN cana-1744 155 77 ) ) PUNCT cana-1744 156 1 + + CCONJ cana-1744 156 2 λ λ X cana-1744 156 3 × × NOUN cana-1744 156 4 ( ( PUNCT cana-1744 156 5 1 1 NUM cana-1744 156 6 + + NUM cana-1744 156 7 δ δ PROPN cana-1744 156 8 ) ) PUNCT cana-1744 156 9 ∗ ∗ NOUN cana-1744 156 10 λ λ X cana-1744 156 11 × × NOUN cana-1744 156 12 ( ( PUNCT cana-1744 156 13 1 1 NUM cana-1744 156 14 + + CCONJ cana-1744 156 15 δ δ PROPN cana-1744 156 16 ) ) PUNCT cana-1744 156 17 µ µ X cana-1744 156 18 𝜒 𝜒 X cana-1744 156 19 ) ) PUNCT cana-1744 156 20 d. d. NOUN cana-1744 156 21 mean mean VERB cana-1744 156 22 number number NOUN cana-1744 156 23 of of ADP cana-1744 156 24 patrons patron NOUN cana-1744 156 25 in in ADP cana-1744 156 26 the the DET cana-1744 156 27 system system NOUN cana-1744 156 28 = = SYM cana-1744 156 29 𝐿𝑠 𝐿𝑠 PROPN cana-1744 156 30 = = SYM cana-1744 156 31 𝐿𝑞 𝐿𝑞 PROPN cana-1744 156 32 + + NUM cana-1744 156 33 λ×(1+δ λ×(1+δ NOUN cana-1744 156 34 ) ) PUNCT cana-1744 156 35 µ µ PRON cana-1744 156 36 proof proof NOUN cana-1744 156 37 communications communication NOUN cana-1744 156 38 on on ADP cana-1744 156 39 applied apply VERB cana-1744 156 40 nonlinear nonlinear ADJ cana-1744 156 41 analysis analysis NOUN cana-1744 156 42 issn issn NOUN cana-1744 156 43 : : PUNCT cana-1744 156 44 1074 1074 NUM cana-1744 156 45 - - PUNCT cana-1744 156 46 133x 133x NUM cana-1744 156 47 vol vol NOUN cana-1744 156 48 32 32 NUM cana-1744 156 49 no no NOUN cana-1744 156 50 . . NOUN cana-1744 156 51 2 2 NUM cana-1744 156 52 ( ( PUNCT cana-1744 156 53 2025 2025 NUM cana-1744 156 54 ) ) PUNCT cana-1744 156 55 312 312 NUM cana-1744 156 56 https://internationalpubls.com https://internationalpubls.com X cana-1744 156 57 when when SCONJ cana-1744 156 58 there there PRON cana-1744 156 59 is be VERB cana-1744 156 60 a a DET cana-1744 156 61 steady steady ADJ cana-1744 156 62 state state NOUN cana-1744 156 63 , , PUNCT cana-1744 156 64 equation equation NOUN cana-1744 156 65 ( ( PUNCT cana-1744 156 66 10 10 NUM cana-1744 156 67 ) ) PUNCT cana-1744 156 68 yields yield VERB cana-1744 156 69 𝑃0(𝑍 𝑃0(𝑍 ADV cana-1744 156 70 ) ) PUNCT cana-1744 156 71 = = PUNCT cana-1744 157 1 ∑ ∑ PUNCT cana-1744 157 2     SPACE cana-1744 157 3 ∞ ∞ NUM cana-1744 157 4 𝑚=0 𝑚=0 PUNCT cana-1744 157 5     SPACE cana-1744 157 6 𝑃𝑚0 𝑃𝑚0 NOUN cana-1744 157 7 ∗ ∗ NOUN cana-1744 157 8 𝑧 𝑧 PROPN cana-1744 157 9 𝑚 𝑚 NOUN cana-1744 157 10 and and CCONJ cana-1744 157 11 𝑃1(𝑍 𝑃1(𝑍 PROPN cana-1744 157 12 ) ) PUNCT cana-1744 157 13 = = PUNCT cana-1744 158 1 ∑ ∑ PUNCT cana-1744 158 2     SPACE cana-1744 158 3 ∞ ∞ NUM cana-1744 158 4 𝑚=0 𝑚=0 PUNCT cana-1744 158 5     SPACE cana-1744 158 6 𝑃𝑚1 𝑃𝑚1 NOUN cana-1744 158 7 ∗ ∗ NOUN cana-1744 158 8 𝑍 𝑍 PROPN cana-1744 158 9 𝑚 𝑚 NOUN cana-1744 158 10 ( ( PUNCT cana-1744 158 11 49 49 NUM cana-1744 158 12 ) ) PUNCT cana-1744 158 13 the the DET cana-1744 158 14 probability probability NOUN cana-1744 158 15 of of ADP cana-1744 158 16 the the DET cana-1744 158 17 server server NOUN cana-1744 158 18 being be AUX cana-1744 158 19 free free ADJ cana-1744 158 20 in in ADP cana-1744 158 21 the the DET cana-1744 158 22 system system NOUN cana-1744 158 23 = = NOUN cana-1744 158 24 𝑃0(1 𝑃0(1 NOUN cana-1744 158 25 ) ) PUNCT cana-1744 159 1 = = PUNCT cana-1744 159 2 ∑ ∑ PUNCT cana-1744 159 3     SPACE cana-1744 159 4 ∞ ∞ NUM cana-1744 159 5 𝑚=0 𝑚=0 PUNCT cana-1744 159 6     SPACE cana-1744 159 7 𝑃𝑚0 𝑃𝑚0 NOUN cana-1744 159 8 = = PROPN cana-1744 159 9 𝑃00 𝑃00 PROPN cana-1744 159 10 ( ( PUNCT cana-1744 159 11 1 1 NUM cana-1744 159 12 − − PROPN cana-1744 159 13 λ λ INTJ cana-1744 159 14 × × NOUN cana-1744 159 15 ( ( PUNCT cana-1744 159 16 1 1 NUM cana-1744 159 17 + + CCONJ cana-1744 159 18 δ δ PROPN cana-1744 159 19 ) ) PUNCT cana-1744 159 20 µ µ PROPN cana-1744 159 21 1 1 NUM cana-1744 159 22 − − PROPN cana-1744 159 23 ( ( PUNCT cana-1744 159 24 λ λ INTJ cana-1744 159 25 × × NOUN cana-1744 159 26 ( ( PUNCT cana-1744 159 27 1 1 NUM cana-1744 159 28 + + CCONJ cana-1744 159 29 δ δ PROPN cana-1744 159 30 ) ) PUNCT cana-1744 159 31 µ µ X cana-1744 159 32 ) ) PUNCT cana-1744 159 33 1 1 NUM cana-1744 159 34 ) ) PUNCT cana-1744 159 35 = = SYM cana-1744 160 1 1 1 NUM cana-1744 160 2 − − NOUN cana-1744 161 1 λ λ INTJ cana-1744 161 2 × × NOUN cana-1744 161 3 ( ( PUNCT cana-1744 161 4 1 1 NUM cana-1744 161 5 + + CCONJ cana-1744 161 6 δ δ PROPN cana-1744 161 7 ) ) PUNCT cana-1744 161 8 µ µ X cana-1744 161 9 ( ( PUNCT cana-1744 161 10 50 50 NUM cana-1744 161 11 ) ) PUNCT cana-1744 161 12 the the DET cana-1744 161 13 probability probability NOUN cana-1744 161 14 of of ADP cana-1744 161 15 the the DET cana-1744 161 16 server server NOUN cana-1744 161 17 being be AUX cana-1744 161 18 engaged engage VERB cana-1744 161 19 in in ADP cana-1744 161 20 the the DET cana-1744 161 21 system system NOUN cana-1744 161 22 = = PUNCT cana-1744 161 23 𝑃1(1 𝑃1(1 X cana-1744 161 24 ) ) PUNCT cana-1744 161 25 = = PUNCT cana-1744 161 26 ∑ ∑ PUNCT cana-1744 161 27     SPACE cana-1744 161 28 ∞ ∞ NUM cana-1744 161 29 𝑚=0 𝑚=0 PUNCT cana-1744 161 30     SPACE cana-1744 161 31 𝑃𝑚1 𝑃𝑚1 NOUN cana-1744 161 32 = = SYM cana-1744 161 33 𝑃00 𝑃00 PROPN cana-1744 161 34 ∗ ∗ NOUN cana-1744 161 35 ( ( PUNCT cana-1744 161 36 λ λ X cana-1744 161 37 × × NOUN cana-1744 161 38 ( ( PUNCT cana-1744 161 39 1 1 NUM cana-1744 161 40 + + CCONJ cana-1744 161 41 δ δ PROPN cana-1744 161 42 ) ) PUNCT cana-1744 161 43 µ µ PROPN cana-1744 161 44 1 1 NUM cana-1744 161 45 − − PROPN cana-1744 161 46 ( ( PUNCT cana-1744 161 47 λ λ INTJ cana-1744 161 48 × × NOUN cana-1744 161 49 ( ( PUNCT cana-1744 161 50 1 1 NUM cana-1744 161 51 + + CCONJ cana-1744 161 52 δ δ PROPN cana-1744 161 53 ) ) PUNCT cana-1744 161 54 µ µ X cana-1744 161 55 ) ) PUNCT cana-1744 161 56 1 1 NUM cana-1744 161 57 ) ) PUNCT cana-1744 162 1 = = PUNCT cana-1744 162 2 λ λ X cana-1744 162 3 × × NOUN cana-1744 162 4 ( ( PUNCT cana-1744 162 5 1 1 NUM cana-1744 162 6 + + CCONJ cana-1744 162 7 δ δ PROPN cana-1744 162 8 ) ) PUNCT cana-1744 162 9 µ µ X cana-1744 162 10 ( ( PUNCT cana-1744 162 11 51 51 NUM cana-1744 162 12 ) ) PUNCT cana-1744 162 13 differentiate differentiate VERB cana-1744 162 14 the the DET cana-1744 162 15 equation equation NOUN cana-1744 162 16 ( ( PUNCT cana-1744 162 17 40 40 NUM cana-1744 162 18 ) ) PUNCT cana-1744 162 19 for for ADP cana-1744 162 20 z z PROPN cana-1744 162 21 , , PUNCT cana-1744 162 22 we we PRON cana-1744 162 23 obtain obtain VERB cana-1744 162 24 𝑃0 𝑃0 NOUN cana-1744 162 25 ′(𝑍 ′(𝑍 NOUN cana-1744 162 26 ) ) PUNCT cana-1744 163 1 = = PUNCT cana-1744 163 2 𝑃00 𝑃00 PROPN cana-1744 163 3 ( ( PUNCT cana-1744 163 4 λ λ PROPN cana-1744 163 5 × × NOUN cana-1744 163 6 ( ( PUNCT cana-1744 163 7 1 1 NUM cana-1744 163 8 + + CCONJ cana-1744 163 9 δ δ PROPN cana-1744 163 10 ) ) PUNCT cana-1744 163 11 𝜒 𝜒 NOUN cana-1744 163 12 ) ) PUNCT cana-1744 163 13 ∗ ∗ NOUN cana-1744 163 14 ( ( PUNCT cana-1744 163 15 𝑍𝛿′(𝑍 𝑍𝛿′(𝑍 X cana-1744 163 16 ) ) PUNCT cana-1744 163 17 + + NUM cana-1744 163 18 𝛿(𝑍 𝛿(𝑍 NUM cana-1744 163 19 ) ) PUNCT cana-1744 163 20 ) ) PUNCT cana-1744 163 21 ( ( PUNCT cana-1744 163 22 1 1 NUM cana-1744 163 23 − − PROPN cana-1744 164 1 λ λ INTJ cana-1744 164 2 × × NOUN cana-1744 164 3 ( ( PUNCT cana-1744 164 4 1 1 NUM cana-1744 164 5 + + CCONJ cana-1744 164 6 δ)𝑍 δ)𝑍 VERB cana-1744 164 7 𝜒 𝜒 PRON cana-1744 164 8 𝛿(𝑍 𝛿(𝑍 NUM cana-1744 164 9 ) ) PUNCT cana-1744 164 10 ) ) PUNCT cana-1744 164 11 2 2 NUM cana-1744 164 12 ( ( PUNCT cana-1744 164 13 52 52 NUM cana-1744 164 14 ) ) PUNCT cana-1744 164 15 𝑃0 𝑃0 NOUN cana-1744 164 16 ′(1 ′(1 PROPN cana-1744 164 17 ) ) PUNCT cana-1744 164 18 = = SYM cana-1744 164 19 𝑃00 𝑃00 PROPN cana-1744 164 20 ( ( PUNCT cana-1744 164 21 λ λ PROPN cana-1744 164 22 × × NOUN cana-1744 164 23 ( ( PUNCT cana-1744 164 24 1 1 NUM cana-1744 164 25 + + CCONJ cana-1744 164 26 δ δ PROPN cana-1744 164 27 ) ) PUNCT cana-1744 164 28 𝜒 𝜒 NOUN cana-1744 164 29 ) ) PUNCT cana-1744 164 30 ∗ ∗ NOUN cana-1744 164 31 ( ( PUNCT cana-1744 164 32 𝛿′(1 𝛿′(1 PROPN cana-1744 164 33 ) ) PUNCT cana-1744 164 34 + + CCONJ cana-1744 165 1 𝛿(1 𝛿(1 PROPN cana-1744 165 2 ) ) PUNCT cana-1744 165 3 ) ) PUNCT cana-1744 166 1 ( ( PUNCT cana-1744 166 2 1 1 NUM cana-1744 166 3 − − PROPN cana-1744 166 4 λ λ INTJ cana-1744 166 5 × × NOUN cana-1744 166 6 ( ( PUNCT cana-1744 166 7 1 1 NUM cana-1744 166 8 + + CCONJ cana-1744 166 9 δ δ NOUN cana-1744 166 10 ) ) PUNCT cana-1744 166 11 𝜒 𝜒 PRON cana-1744 166 12 𝛿(1 𝛿(1 PROPN cana-1744 166 13 ) ) PUNCT cana-1744 166 14 ) ) PUNCT cana-1744 166 15 2 2 NUM cana-1744 166 16 = = SYM cana-1744 166 17 ( ( PUNCT cana-1744 166 18 λ λ INTJ cana-1744 166 19 × × NOUN cana-1744 166 20 ( ( PUNCT cana-1744 166 21 1 1 NUM cana-1744 166 22 + + CCONJ cana-1744 166 23 δ δ PROPN cana-1744 166 24 ) ) PUNCT cana-1744 166 25 𝜒 𝜒 NOUN cana-1744 166 26 ) ) PUNCT cana-1744 166 27 ∗ ∗ NOUN cana-1744 166 28 ( ( PUNCT cana-1744 166 29 𝛿′(1 𝛿′(1 PROPN cana-1744 166 30 ) ) PUNCT cana-1744 166 31 + + CCONJ cana-1744 166 32 𝛿(1 𝛿(1 PROPN cana-1744 166 33 ) ) PUNCT cana-1744 166 34 ) ) PUNCT cana-1744 166 35 ∗ ∗ NOUN cana-1744 166 36 ( ( PUNCT cana-1744 166 37 1 1 NUM cana-1744 166 38 − − PROPN cana-1744 166 39 λ λ INTJ cana-1744 166 40 × × NOUN cana-1744 166 41 ( ( PUNCT cana-1744 166 42 1 1 NUM cana-1744 166 43 + + CCONJ cana-1744 166 44 δ δ PROPN cana-1744 166 45 ) ) PUNCT cana-1744 166 46 µ µ X cana-1744 166 47 ) ) PUNCT cana-1744 166 48 2 2 NUM cana-1744 166 49 ( ( PUNCT cana-1744 166 50 1 1 NUM cana-1744 166 51 − − PROPN cana-1744 166 52 λ λ INTJ cana-1744 166 53 × × NOUN cana-1744 166 54 ( ( PUNCT cana-1744 166 55 1 1 NUM cana-1744 166 56 + + CCONJ cana-1744 166 57 δ δ PROPN cana-1744 166 58 ) ) PUNCT cana-1744 166 59 µ µ X cana-1744 166 60 1 1 NUM cana-1744 166 61 ) ) PUNCT cana-1744 166 62 ( ( PUNCT cana-1744 166 63 53 53 NUM cana-1744 166 64 ) ) PUNCT cana-1744 166 65 𝑃0 𝑃0 NOUN cana-1744 166 66 ′(1 ′(1 PROPN cana-1744 166 67 ) ) PUNCT cana-1744 166 68 = = PUNCT cana-1744 166 69 ( ( PUNCT cana-1744 166 70 λ λ INTJ cana-1744 166 71 × × NOUN cana-1744 166 72 ( ( PUNCT cana-1744 166 73 1 1 NUM cana-1744 166 74 + + CCONJ cana-1744 166 75 δ δ PROPN cana-1744 166 76 ) ) PUNCT cana-1744 166 77 𝜒 𝜒 NOUN cana-1744 166 78 ) ) PUNCT cana-1744 166 79 ∗ ∗ NOUN cana-1744 166 80 ( ( PUNCT cana-1744 166 81 ( ( PUNCT cana-1744 166 82 λ λ INTJ cana-1744 166 83 × × NOUN cana-1744 166 84 ( ( PUNCT cana-1744 166 85 1 1 NUM cana-1744 166 86 + + CCONJ cana-1744 166 87 δ δ PROPN cana-1744 166 88 ) ) PUNCT cana-1744 166 89 ) ) PUNCT cana-1744 166 90 2 2 NUM cana-1744 166 91 𝐸(𝑌2 𝐸(𝑌2 NOUN cana-1744 166 92 ) ) PUNCT cana-1744 166 93 2 2 NUM cana-1744 167 1 + + NUM cana-1744 167 2 λ λ PROPN cana-1744 167 3 × × NOUN cana-1744 167 4 ( ( PUNCT cana-1744 167 5 1 1 NUM cana-1744 167 6 + + CCONJ cana-1744 167 7 δ δ PROPN cana-1744 167 8 ) ) PUNCT cana-1744 167 9 µ µ NOUN cana-1744 167 10 ∗ ∗ NOUN cana-1744 167 11 ( ( PUNCT cana-1744 167 12 1 1 NUM cana-1744 167 13 − − PROPN cana-1744 168 1 λ λ INTJ cana-1744 168 2 × × NOUN cana-1744 168 3 ( ( PUNCT cana-1744 168 4 1 1 NUM cana-1744 168 5 + + CCONJ cana-1744 168 6 δ δ PROPN cana-1744 168 7 ) ) PUNCT cana-1744 168 8 µ µ NOUN cana-1744 168 9 ) ) PUNCT cana-1744 168 10 ) ) PUNCT cana-1744 169 1 ( ( PUNCT cana-1744 169 2 1 1 NUM cana-1744 169 3 − − PROPN cana-1744 169 4 λ λ INTJ cana-1744 169 5 × × NOUN cana-1744 169 6 ( ( PUNCT cana-1744 169 7 1 1 NUM cana-1744 169 8 + + CCONJ cana-1744 169 9 δ δ PROPN cana-1744 169 10 ) ) PUNCT cana-1744 169 11 µ µ X cana-1744 169 12 1 1 NUM cana-1744 169 13 ) ) PUNCT cana-1744 169 14 ( ( PUNCT cana-1744 169 15 54 54 NUM cana-1744 169 16 ) ) PUNCT cana-1744 169 17 differentiate differentiate VERB cana-1744 169 18 the the DET cana-1744 169 19 equation equation NOUN cana-1744 169 20 ( ( PUNCT cana-1744 169 21 42 42 NUM cana-1744 169 22 ) ) PUNCT cana-1744 169 23 via via ADP cana-1744 169 24 respect respect NOUN cana-1744 169 25 to to ADP cana-1744 169 26 z z NOUN cana-1744 169 27 , , PUNCT cana-1744 169 28 we we PRON cana-1744 169 29 obtain obtain VERB cana-1744 169 30 𝑃1 𝑃1 NOUN cana-1744 169 31 ′(𝑍 ′(𝑍 NOUN cana-1744 169 32 ) ) PUNCT cana-1744 170 1 = = PUNCT cana-1744 170 2 𝑃0(𝑍 𝑃0(𝑍 ADV cana-1744 170 3 ) ) PUNCT cana-1744 170 4 ∗ ∗ NOUN cana-1744 170 5 𝛿 𝛿 PROPN cana-1744 170 6 ′(𝑧 ′(𝑧 NOUN cana-1744 170 7 ) ) PUNCT cana-1744 171 1 + + CCONJ cana-1744 171 2 𝑃0 𝑃0 NOUN cana-1744 171 3 ′(𝑍 ′(𝑍 NOUN cana-1744 171 4 ) ) PUNCT cana-1744 171 5 ∗ ∗ NOUN cana-1744 171 6 𝛿(𝑍 𝛿(𝑍 NUM cana-1744 171 7 ) ) PUNCT cana-1744 171 8 ( ( PUNCT cana-1744 171 9 55 55 NUM cana-1744 171 10 ) ) PUNCT cana-1744 171 11 𝑃1 𝑃1 NOUN cana-1744 171 12 ′(1 ′(1 PROPN cana-1744 171 13 ) ) PUNCT cana-1744 171 14 = = PUNCT cana-1744 172 1 ( ( PUNCT cana-1744 172 2 λ λ INTJ cana-1744 172 3 × × NOUN cana-1744 172 4 ( ( PUNCT cana-1744 172 5 1 1 NUM cana-1744 172 6 + + CCONJ cana-1744 172 7 δ)2𝐸(𝑌2 δ)2𝐸(𝑌2 PROPN cana-1744 172 8 ) ) PUNCT cana-1744 172 9 2 2 NUM cana-1744 173 1 + + NUM cana-1744 173 2 λ λ PROPN cana-1744 173 3 × × NOUN cana-1744 173 4 ( ( PUNCT cana-1744 173 5 1 1 NUM cana-1744 173 6 + + CCONJ cana-1744 173 7 δ δ PROPN cana-1744 173 8 ) ) PUNCT cana-1744 173 9 𝜎 𝜎 PROPN cana-1744 173 10 ( ( PUNCT cana-1744 173 11 λ λ X cana-1744 173 12 × × NOUN cana-1744 173 13 ( ( PUNCT cana-1744 173 14 1 1 NUM cana-1744 173 15 + + CCONJ cana-1744 173 16 δ δ PROPN cana-1744 173 17 ) ) PUNCT cana-1744 173 18 µ µ X cana-1744 173 19 ) ) PUNCT cana-1744 173 20 2 2 NUM cana-1744 173 21 ) ) PUNCT cana-1744 173 22 ( ( PUNCT cana-1744 173 23 1 1 NUM cana-1744 173 24 − − PROPN cana-1744 173 25 ( ( PUNCT cana-1744 173 26 λ λ INTJ cana-1744 173 27 × × NOUN cana-1744 173 28 ( ( PUNCT cana-1744 173 29 1 1 NUM cana-1744 173 30 + + CCONJ cana-1744 173 31 δ δ PROPN cana-1744 173 32 ) ) PUNCT cana-1744 173 33 µ µ X cana-1744 173 34 ) ) PUNCT cana-1744 173 35 1 1 NUM cana-1744 173 36 ) ) PUNCT cana-1744 173 37 ( ( PUNCT cana-1744 173 38 56 56 X cana-1744 173 39 ) ) PUNCT cana-1744 173 40 communications communication NOUN cana-1744 173 41 on on ADP cana-1744 173 42 applied apply VERB cana-1744 173 43 nonlinear nonlinear ADJ cana-1744 173 44 analysis analysis NOUN cana-1744 173 45 issn issn NOUN cana-1744 173 46 : : PUNCT cana-1744 173 47 1074 1074 NUM cana-1744 173 48 - - PUNCT cana-1744 173 49 133x 133x NUM cana-1744 173 50 vol vol NOUN cana-1744 173 51 32 32 NUM cana-1744 173 52 no no NOUN cana-1744 173 53 . . NOUN cana-1744 173 54 2 2 NUM cana-1744 173 55 ( ( PUNCT cana-1744 173 56 2025 2025 NUM cana-1744 173 57 ) ) PUNCT cana-1744 173 58 313 313 NUM cana-1744 173 59 https://internationalpubls.com https://internationalpubls.com NUM cana-1744 173 60 mean mean VERB cana-1744 173 61 number number NOUN cana-1744 173 62 of of ADP cana-1744 173 63 patrons patron NOUN cana-1744 173 64 in in ADP cana-1744 173 65 the the DET cana-1744 173 66 group group NOUN cana-1744 173 67 = = SYM cana-1744 173 68 ( ( PUNCT cana-1744 173 69 𝑃′0(𝑍 𝑃′0(𝑍 PROPN cana-1744 173 70 ) ) PUNCT cana-1744 173 71 + + NUM cana-1744 173 72 𝑃1(𝑍)|𝑧=1 𝑃1(𝑍)|𝑧=1 NOUN cana-1744 173 73 ( ( PUNCT cana-1744 173 74 𝑃′0(𝑍 𝑃′0(𝑍 PROPN cana-1744 173 75 ) ) PUNCT cana-1744 173 76 + + NUM cana-1744 174 1 𝑃1(𝑍))|𝑍=1 𝑃1(𝑍))|𝑍=1 PROPN cana-1744 174 2 = = SYM cana-1744 174 3 ( ( PUNCT cana-1744 174 4 λ λ INTJ cana-1744 174 5 × × NOUN cana-1744 174 6 ( ( PUNCT cana-1744 174 7 1 1 NUM cana-1744 174 8 + + CCONJ cana-1744 174 9 δ δ PROPN cana-1744 174 10 ) ) PUNCT cana-1744 174 11 𝜒 𝜒 NOUN cana-1744 174 12 ) ) PUNCT cana-1744 174 13 ∗ ∗ NOUN cana-1744 174 14 ( ( PUNCT cana-1744 174 15 ( ( PUNCT cana-1744 174 16 λ λ INTJ cana-1744 174 17 × × NOUN cana-1744 174 18 ( ( PUNCT cana-1744 174 19 1 1 NUM cana-1744 174 20 + + CCONJ cana-1744 174 21 δ δ PROPN cana-1744 174 22 ) ) PUNCT cana-1744 174 23 ) ) PUNCT cana-1744 174 24 2 2 NUM cana-1744 174 25 𝐸(𝑌2 𝐸(𝑌2 NOUN cana-1744 174 26 ) ) PUNCT cana-1744 174 27 2 2 NUM cana-1744 175 1 + + NUM cana-1744 175 2 λ λ PROPN cana-1744 175 3 × × NOUN cana-1744 175 4 ( ( PUNCT cana-1744 175 5 1 1 NUM cana-1744 175 6 + + CCONJ cana-1744 175 7 δ δ PROPN cana-1744 175 8 ) ) PUNCT cana-1744 175 9 µ µ X cana-1744 175 10 ( ( PUNCT cana-1744 175 11 1 1 NUM cana-1744 175 12 − − PROPN cana-1744 175 13 λ λ INTJ cana-1744 175 14 × × NOUN cana-1744 175 15 ( ( PUNCT cana-1744 175 16 1 1 NUM cana-1744 175 17 + + CCONJ cana-1744 175 18 δ δ PROPN cana-1744 175 19 ) ) PUNCT cana-1744 175 20 µ µ NOUN cana-1744 175 21 ) ) PUNCT cana-1744 175 22 ) ) PUNCT cana-1744 175 23 ( ( PUNCT cana-1744 175 24 1 1 NUM cana-1744 175 25 − − PROPN cana-1744 175 26 ( ( PUNCT cana-1744 175 27 λ λ INTJ cana-1744 175 28 × × NOUN cana-1744 175 29 ( ( PUNCT cana-1744 175 30 1 1 NUM cana-1744 175 31 + + CCONJ cana-1744 175 32 δ δ PROPN cana-1744 175 33 ) ) PUNCT cana-1744 175 34 µ µ X cana-1744 175 35 ) ) PUNCT cana-1744 175 36 1 1 NUM cana-1744 175 37 ) ) PUNCT cana-1744 175 38 + + CCONJ cana-1744 175 39 ( ( PUNCT cana-1744 175 40 ( ( PUNCT cana-1744 175 41 λ λ INTJ cana-1744 175 42 × × NOUN cana-1744 175 43 ( ( PUNCT cana-1744 175 44 1 1 NUM cana-1744 175 45 + + NUM cana-1744 175 46 δ))2𝐸(𝑌2 δ))2𝐸(𝑌2 ADJ cana-1744 175 47 ) ) PUNCT cana-1744 175 48 2 2 NUM cana-1744 176 1 + + NUM cana-1744 176 2 λ λ PROPN cana-1744 176 3 × × NOUN cana-1744 176 4 ( ( PUNCT cana-1744 176 5 1 1 NUM cana-1744 176 6 + + CCONJ cana-1744 176 7 δ δ NOUN cana-1744 176 8 ) ) PUNCT cana-1744 176 9 𝜒 𝜒 NOUN cana-1744 176 10 ∗ ∗ NOUN cana-1744 176 11 ( ( PUNCT cana-1744 176 12 λ λ X cana-1744 176 13 × × NOUN cana-1744 176 14 ( ( PUNCT cana-1744 176 15 1 1 NUM cana-1744 176 16 + + CCONJ cana-1744 176 17 δ δ PROPN cana-1744 176 18 ) ) PUNCT cana-1744 176 19 µ µ X cana-1744 176 20 ) ) PUNCT cana-1744 176 21 2 2 NUM cana-1744 176 22 ) ) PUNCT cana-1744 176 23 ( ( PUNCT cana-1744 176 24 1 1 NUM cana-1744 176 25 − − PROPN cana-1744 176 26 𝜌1 𝜌1 NOUN cana-1744 176 27 ) ) PUNCT cana-1744 176 28 ( ( PUNCT cana-1744 176 29 57 57 NUM cana-1744 176 30 ) ) PUNCT cana-1744 176 31 = = SYM cana-1744 176 32 1 1 NUM cana-1744 176 33 ( ( PUNCT cana-1744 176 34 1 1 NUM cana-1744 176 35 − − PROPN cana-1744 176 36 ( ( PUNCT cana-1744 176 37 λ λ INTJ cana-1744 176 38 × × NOUN cana-1744 176 39 ( ( PUNCT cana-1744 176 40 1 1 NUM cana-1744 176 41 + + CCONJ cana-1744 176 42 δ δ PROPN cana-1744 176 43 ) ) PUNCT cana-1744 176 44 µ µ X cana-1744 176 45 ) ) PUNCT cana-1744 176 46 1 1 NUM cana-1744 176 47 ) ) PUNCT cana-1744 176 48 ( ( PUNCT cana-1744 176 49 ( ( PUNCT cana-1744 176 50 λ λ INTJ cana-1744 176 51 × × NOUN cana-1744 176 52 ( ( PUNCT cana-1744 176 53 1 1 NUM cana-1744 176 54 + + NUM cana-1744 176 55 δ))2𝐸(𝑌2 δ))2𝐸(𝑌2 ADJ cana-1744 176 56 ) ) PUNCT cana-1744 176 57 2 2 NUM cana-1744 176 58 ( ( PUNCT cana-1744 176 59 1 1 NUM cana-1744 176 60 + + NUM cana-1744 176 61 λ λ PROPN cana-1744 176 62 × × NOUN cana-1744 176 63 ( ( PUNCT cana-1744 176 64 1 1 NUM cana-1744 176 65 + + CCONJ cana-1744 176 66 δ δ PROPN cana-1744 176 67 ) ) PUNCT cana-1744 176 68 𝜒 𝜒 NOUN cana-1744 176 69 ) ) PUNCT cana-1744 177 1 + + CCONJ cana-1744 177 2 λ λ X cana-1744 177 3 × × NOUN cana-1744 177 4 ( ( PUNCT cana-1744 177 5 1 1 NUM cana-1744 177 6 + + NUM cana-1744 177 7 δ δ PROPN cana-1744 177 8 ) ) PUNCT cana-1744 177 9 ∗ ∗ NOUN cana-1744 177 10 λ λ X cana-1744 177 11 × × NOUN cana-1744 177 12 ( ( PUNCT cana-1744 177 13 1 1 NUM cana-1744 177 14 + + CCONJ cana-1744 177 15 δ δ PROPN cana-1744 177 16 ) ) PUNCT cana-1744 177 17 µ µ X cana-1744 177 18 𝜒 𝜒 X cana-1744 177 19 ) ) PUNCT cana-1744 177 20 l𝑞 l𝑞 PROPN cana-1744 177 21 = = SYM cana-1744 177 22 1 1 NUM cana-1744 177 23 ( ( PUNCT cana-1744 177 24 1 1 NUM cana-1744 177 25 − − PROPN cana-1744 177 26 ( ( PUNCT cana-1744 177 27 λ λ INTJ cana-1744 177 28 × × NOUN cana-1744 177 29 ( ( PUNCT cana-1744 177 30 1 1 NUM cana-1744 177 31 + + CCONJ cana-1744 177 32 δ δ PROPN cana-1744 177 33 ) ) PUNCT cana-1744 177 34 µ µ X cana-1744 177 35 ) ) PUNCT cana-1744 177 36 1 1 NUM cana-1744 177 37 ) ) PUNCT cana-1744 177 38 ( ( PUNCT cana-1744 177 39 ( ( PUNCT cana-1744 177 40 λ λ INTJ cana-1744 177 41 × × NOUN cana-1744 177 42 ( ( PUNCT cana-1744 177 43 1 1 NUM cana-1744 177 44 + + NUM cana-1744 177 45 δ))2𝐸(𝑌2 δ))2𝐸(𝑌2 ADJ cana-1744 177 46 ) ) PUNCT cana-1744 177 47 2 2 NUM cana-1744 177 48 ( ( PUNCT cana-1744 177 49 1 1 NUM cana-1744 178 1 + + NUM cana-1744 178 2 λ λ PROPN cana-1744 178 3 × × NOUN cana-1744 178 4 ( ( PUNCT cana-1744 178 5 1 1 NUM cana-1744 178 6 + + CCONJ cana-1744 178 7 δ δ PROPN cana-1744 178 8 ) ) PUNCT cana-1744 178 9 𝜒 𝜒 NOUN cana-1744 178 10 ) ) PUNCT cana-1744 179 1 + + CCONJ cana-1744 179 2 λ λ X cana-1744 179 3 × × NOUN cana-1744 179 4 ( ( PUNCT cana-1744 179 5 1 1 NUM cana-1744 179 6 + + NUM cana-1744 179 7 δ δ PROPN cana-1744 179 8 ) ) PUNCT cana-1744 179 9 ∗ ∗ NOUN cana-1744 179 10 λ λ X cana-1744 179 11 × × NOUN cana-1744 179 12 ( ( PUNCT cana-1744 179 13 1 1 NUM cana-1744 179 14 + + CCONJ cana-1744 179 15 δ δ PROPN cana-1744 179 16 ) ) PUNCT cana-1744 179 17 µ µ X cana-1744 179 18 𝜒 𝜒 X cana-1744 179 19 ) ) PUNCT cana-1744 179 20 ( ( PUNCT cana-1744 179 21 58 58 X cana-1744 179 22 ) ) PUNCT cana-1744 179 23 average average ADJ cana-1744 179 24 number number NOUN cana-1744 179 25 of of ADP cana-1744 179 26 customers customer NOUN cana-1744 179 27 in in ADP cana-1744 179 28 the the DET cana-1744 179 29 system system NOUN cana-1744 179 30 = = PUNCT cana-1744 179 31 𝑑 𝑑 PROPN cana-1744 179 32 𝑑𝑍 𝑑𝑍 PROPN cana-1744 179 33 ( ( PUNCT cana-1744 179 34 𝑃0(z 𝑃0(z PROPN cana-1744 179 35 ) ) PUNCT cana-1744 179 36 + + CCONJ cana-1744 180 1 𝑍𝑃1(𝑍))| 𝑍𝑃1(𝑍))| X cana-1744 180 2 𝑍=1 𝑍=1 X cana-1744 180 3 = = SYM cana-1744 180 4 𝐿𝑞 𝐿𝑞 PROPN cana-1744 180 5 + + CCONJ cana-1744 180 6 𝑃1(1 𝑃1(1 X cana-1744 180 7 ) ) PUNCT cana-1744 180 8 = = SYM cana-1744 181 1 𝐿𝑞 𝐿𝑞 NOUN cana-1744 181 2 + + CCONJ cana-1744 181 3 λ λ X cana-1744 181 4 × × NOUN cana-1744 181 5 ( ( PUNCT cana-1744 181 6 1 1 NUM cana-1744 181 7 + + CCONJ cana-1744 181 8 δ δ PROPN cana-1744 181 9 ) ) PUNCT cana-1744 181 10 µ µ PRON cana-1744 181 11 4 4 NUM cana-1744 181 12 . . PUNCT cana-1744 182 1 stability stability NOUN cana-1744 182 2 condition condition VERB cana-1744 182 3 the the DET cana-1744 182 4 consideration consideration NOUN cana-1744 182 5 of of ADP cana-1744 182 6 stability stability NOUN cana-1744 182 7 has have VERB cana-1744 182 8 great great ADJ cana-1744 182 9 significance significance NOUN cana-1744 182 10 for for ADP cana-1744 182 11 every every DET cana-1744 182 12 queuing queuing NOUN cana-1744 182 13 system system NOUN cana-1744 182 14 . . PUNCT cana-1744 183 1 a a DET cana-1744 183 2 stable stable ADJ cana-1744 183 3 single single ADJ cana-1744 183 4 server server NOUN cana-1744 183 5 retrial retrial NOUN cana-1744 183 6 encouraged encourage VERB cana-1744 183 7 arrival arrival NOUN cana-1744 183 8 queuing queue VERB cana-1744 183 9 system system NOUN cana-1744 183 10 is be AUX cana-1744 183 11 one one NUM cana-1744 183 12 that that PRON cana-1744 183 13 has have VERB cana-1744 183 14 a a DET cana-1744 183 15 persistent persistent ADJ cana-1744 183 16 retry retry NOUN cana-1744 183 17 policy policy NOUN cana-1744 183 18 . . PUNCT cana-1744 184 1 ( ( PUNCT cana-1744 184 2 1 1 NUM cana-1744 184 3 + + NUM cana-1744 184 4 λ λ PROPN cana-1744 184 5 × × NOUN cana-1744 184 6 ( ( PUNCT cana-1744 184 7 1 1 NUM cana-1744 184 8 + + CCONJ cana-1744 184 9 δ δ PROPN cana-1744 184 10 ) ) PUNCT cana-1744 184 11 𝜒 𝜒 NOUN cana-1744 184 12 ) ) PUNCT cana-1744 184 13 ∗ ∗ NOUN cana-1744 184 14 λ λ X cana-1744 184 15 × × NOUN cana-1744 184 16 ( ( PUNCT cana-1744 184 17 1 1 NUM cana-1744 184 18 + + NUM cana-1744 184 19 δ)𝐸(𝑌 δ)𝐸(𝑌 NOUN cana-1744 184 20 ) ) PUNCT cana-1744 184 21 < < X cana-1744 185 1 1 1 NUM cana-1744 185 2 • • NOUN cana-1744 185 3 if if SCONJ cana-1744 185 4 the the DET cana-1744 185 5 stability stability NOUN cana-1744 185 6 condition condition NOUN cana-1744 185 7 of of ADP cana-1744 185 8 the the DET cana-1744 185 9 exponential exponential ADJ cana-1744 185 10 distribution distribution NOUN cana-1744 185 11 is be AUX cana-1744 185 12 ( ( PUNCT cana-1744 185 13 1 1 NUM cana-1744 186 1 + + NUM cana-1744 186 2 λ λ PROPN cana-1744 186 3 × × NOUN cana-1744 186 4 ( ( PUNCT cana-1744 186 5 1 1 NUM cana-1744 186 6 + + CCONJ cana-1744 186 7 δ δ PROPN cana-1744 186 8 ) ) PUNCT cana-1744 186 9 𝜒 𝜒 NOUN cana-1744 186 10 ) ) PUNCT cana-1744 187 1 λ λ X cana-1744 187 2 × × NOUN cana-1744 187 3 ( ( PUNCT cana-1744 187 4 1 1 NUM cana-1744 187 5 + + CCONJ cana-1744 187 6 δ δ NOUN cana-1744 187 7 ) ) PUNCT cana-1744 187 8 𝜇 𝜇 ADP cana-1744 187 9 < < X cana-1744 187 10 1 1 NUM cana-1744 187 11 • • NOUN cana-1744 187 12 if if SCONJ cana-1744 187 13 the the DET cana-1744 187 14 stability stability NOUN cana-1744 187 15 condition condition NOUN cana-1744 187 16 of of ADP cana-1744 187 17 the the DET cana-1744 187 18 erlaang erlaang PROPN cana-1744 187 19 distribution distribution NOUN cana-1744 187 20 is be AUX cana-1744 187 21 ( ( PUNCT cana-1744 187 22 1 1 NUM cana-1744 188 1 + + NUM cana-1744 188 2 λ λ PROPN cana-1744 188 3 × × NOUN cana-1744 188 4 ( ( PUNCT cana-1744 188 5 1 1 NUM cana-1744 188 6 + + CCONJ cana-1744 188 7 δ δ PROPN cana-1744 188 8 ) ) PUNCT cana-1744 188 9 𝜒 𝜒 NOUN cana-1744 188 10 ) ) PUNCT cana-1744 188 11 𝑟λ 𝑟λ ADP cana-1744 188 12 × × NOUN cana-1744 188 13 ( ( PUNCT cana-1744 188 14 1 1 NUM cana-1744 188 15 + + CCONJ cana-1744 188 16 δ δ NOUN cana-1744 188 17 ) ) PUNCT cana-1744 188 18 𝜇 𝜇 ADP cana-1744 188 19 < < X cana-1744 188 20 1 1 NUM cana-1744 188 21 5 5 NUM cana-1744 188 22 . . PUNCT cana-1744 188 23 special special ADJ cana-1744 188 24 privilege privilege NOUN cana-1744 188 25 we we PRON cana-1744 188 26 note note VERB cana-1744 188 27 that that SCONJ cana-1744 188 28 many many ADJ cana-1744 188 29 particular particular ADJ cana-1744 188 30 cases case NOUN cana-1744 188 31 of of ADP cana-1744 188 32 this this DET cana-1744 188 33 work work NOUN cana-1744 188 34 can can AUX cana-1744 188 35 be be AUX cana-1744 188 36 derived derive VERB cana-1744 188 37 for for ADP cana-1744 188 38 various various ADJ cana-1744 188 39 service service NOUN cana-1744 188 40 time time NOUN cana-1744 188 41 distributions distribution NOUN cana-1744 188 42 privilege-1 privilege-1 PROPN cana-1744 188 43 : : PUNCT cana-1744 188 44 an an DET cana-1744 188 45 exponential exponential ADJ cana-1744 188 46 distribution distribution NOUN cana-1744 188 47 is be AUX cana-1744 188 48 used use VERB cana-1744 188 49 to to PART cana-1744 188 50 describe describe VERB cana-1744 188 51 the the DET cana-1744 188 52 service service NOUN cana-1744 188 53 time time NOUN cana-1744 188 54 distribution distribution NOUN cana-1744 188 55 . . PUNCT cana-1744 189 1 the the DET cana-1744 189 2 pdf pdf NOUN cana-1744 189 3 of of ADP cana-1744 189 4 exponential exponential ADJ cana-1744 189 5 distribution distribution NOUN cana-1744 189 6 are be AUX cana-1744 189 7 , , PUNCT cana-1744 189 8 𝑎(𝑦 𝑎(𝑦 NOUN cana-1744 189 9 ) ) PUNCT cana-1744 189 10 = = PUNCT cana-1744 189 11 𝜇𝑒−𝜇𝑦 𝜇𝑒−𝜇𝑦 NOUN cana-1744 189 12 , , PUNCT cana-1744 189 13 𝑦 𝑦 NOUN cana-1744 189 14 > > X cana-1744 189 15 0 0 PUNCT cana-1744 190 1 ( ( PUNCT cana-1744 190 2 59 59 NUM cana-1744 190 3 ) ) PUNCT cana-1744 190 4 communications communication NOUN cana-1744 190 5 on on ADP cana-1744 190 6 applied apply VERB cana-1744 190 7 nonlinear nonlinear ADJ cana-1744 190 8 analysis analysis NOUN cana-1744 190 9 issn issn NOUN cana-1744 190 10 : : PUNCT cana-1744 190 11 1074 1074 NUM cana-1744 190 12 - - PUNCT cana-1744 190 13 133x 133x NUM cana-1744 190 14 vol vol NOUN cana-1744 190 15 32 32 NUM cana-1744 190 16 no no NOUN cana-1744 190 17 . . NOUN cana-1744 190 18 2 2 NUM cana-1744 190 19 ( ( PUNCT cana-1744 190 20 2025 2025 NUM cana-1744 190 21 ) ) PUNCT cana-1744 190 22 314 314 NUM cana-1744 190 23 https://internationalpubls.com https://internationalpubls.com X cana-1744 190 24 e(y e(y X cana-1744 190 25 ) ) PUNCT cana-1744 190 26 = = SYM cana-1744 190 27 1 1 NUM cana-1744 190 28 𝜇 𝜇 ADP cana-1744 190 29 and and CCONJ cana-1744 190 30 e(y2 e(y2 NOUN cana-1744 190 31 ) ) PUNCT cana-1744 190 32 = = SYM cana-1744 190 33 2 2 NUM cana-1744 190 34 𝜇2 𝜇2 NOUN cana-1744 190 35 ( ( PUNCT cana-1744 190 36 60 60 NUM cana-1744 190 37 ) ) PUNCT cana-1744 190 38 the the DET cana-1744 190 39 lt lt PROPN cana-1744 190 40 of of ADP cana-1744 190 41 𝑎(𝑦 𝑎(𝑦 PROPN cana-1744 190 42 ) ) PUNCT cana-1744 190 43 is be AUX cana-1744 190 44 𝑎‾(𝑐 𝑎‾(𝑐 NOUN cana-1744 190 45 ) ) PUNCT cana-1744 190 46 = = PUNCT cana-1744 190 47 𝜇 𝜇 ADP cana-1744 190 48 𝑐+𝜇 𝑐+𝜇 PROPN cana-1744 190 49 ( ( PUNCT cana-1744 190 50 61 61 NUM cana-1744 190 51 ) ) PUNCT cana-1744 190 52 𝑎‾(λ 𝑎‾(λ PROPN cana-1744 190 53 × × NOUN cana-1744 190 54 ( ( PUNCT cana-1744 190 55 1 1 NUM cana-1744 190 56 + + NUM cana-1744 190 57 δ δ NOUN cana-1744 190 58 ) ) PUNCT cana-1744 190 59 − − PROPN cana-1744 191 1 λ λ INTJ cana-1744 191 2 × × NOUN cana-1744 191 3 ( ( PUNCT cana-1744 191 4 1 1 NUM cana-1744 191 5 + + CCONJ cana-1744 191 6 δ δ PROPN cana-1744 191 7 ) ) PUNCT cana-1744 191 8 ∗ ∗ NOUN cana-1744 191 9 𝑍 𝑍 PROPN cana-1744 191 10 ) ) PUNCT cana-1744 191 11 = = PUNCT cana-1744 191 12 𝜇 𝜇 ADP cana-1744 191 13 λ λ X cana-1744 191 14 × × NOUN cana-1744 191 15 ( ( PUNCT cana-1744 191 16 1 1 NUM cana-1744 191 17 + + CCONJ cana-1744 191 18 δ δ NOUN cana-1744 191 19 ) ) PUNCT cana-1744 191 20 − − PROPN cana-1744 192 1 λ λ INTJ cana-1744 192 2 × × NOUN cana-1744 192 3 ( ( PUNCT cana-1744 192 4 1 1 NUM cana-1744 192 5 + + CCONJ cana-1744 192 6 δ δ PROPN cana-1744 192 7 ) ) PUNCT cana-1744 192 8 ∗ ∗ NOUN cana-1744 192 9 𝑍 𝑍 PROPN cana-1744 192 10 + + CCONJ cana-1744 192 11 𝜇 𝜇 X cana-1744 192 12 = = SYM cana-1744 192 13 1 1 NUM cana-1744 192 14 1 1 NUM cana-1744 192 15 + + NUM cana-1744 192 16 λ λ PROPN cana-1744 192 17 × × NOUN cana-1744 192 18 ( ( PUNCT cana-1744 192 19 1 1 NUM cana-1744 192 20 + + CCONJ cana-1744 192 21 δ δ PROPN cana-1744 192 22 ) ) PUNCT cana-1744 192 23 µ µ NOUN cana-1744 192 24 − − PROPN cana-1744 192 25 ( ( PUNCT cana-1744 192 26 λ λ INTJ cana-1744 192 27 × × NOUN cana-1744 192 28 ( ( PUNCT cana-1744 192 29 1 1 NUM cana-1744 192 30 + + CCONJ cana-1744 192 31 δ δ PROPN cana-1744 192 32 ) ) PUNCT cana-1744 192 33 µ µ X cana-1744 192 34 ) ) PUNCT cana-1744 192 35 𝑍 𝑍 PROPN cana-1744 192 36 ( ( PUNCT cana-1744 192 37 62 62 NUM cana-1744 192 38 ) ) PUNCT cana-1744 192 39 𝛿(𝑍 𝛿(𝑍 NUM cana-1744 192 40 ) ) PUNCT cana-1744 193 1 = = SYM cana-1744 193 2 1 1 NUM cana-1744 193 3 − − NOUN cana-1744 193 4 𝑎‾ 𝑎‾ ADV cana-1744 193 5 𝑎‾ 𝑎‾ NOUN cana-1744 193 6 − − PROPN cana-1744 193 7 𝑍 𝑍 PROPN cana-1744 193 8 = = SYM cana-1744 193 9 1 1 NUM cana-1744 193 10 − − NUM cana-1744 193 11 1 1 NUM cana-1744 193 12 1 1 NUM cana-1744 193 13 + + NUM cana-1744 193 14 λ λ PROPN cana-1744 193 15 × × NOUN cana-1744 193 16 ( ( PUNCT cana-1744 193 17 1 1 NUM cana-1744 193 18 + + CCONJ cana-1744 193 19 δ δ PROPN cana-1744 193 20 ) ) PUNCT cana-1744 193 21 µ µ NOUN cana-1744 193 22 − − PROPN cana-1744 194 1 ( ( PUNCT cana-1744 194 2 λ λ INTJ cana-1744 194 3 × × NOUN cana-1744 194 4 ( ( PUNCT cana-1744 194 5 1 1 NUM cana-1744 194 6 + + CCONJ cana-1744 194 7 δ δ PROPN cana-1744 194 8 ) ) PUNCT cana-1744 194 9 µ µ X cana-1744 194 10 ) ) PUNCT cana-1744 194 11 𝑍 𝑍 PROPN cana-1744 194 12 1 1 NUM cana-1744 194 13 1 1 NUM cana-1744 194 14 + + CCONJ cana-1744 194 15 ( ( PUNCT cana-1744 194 16 λ λ INTJ cana-1744 194 17 × × NOUN cana-1744 194 18 ( ( PUNCT cana-1744 194 19 1 1 NUM cana-1744 194 20 + + CCONJ cana-1744 194 21 δ δ PROPN cana-1744 194 22 ) ) PUNCT cana-1744 194 23 µ µ X cana-1744 194 24 ) ) PUNCT cana-1744 194 25 − − PROPN cana-1744 195 1 ( ( PUNCT cana-1744 195 2 λ λ INTJ cana-1744 195 3 × × NOUN cana-1744 195 4 ( ( PUNCT cana-1744 195 5 1 1 NUM cana-1744 195 6 + + CCONJ cana-1744 195 7 δ δ PROPN cana-1744 195 8 ) ) PUNCT cana-1744 195 9 µ µ X cana-1744 195 10 ) ) PUNCT cana-1744 195 11 𝑍 𝑍 PROPN cana-1744 195 12 − − NOUN cana-1744 195 13 𝑍 𝑍 NOUN cana-1744 195 14 = = SYM cana-1744 195 15 λ λ X cana-1744 195 16 × × NOUN cana-1744 195 17 ( ( PUNCT cana-1744 195 18 1 1 NUM cana-1744 195 19 + + CCONJ cana-1744 195 20 δ δ PROPN cana-1744 195 21 ) ) PUNCT cana-1744 195 22 µ µ PROPN cana-1744 195 23 1 1 NUM cana-1744 195 24 − − PROPN cana-1744 195 25 ( ( PUNCT cana-1744 195 26 λ λ INTJ cana-1744 195 27 × × NOUN cana-1744 195 28 ( ( PUNCT cana-1744 195 29 1 1 NUM cana-1744 195 30 + + CCONJ cana-1744 195 31 δ δ PROPN cana-1744 195 32 ) ) PUNCT cana-1744 195 33 µ µ X cana-1744 195 34 ) ) PUNCT cana-1744 195 35 𝑍 𝑍 PROPN cana-1744 195 36 ( ( PUNCT cana-1744 195 37 63 63 NUM cana-1744 195 38 ) ) PUNCT cana-1744 195 39 𝑃0(𝑍 𝑃0(𝑍 NOUN cana-1744 195 40 ) ) PUNCT cana-1744 195 41 = = VERB cana-1744 195 42 𝑝00 𝑝00 VERB cana-1744 195 43 1 1 NUM cana-1744 195 44 − − PROPN cana-1744 196 1 ( ( PUNCT cana-1744 196 2 λ λ INTJ cana-1744 196 3 × × NOUN cana-1744 196 4 ( ( PUNCT cana-1744 196 5 1 1 NUM cana-1744 196 6 + + CCONJ cana-1744 196 7 δ)𝑍 δ)𝑍 VERB cana-1744 196 8 𝜒 𝜒 X cana-1744 196 9 ) ) PUNCT cana-1744 196 10 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 196 11 ) ) PUNCT cana-1744 197 1 = = PRON cana-1744 197 2 𝑝00 𝑝00 VERB cana-1744 197 3 1 1 NUM cana-1744 197 4 − − PROPN cana-1744 197 5 ( ( PUNCT cana-1744 197 6 λ λ INTJ cana-1744 197 7 × × NOUN cana-1744 197 8 ( ( PUNCT cana-1744 197 9 1 1 NUM cana-1744 197 10 + + CCONJ cana-1744 197 11 δ)𝑍 δ)𝑍 NOUN cana-1744 197 12 𝜒 𝜒 X cana-1744 197 13 ) ) PUNCT cana-1744 197 14 ( ( PUNCT cana-1744 197 15 λ λ X cana-1744 197 16 × × NOUN cana-1744 197 17 ( ( PUNCT cana-1744 197 18 1 1 NUM cana-1744 197 19 + + CCONJ cana-1744 197 20 δ δ PROPN cana-1744 197 21 ) ) PUNCT cana-1744 197 22 µ µ PROPN cana-1744 197 23 1 1 NUM cana-1744 197 24 − − PROPN cana-1744 198 1 ( ( PUNCT cana-1744 198 2 λ λ INTJ cana-1744 198 3 × × NOUN cana-1744 198 4 ( ( PUNCT cana-1744 198 5 1 1 NUM cana-1744 198 6 + + CCONJ cana-1744 198 7 δ δ PROPN cana-1744 198 8 ) ) PUNCT cana-1744 198 9 µ µ X cana-1744 198 10 ) ) PUNCT cana-1744 198 11 𝑍 𝑍 PROPN cana-1744 198 12 ) ) PUNCT cana-1744 198 13 ( ( PUNCT cana-1744 198 14 64 64 NUM cana-1744 198 15 ) ) PUNCT cana-1744 198 16 after after ADP cana-1744 198 17 the the DET cana-1744 198 18 solution solution NOUN cana-1744 198 19 of of ADP cana-1744 198 20 equation equation NOUN cana-1744 198 21 ( ( PUNCT cana-1744 198 22 64 64 NUM cana-1744 198 23 ) ) PUNCT cana-1744 198 24 , , PUNCT cana-1744 198 25 we we PRON cana-1744 198 26 obtain obtain VERB cana-1744 198 27 𝑃0(𝑍 𝑃0(𝑍 PRON cana-1744 198 28 ) ) PUNCT cana-1744 198 29 = = PUNCT cana-1744 198 30 𝑃00(1− 𝑃00(1− X cana-1744 198 31 λ×(1+δ λ×(1+δ NUM cana-1744 198 32 ) ) PUNCT cana-1744 198 33 µ µ X cana-1744 198 34 ) ) PUNCT cana-1744 198 35 𝑍 𝑍 PROPN cana-1744 198 36 ) ) PUNCT cana-1744 198 37 1− 1− NUM cana-1744 198 38 ( ( PUNCT cana-1744 198 39 λ×(1+δ λ×(1+δ NOUN cana-1744 198 40 ) ) PUNCT cana-1744 198 41 µ µ X cana-1744 198 42 ) ) PUNCT cana-1744 198 43 1𝑍 1𝑍 NUM cana-1744 198 44 where where SCONJ cana-1744 198 45 𝜌 𝜌 X cana-1744 198 46 = = SYM cana-1744 198 47 λ×(1+δ λ×(1+δ NOUN cana-1744 198 48 ) ) PUNCT cana-1744 198 49 𝜇 𝜇 ADP cana-1744 198 50 and and CCONJ cana-1744 198 51 𝜌1 𝜌1 NOUN cana-1744 198 52 = = SYM cana-1744 198 53 ( ( PUNCT cana-1744 198 54 λ×(1+δ)+𝜒 λ×(1+δ)+𝜒 NOUN cana-1744 198 55 ) ) PUNCT cana-1744 198 56 𝜒𝜇 𝜒𝜇 ADP cana-1744 199 1 ( ( PUNCT cana-1744 199 2 65 65 NUM cana-1744 199 3 ) ) PUNCT cana-1744 199 4 the the DET cana-1744 199 5 equation equation NOUN cana-1744 199 6 ( ( PUNCT cana-1744 199 7 65 65 NUM cana-1744 199 8 ) ) PUNCT cana-1744 199 9 means mean VERB cana-1744 199 10 the the DET cana-1744 199 11 steady steady ADJ cana-1744 199 12 - - PUNCT cana-1744 199 13 state state NOUN cana-1744 199 14 probability probability NOUN cana-1744 199 15 of of ADP cana-1744 199 16 patrons patron NOUN cana-1744 199 17 in in ADP cana-1744 199 18 the the DET cana-1744 199 19 group group NOUN cana-1744 199 20 , , PUNCT cana-1744 199 21 server server NOUN cana-1744 199 22 is be AUX cana-1744 199 23 free free ADJ cana-1744 199 24 in in ADP cana-1744 199 25 the the DET cana-1744 199 26 system system NOUN cana-1744 199 27 . . PUNCT cana-1744 200 1 communications communication NOUN cana-1744 200 2 on on ADP cana-1744 200 3 applied apply VERB cana-1744 200 4 nonlinear nonlinear ADJ cana-1744 200 5 analysis analysis NOUN cana-1744 200 6 issn issn NOUN cana-1744 200 7 : : PUNCT cana-1744 200 8 1074 1074 NUM cana-1744 200 9 - - PUNCT cana-1744 200 10 133x 133x NUM cana-1744 200 11 vol vol NOUN cana-1744 200 12 32 32 NUM cana-1744 200 13 no no NOUN cana-1744 200 14 . . NOUN cana-1744 200 15 2 2 NUM cana-1744 200 16 ( ( PUNCT cana-1744 200 17 2025 2025 NUM cana-1744 200 18 ) ) PUNCT cana-1744 200 19 315 315 NUM cana-1744 200 20 https://internationalpubls.com https://internationalpubls.com SYM cana-1744 200 21 𝑃1(𝑍 𝑃1(𝑍 PROPN cana-1744 200 22 ) ) PUNCT cana-1744 200 23 = = SYM cana-1744 200 24 𝑃00 𝑃00 PROPN cana-1744 200 25 ( ( PUNCT cana-1744 200 26 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 200 27 ) ) PUNCT cana-1744 200 28 1 1 NUM cana-1744 200 29 − − PROPN cana-1744 200 30 ( ( PUNCT cana-1744 200 31 λ λ INTJ cana-1744 200 32 × × NOUN cana-1744 200 33 ( ( PUNCT cana-1744 200 34 1 1 NUM cana-1744 200 35 + + CCONJ cana-1744 200 36 δ)𝑍 δ)𝑍 VERB cana-1744 200 37 𝜒 𝜒 X cana-1744 200 38 ) ) PUNCT cana-1744 200 39 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 200 40 ) ) PUNCT cana-1744 200 41 ) ) PUNCT cana-1744 201 1 = = SYM cana-1744 201 2 𝑃00 𝑃00 PROPN cana-1744 201 3 ( ( PUNCT cana-1744 201 4 λ λ PROPN cana-1744 201 5 × × NOUN cana-1744 201 6 ( ( PUNCT cana-1744 201 7 1 1 NUM cana-1744 201 8 + + CCONJ cana-1744 201 9 δ δ PROPN cana-1744 201 10 ) ) PUNCT cana-1744 201 11 µ µ PROPN cana-1744 201 12 1 1 NUM cana-1744 201 13 − − PROPN cana-1744 201 14 ( ( PUNCT cana-1744 201 15 λ λ INTJ cana-1744 201 16 × × NOUN cana-1744 201 17 ( ( PUNCT cana-1744 201 18 1 1 NUM cana-1744 201 19 + + CCONJ cana-1744 201 20 δ δ PROPN cana-1744 201 21 ) ) PUNCT cana-1744 201 22 µ µ X cana-1744 201 23 ) ) PUNCT cana-1744 201 24 𝑍 𝑍 PROPN cana-1744 201 25 1 1 NUM cana-1744 201 26 − − NOUN cana-1744 201 27 ( ( PUNCT cana-1744 201 28 λ λ INTJ cana-1744 201 29 × × NOUN cana-1744 201 30 ( ( PUNCT cana-1744 201 31 1 1 NUM cana-1744 201 32 + + CCONJ cana-1744 201 33 δ)𝑍 δ)𝑍 NOUN cana-1744 201 34 𝜒 𝜒 X cana-1744 201 35 ) ) PUNCT cana-1744 201 36 ( ( PUNCT cana-1744 201 37 λ λ X cana-1744 201 38 × × NOUN cana-1744 201 39 ( ( PUNCT cana-1744 201 40 1 1 NUM cana-1744 201 41 + + CCONJ cana-1744 201 42 δ δ PROPN cana-1744 201 43 ) ) PUNCT cana-1744 201 44 µ µ PROPN cana-1744 201 45 1 1 NUM cana-1744 201 46 − − PROPN cana-1744 201 47 ( ( PUNCT cana-1744 201 48 λ λ INTJ cana-1744 201 49 × × NOUN cana-1744 201 50 ( ( PUNCT cana-1744 201 51 1 1 NUM cana-1744 201 52 + + CCONJ cana-1744 201 53 δ δ PROPN cana-1744 201 54 ) ) PUNCT cana-1744 201 55 µ µ X cana-1744 201 56 ) ) PUNCT cana-1744 201 57 𝑍 𝑍 PROPN cana-1744 201 58 ) ) PUNCT cana-1744 201 59 ) ) PUNCT cana-1744 201 60 ( ( PUNCT cana-1744 201 61 66 66 NUM cana-1744 201 62 ) ) PUNCT cana-1744 201 63 after after ADP cana-1744 201 64 the the DET cana-1744 201 65 solution solution NOUN cana-1744 201 66 of of ADP cana-1744 201 67 equation equation NOUN cana-1744 201 68 ( ( PUNCT cana-1744 201 69 66 66 NUM cana-1744 201 70 ) ) PUNCT cana-1744 201 71 , , PUNCT cana-1744 201 72 we we PRON cana-1744 201 73 obtain obtain VERB cana-1744 201 74 𝑃1(𝑍 𝑃1(𝑍 PROPN cana-1744 201 75 ) ) PUNCT cana-1744 201 76 = = SYM cana-1744 201 77 𝑃00 𝑃00 PROPN cana-1744 201 78 ( ( PUNCT cana-1744 201 79 λ λ PROPN cana-1744 201 80 × × NOUN cana-1744 201 81 ( ( PUNCT cana-1744 201 82 1 1 NUM cana-1744 201 83 + + CCONJ cana-1744 201 84 δ δ PROPN cana-1744 201 85 ) ) PUNCT cana-1744 201 86 µ µ PROPN cana-1744 201 87 1 1 NUM cana-1744 201 88 − − PROPN cana-1744 201 89 ( ( PUNCT cana-1744 201 90 λ λ INTJ cana-1744 201 91 × × NOUN cana-1744 201 92 ( ( PUNCT cana-1744 201 93 1 1 NUM cana-1744 201 94 + + CCONJ cana-1744 201 95 δ δ PROPN cana-1744 201 96 ) ) PUNCT cana-1744 201 97 µ µ X cana-1744 201 98 ) ) PUNCT cana-1744 201 99 1𝑍 1𝑍 PROPN cana-1744 201 100 ) ) PUNCT cana-1744 201 101 ( ( PUNCT cana-1744 201 102 67 67 NUM cana-1744 201 103 ) ) PUNCT cana-1744 201 104 the the DET cana-1744 201 105 equation equation NOUN cana-1744 201 106 ( ( PUNCT cana-1744 201 107 65 65 NUM cana-1744 201 108 ) ) PUNCT cana-1744 201 109 means mean VERB cana-1744 201 110 the the DET cana-1744 201 111 steady steady ADJ cana-1744 201 112 - - PUNCT cana-1744 201 113 state state NOUN cana-1744 201 114 probability probability NOUN cana-1744 201 115 of of ADP cana-1744 201 116 patrons patron NOUN cana-1744 201 117 in in ADP cana-1744 201 118 the the DET cana-1744 201 119 group group NOUN cana-1744 201 120 , , PUNCT cana-1744 201 121 server server NOUN cana-1744 201 122 is be AUX cana-1744 201 123 engaged engage VERB cana-1744 201 124 in in ADP cana-1744 201 125 the the DET cana-1744 201 126 system system NOUN cana-1744 201 127 . . PUNCT cana-1744 202 1 l𝑞 l𝑞 PROPN cana-1744 202 2 = = SYM cana-1744 202 3 𝑃00 𝑃00 PROPN cana-1744 202 4 ( ( PUNCT cana-1744 202 5 1 1 NUM cana-1744 202 6 − − PROPN cana-1744 202 7 ( ( PUNCT cana-1744 202 8 λ λ INTJ cana-1744 202 9 × × NOUN cana-1744 202 10 ( ( PUNCT cana-1744 202 11 1 1 NUM cana-1744 202 12 + + CCONJ cana-1744 202 13 δ δ PROPN cana-1744 202 14 ) ) PUNCT cana-1744 202 15 µ µ X cana-1744 202 16 ) ) PUNCT cana-1744 202 17 1 1 NUM cana-1744 202 18 ) ) PUNCT cana-1744 202 19 2 2 NUM cana-1744 202 20 ( ( PUNCT cana-1744 202 21 λ λ X cana-1744 202 22 × × NOUN cana-1744 202 23 ( ( PUNCT cana-1744 202 24 1 1 NUM cana-1744 202 25 + + NUM cana-1744 202 26 δ)2𝐸(𝑌2 δ)2𝐸(𝑌2 PROPN cana-1744 202 27 ) ) PUNCT cana-1744 202 28 2 2 NUM cana-1744 202 29 ( ( PUNCT cana-1744 202 30 1 1 NUM cana-1744 203 1 + + NUM cana-1744 203 2 λ λ PROPN cana-1744 203 3 × × NOUN cana-1744 203 4 ( ( PUNCT cana-1744 203 5 1 1 NUM cana-1744 203 6 + + CCONJ cana-1744 203 7 δ δ PROPN cana-1744 203 8 ) ) PUNCT cana-1744 203 9 𝜒 𝜒 NOUN cana-1744 203 10 ) ) PUNCT cana-1744 204 1 + + CCONJ cana-1744 204 2 λ λ X cana-1744 204 3 × × NOUN cana-1744 204 4 ( ( PUNCT cana-1744 204 5 1 1 NUM cana-1744 204 6 + + CCONJ cana-1744 204 7 δ δ PROPN cana-1744 204 8 ) ) PUNCT cana-1744 204 9 ∗ ∗ NOUN cana-1744 204 10 ( ( PUNCT cana-1744 204 11 λ λ X cana-1744 204 12 × × NOUN cana-1744 204 13 ( ( PUNCT cana-1744 204 14 1 1 NUM cana-1744 204 15 + + CCONJ cana-1744 204 16 δ δ PROPN cana-1744 204 17 ) ) PUNCT cana-1744 204 18 µ µ X cana-1744 204 19 ) ) PUNCT cana-1744 204 20 𝜒 𝜒 NOUN cana-1744 204 21 ) ) PUNCT cana-1744 204 22 = = SYM cana-1744 204 23 𝑃00 𝑃00 PROPN cana-1744 204 24 ( ( PUNCT cana-1744 204 25 1 1 NUM cana-1744 204 26 − − PROPN cana-1744 204 27 ( ( PUNCT cana-1744 204 28 λ λ INTJ cana-1744 204 29 × × NOUN cana-1744 204 30 ( ( PUNCT cana-1744 204 31 1 1 NUM cana-1744 204 32 + + CCONJ cana-1744 204 33 δ δ PROPN cana-1744 204 34 ) ) PUNCT cana-1744 204 35 µ µ X cana-1744 204 36 ) ) PUNCT cana-1744 204 37 1 1 NUM cana-1744 204 38 ) ) PUNCT cana-1744 204 39 2 2 NUM cana-1744 204 40 ( ( PUNCT cana-1744 204 41 ( ( PUNCT cana-1744 204 42 λ λ INTJ cana-1744 204 43 × × NOUN cana-1744 204 44 ( ( PUNCT cana-1744 204 45 1 1 NUM cana-1744 204 46 + + NUM cana-1744 204 47 δ))2 δ))2 PROPN cana-1744 204 48 ( ( PUNCT cana-1744 204 49 2 2 NUM cana-1744 204 50 𝜇2 𝜇2 NOUN cana-1744 204 51 ) ) PUNCT cana-1744 204 52 2 2 NUM cana-1744 204 53 ( ( PUNCT cana-1744 204 54 1 1 NUM cana-1744 204 55 + + NUM cana-1744 204 56 λ λ PROPN cana-1744 204 57 × × NOUN cana-1744 204 58 ( ( PUNCT cana-1744 204 59 1 1 NUM cana-1744 204 60 + + CCONJ cana-1744 204 61 δ δ PROPN cana-1744 204 62 ) ) PUNCT cana-1744 204 63 𝜒 𝜒 NOUN cana-1744 204 64 ) ) PUNCT cana-1744 205 1 + + CCONJ cana-1744 205 2 λ λ X cana-1744 205 3 × × NOUN cana-1744 205 4 ( ( PUNCT cana-1744 205 5 1 1 NUM cana-1744 205 6 + + CCONJ cana-1744 205 7 δ δ NOUN cana-1744 205 8 ) ) PUNCT cana-1744 205 9 ( ( PUNCT cana-1744 205 10 λ λ X cana-1744 205 11 × × NOUN cana-1744 205 12 ( ( PUNCT cana-1744 205 13 1 1 NUM cana-1744 205 14 + + CCONJ cana-1744 205 15 δ δ PROPN cana-1744 205 16 ) ) PUNCT cana-1744 205 17 µ µ X cana-1744 205 18 ) ) PUNCT cana-1744 205 19 𝜒 𝜒 NOUN cana-1744 205 20 ) ) PUNCT cana-1744 205 21 ( ( PUNCT cana-1744 205 22 68 68 NUM cana-1744 205 23 ) ) PUNCT cana-1744 205 24 after after ADP cana-1744 205 25 the the DET cana-1744 205 26 solution solution NOUN cana-1744 205 27 of of ADP cana-1744 205 28 equation equation NOUN cana-1744 205 29 ( ( PUNCT cana-1744 205 30 68 68 NUM cana-1744 205 31 ) ) PUNCT cana-1744 205 32 , , PUNCT cana-1744 205 33 we we PRON cana-1744 205 34 obtain obtain VERB cana-1744 205 35 l𝑞 l𝑞 PRON cana-1744 205 36 = = PUNCT cana-1744 205 37 ( ( PUNCT cana-1744 205 38 λ λ INTJ cana-1744 205 39 × × NOUN cana-1744 205 40 ( ( PUNCT cana-1744 205 41 1 1 NUM cana-1744 205 42 + + CCONJ cana-1744 205 43 δ δ PROPN cana-1744 205 44 ) ) PUNCT cana-1744 205 45 µ µ X cana-1744 205 46 ) ) PUNCT cana-1744 205 47 1 1 NUM cana-1744 205 48 ( ( PUNCT cana-1744 205 49 1 1 NUM cana-1744 205 50 − − PROPN cana-1744 205 51 ( ( PUNCT cana-1744 205 52 λ λ INTJ cana-1744 205 53 × × NOUN cana-1744 205 54 ( ( PUNCT cana-1744 205 55 1 1 NUM cana-1744 205 56 + + CCONJ cana-1744 205 57 δ δ PROPN cana-1744 205 58 ) ) PUNCT cana-1744 205 59 µ µ X cana-1744 205 60 ) ) PUNCT cana-1744 205 61 1 1 NUM cana-1744 205 62 ) ) PUNCT cana-1744 205 63 ( ( PUNCT cana-1744 205 64 λ λ X cana-1744 205 65 × × NOUN cana-1744 205 66 ( ( PUNCT cana-1744 205 67 1 1 NUM cana-1744 205 68 + + CCONJ cana-1744 205 69 δ δ PROPN cana-1744 205 70 ) ) PUNCT cana-1744 205 71 µ µ PROPN cana-1744 206 1 + + X cana-1744 206 2 λ λ X cana-1744 206 3 × × NOUN cana-1744 206 4 ( ( PUNCT cana-1744 206 5 1 1 NUM cana-1744 206 6 + + CCONJ cana-1744 206 7 δ δ NOUN cana-1744 206 8 ) ) PUNCT cana-1744 206 9 λ λ PROPN cana-1744 206 10 × × NOUN cana-1744 206 11 ( ( PUNCT cana-1744 206 12 1 1 NUM cana-1744 206 13 + + CCONJ cana-1744 206 14 δ δ NOUN cana-1744 206 15 ) ) PUNCT cana-1744 206 16 + + NUM cana-1744 206 17 𝜒 𝜒 X cana-1744 206 18 ) ) PUNCT cana-1744 206 19 ( ( PUNCT cana-1744 206 20 69 69 NUM cana-1744 206 21 ) ) PUNCT cana-1744 206 22 the the DET cana-1744 206 23 equation equation NOUN cana-1744 206 24 ( ( PUNCT cana-1744 206 25 69 69 NUM cana-1744 206 26 ) ) PUNCT cana-1744 206 27 means mean VERB cana-1744 206 28 the the DET cana-1744 206 29 mean mean ADJ cana-1744 206 30 number number NOUN cana-1744 206 31 of of ADP cana-1744 206 32 patrons patron NOUN cana-1744 206 33 in in ADP cana-1744 206 34 the the DET cana-1744 206 35 group group NOUN cana-1744 206 36 communications communication NOUN cana-1744 206 37 on on ADP cana-1744 206 38 applied apply VERB cana-1744 206 39 nonlinear nonlinear ADJ cana-1744 206 40 analysis analysis NOUN cana-1744 206 41 issn issn NOUN cana-1744 206 42 : : PUNCT cana-1744 206 43 1074 1074 NUM cana-1744 206 44 - - PUNCT cana-1744 206 45 133x 133x NUM cana-1744 206 46 vol vol NOUN cana-1744 206 47 32 32 NUM cana-1744 206 48 no no NOUN cana-1744 206 49 . . NOUN cana-1744 206 50 2 2 NUM cana-1744 206 51 ( ( PUNCT cana-1744 206 52 2025 2025 NUM cana-1744 206 53 ) ) PUNCT cana-1744 206 54 316 316 NUM cana-1744 206 55 https://internationalpubls.com https://internationalpubls.com X cana-1744 207 1 l𝑠 l𝑠 NOUN cana-1744 207 2 = = PUNCT cana-1744 207 3 l𝑞 l𝑞 PROPN cana-1744 208 1 + + CCONJ cana-1744 208 2 λ λ X cana-1744 208 3 × × NOUN cana-1744 208 4 ( ( PUNCT cana-1744 208 5 1 1 NUM cana-1744 208 6 + + CCONJ cana-1744 208 7 δ δ PROPN cana-1744 208 8 ) ) PUNCT cana-1744 208 9 µ µ X cana-1744 208 10 = = PUNCT cana-1744 208 11 ( ( PUNCT cana-1744 208 12 λ λ INTJ cana-1744 208 13 × × NOUN cana-1744 208 14 ( ( PUNCT cana-1744 208 15 1 1 NUM cana-1744 208 16 + + CCONJ cana-1744 208 17 δ δ PROPN cana-1744 208 18 ) ) PUNCT cana-1744 208 19 µ µ X cana-1744 208 20 ) ) PUNCT cana-1744 208 21 1 1 NUM cana-1744 208 22 ( ( PUNCT cana-1744 208 23 1 1 NUM cana-1744 208 24 − − PROPN cana-1744 208 25 ( ( PUNCT cana-1744 208 26 λ λ INTJ cana-1744 208 27 × × NOUN cana-1744 208 28 ( ( PUNCT cana-1744 208 29 1 1 NUM cana-1744 208 30 + + CCONJ cana-1744 208 31 δ δ PROPN cana-1744 208 32 ) ) PUNCT cana-1744 208 33 µ µ X cana-1744 208 34 ) ) PUNCT cana-1744 208 35 1 1 NUM cana-1744 208 36 ) ) PUNCT cana-1744 208 37 ( ( PUNCT cana-1744 208 38 λ λ X cana-1744 208 39 × × NOUN cana-1744 208 40 ( ( PUNCT cana-1744 208 41 1 1 NUM cana-1744 208 42 + + CCONJ cana-1744 208 43 δ δ PROPN cana-1744 208 44 ) ) PUNCT cana-1744 208 45 µ µ PROPN cana-1744 209 1 + + X cana-1744 209 2 λ λ X cana-1744 209 3 × × NOUN cana-1744 209 4 ( ( PUNCT cana-1744 209 5 1 1 NUM cana-1744 209 6 + + CCONJ cana-1744 209 7 δ δ NOUN cana-1744 209 8 ) ) PUNCT cana-1744 209 9 λ λ PROPN cana-1744 209 10 × × NOUN cana-1744 209 11 ( ( PUNCT cana-1744 209 12 1 1 NUM cana-1744 209 13 + + CCONJ cana-1744 209 14 δ δ NOUN cana-1744 209 15 ) ) PUNCT cana-1744 209 16 + + SYM cana-1744 209 17 𝜒 𝜒 X cana-1744 209 18 ) ) PUNCT cana-1744 210 1 + + CCONJ cana-1744 210 2 λ λ X cana-1744 210 3 × × NOUN cana-1744 210 4 ( ( PUNCT cana-1744 210 5 1 1 NUM cana-1744 210 6 + + CCONJ cana-1744 210 7 δ δ PROPN cana-1744 210 8 ) ) PUNCT cana-1744 210 9 µ µ X cana-1744 210 10 ( ( PUNCT cana-1744 210 11 70 70 NUM cana-1744 210 12 ) ) PUNCT cana-1744 210 13 the the DET cana-1744 210 14 equation equation NOUN cana-1744 210 15 ( ( PUNCT cana-1744 210 16 70 70 NUM cana-1744 210 17 ) ) PUNCT cana-1744 210 18 means mean VERB cana-1744 210 19 the the DET cana-1744 210 20 mean mean ADJ cana-1744 210 21 number number NOUN cana-1744 210 22 of of ADP cana-1744 210 23 patrons patron NOUN cana-1744 210 24 in in ADP cana-1744 210 25 the the DET cana-1744 210 26 system system NOUN cana-1744 210 27 . . PUNCT cana-1744 211 1 case-2 case-2 NUM cana-1744 211 2 : : PUNCT cana-1744 211 3 an an DET cana-1744 211 4 erlang erlang NOUN cana-1744 211 5 distribution distribution NOUN cana-1744 211 6 under under ADP cana-1744 211 7 r r NOUN cana-1744 211 8 phases phase NOUN cana-1744 211 9 describes describe VERB cana-1744 211 10 the the DET cana-1744 211 11 service service NOUN cana-1744 211 12 time time NOUN cana-1744 211 13 distribution distribution NOUN cana-1744 211 14 . . PUNCT cana-1744 212 1 this this PRON cana-1744 212 2 privileges privilege VERB cana-1744 212 3 single single ADJ cana-1744 212 4 server server PROPN cana-1744 212 5 erlang erlang PROPN cana-1744 212 6 retrial retrial NOUN cana-1744 212 7 queuing queuing NOUN cana-1744 212 8 model model NOUN cana-1744 212 9 under under ADP cana-1744 212 10 a a DET cana-1744 212 11 persistent persistent ADJ cana-1744 212 12 retrial retrial ADJ cana-1744 212 13 technique technique NOUN cana-1744 212 14 the the DET cana-1744 212 15 erlang erlang PROPN cana-1744 212 16 distribution distribution NOUN cana-1744 212 17 is be AUX cana-1744 212 18 given give VERB cana-1744 212 19 that that DET cana-1744 212 20 𝑎(𝑦 𝑎(𝑦 NOUN cana-1744 212 21 ) ) PUNCT cana-1744 212 22 = = PUNCT cana-1744 212 23 𝜇𝑟𝑦𝑟−1𝑒−𝜇𝑦 𝜇𝑟𝑦𝑟−1𝑒−𝜇𝑦 NOUN cana-1744 212 24 ( ( PUNCT cana-1744 212 25 𝑟 𝑟 NOUN cana-1744 212 26 − − PROPN cana-1744 212 27 1 1 NUM cana-1744 212 28 ) ) PUNCT cana-1744 212 29 ! ! PUNCT cana-1744 213 1 𝜇𝑒−𝜇𝑦 𝜇𝑒−𝜇𝑦 NOUN cana-1744 213 2 , , PUNCT cana-1744 213 3 𝑦 𝑦 NOUN cana-1744 213 4 > > X cana-1744 213 5 0 0 NUM cana-1744 213 6 for for ADP cana-1744 213 7 an an DET cana-1744 213 8 erlang erlang NOUN cana-1744 213 9 distribution distribution NOUN cana-1744 213 10 , , PUNCT cana-1744 213 11 e(y e(y X cana-1744 213 12 ) ) PUNCT cana-1744 213 13 = = SYM cana-1744 213 14 𝑟 𝑟 NOUN cana-1744 213 15 𝜇 𝜇 X cana-1744 213 16 and and CCONJ cana-1744 213 17 e(y2 e(y2 NOUN cana-1744 213 18 ) ) PUNCT cana-1744 213 19 = = SYM cana-1744 214 1 𝑟(𝑟+1 𝑟(𝑟+1 X cana-1744 214 2 ) ) PUNCT cana-1744 214 3 𝜇2 𝜇2 VERB cana-1744 214 4 the the DET cana-1744 214 5 laplace laplace NOUN cana-1744 214 6 transform transform NOUN cana-1744 214 7 of of ADP cana-1744 214 8 𝑎(𝑦 𝑎(𝑦 NOUN cana-1744 214 9 ) ) PUNCT cana-1744 214 10 is be AUX cana-1744 214 11 𝑎‾(𝑐 𝑎‾(𝑐 NOUN cana-1744 214 12 ) ) PUNCT cana-1744 214 13 = = SYM cana-1744 214 14 ( ( PUNCT cana-1744 214 15 𝜇 𝜇 X cana-1744 214 16 𝑐+𝜇 𝑐+𝜇 PROPN cana-1744 214 17 ) ) PUNCT cana-1744 215 1 𝑟 𝑟 X cana-1744 215 2 𝑎‾(λ 𝑎‾(λ VERB cana-1744 215 3 × × NOUN cana-1744 215 4 ( ( PUNCT cana-1744 215 5 1 1 NUM cana-1744 215 6 + + NUM cana-1744 215 7 δ δ NOUN cana-1744 215 8 ) ) PUNCT cana-1744 215 9 − − PROPN cana-1744 216 1 λ λ INTJ cana-1744 216 2 × × NOUN cana-1744 216 3 ( ( PUNCT cana-1744 216 4 1 1 NUM cana-1744 216 5 + + CCONJ cana-1744 216 6 δ δ PROPN cana-1744 216 7 ) ) PUNCT cana-1744 216 8 ∗ ∗ NOUN cana-1744 216 9 𝑍 𝑍 PROPN cana-1744 216 10 ) ) PUNCT cana-1744 216 11 = = SYM cana-1744 216 12 ( ( PUNCT cana-1744 216 13 𝜇 𝜇 ADP cana-1744 216 14 λ λ X cana-1744 216 15 × × NOUN cana-1744 216 16 ( ( PUNCT cana-1744 216 17 1 1 NUM cana-1744 216 18 + + CCONJ cana-1744 216 19 δ δ NOUN cana-1744 216 20 ) ) PUNCT cana-1744 216 21 − − PROPN cana-1744 217 1 λ λ INTJ cana-1744 217 2 × × NOUN cana-1744 217 3 ( ( PUNCT cana-1744 217 4 1 1 NUM cana-1744 217 5 + + CCONJ cana-1744 217 6 δ δ PROPN cana-1744 217 7 ) ) PUNCT cana-1744 217 8 ∗ ∗ NOUN cana-1744 217 9 𝑍 𝑍 PROPN cana-1744 217 10 + + X cana-1744 217 11 𝜇 𝜇 NOUN cana-1744 217 12 ) ) PUNCT cana-1744 217 13 𝑟 𝑟 NOUN cana-1744 217 14 = = SYM cana-1744 217 15 ( ( PUNCT cana-1744 217 16 𝑟 𝑟 NOUN cana-1744 217 17 𝑟 𝑟 X cana-1744 218 1 + + CCONJ cana-1744 218 2 λ λ X cana-1744 218 3 × × NOUN cana-1744 218 4 ( ( PUNCT cana-1744 218 5 1 1 NUM cana-1744 218 6 + + CCONJ cana-1744 218 7 δ δ PROPN cana-1744 218 8 ) ) PUNCT cana-1744 218 9 µ µ NOUN cana-1744 218 10 − − PROPN cana-1744 218 11 ( ( PUNCT cana-1744 218 12 λ λ INTJ cana-1744 218 13 × × NOUN cana-1744 218 14 ( ( PUNCT cana-1744 218 15 1 1 NUM cana-1744 218 16 + + CCONJ cana-1744 218 17 δ δ PROPN cana-1744 218 18 ) ) PUNCT cana-1744 218 19 µ µ X cana-1744 218 20 ) ) PUNCT cana-1744 218 21 𝑍 𝑍 PROPN cana-1744 218 22 ) ) PUNCT cana-1744 218 23 𝑟 𝑟 NOUN cana-1744 218 24 ( ( PUNCT cana-1744 218 25 71 71 NUM cana-1744 218 26 ) ) PUNCT cana-1744 218 27 𝛿(𝑍 𝛿(𝑍 NUM cana-1744 218 28 ) ) PUNCT cana-1744 219 1 = = SYM cana-1744 219 2 1 1 NUM cana-1744 219 3 − − NOUN cana-1744 219 4 𝑎‾ 𝑎‾ ADV cana-1744 219 5 𝑎‾ 𝑎‾ NOUN cana-1744 219 6 − − PROPN cana-1744 219 7 𝑍 𝑍 PROPN cana-1744 219 8 = = SYM cana-1744 219 9 1 1 NUM cana-1744 219 10 − − PROPN cana-1744 219 11 ( ( PUNCT cana-1744 219 12 𝑟 𝑟 NOUN cana-1744 219 13 𝑟 𝑟 X cana-1744 219 14 + + CCONJ cana-1744 219 15 λ λ X cana-1744 219 16 × × NOUN cana-1744 219 17 ( ( PUNCT cana-1744 219 18 1 1 NUM cana-1744 219 19 + + CCONJ cana-1744 219 20 δ δ PROPN cana-1744 219 21 ) ) PUNCT cana-1744 219 22 µ µ NOUN cana-1744 219 23 − − PROPN cana-1744 219 24 ( ( PUNCT cana-1744 219 25 λ λ INTJ cana-1744 219 26 × × NOUN cana-1744 219 27 ( ( PUNCT cana-1744 219 28 1 1 NUM cana-1744 219 29 + + CCONJ cana-1744 219 30 δ δ PROPN cana-1744 219 31 ) ) PUNCT cana-1744 219 32 µ µ X cana-1744 219 33 ) ) PUNCT cana-1744 219 34 𝑍 𝑍 PROPN cana-1744 219 35 ) ) PUNCT cana-1744 219 36 𝑟 𝑟 NOUN cana-1744 219 37 ( ( PUNCT cana-1744 219 38 𝑟 𝑟 NOUN cana-1744 219 39 𝑟 𝑟 X cana-1744 219 40 + + CCONJ cana-1744 219 41 λ λ X cana-1744 219 42 × × NOUN cana-1744 219 43 ( ( PUNCT cana-1744 219 44 1 1 NUM cana-1744 219 45 + + CCONJ cana-1744 219 46 δ δ PROPN cana-1744 219 47 ) ) PUNCT cana-1744 219 48 µ µ NOUN cana-1744 219 49 − − PROPN cana-1744 219 50 ( ( PUNCT cana-1744 219 51 λ λ INTJ cana-1744 219 52 × × NOUN cana-1744 219 53 ( ( PUNCT cana-1744 219 54 1 1 NUM cana-1744 219 55 + + CCONJ cana-1744 219 56 δ δ PROPN cana-1744 219 57 ) ) PUNCT cana-1744 219 58 µ µ X cana-1744 219 59 ) ) PUNCT cana-1744 219 60 ∗ ∗ NOUN cana-1744 219 61 𝑍 𝑍 PROPN cana-1744 219 62 ) ) PUNCT cana-1744 219 63 𝑟 𝑟 NOUN cana-1744 219 64 − − PROPN cana-1744 219 65 𝑍 𝑍 PROPN cana-1744 219 66 = = SYM cana-1744 219 67 ( ( PUNCT cana-1744 219 68 𝑟 𝑟 NOUN cana-1744 219 69 + + CCONJ cana-1744 219 70 λ λ X cana-1744 219 71 × × NOUN cana-1744 219 72 ( ( PUNCT cana-1744 219 73 1 1 NUM cana-1744 219 74 + + CCONJ cana-1744 219 75 δ δ PROPN cana-1744 219 76 ) ) PUNCT cana-1744 219 77 µ µ NOUN cana-1744 219 78 − − PROPN cana-1744 219 79 ( ( PUNCT cana-1744 219 80 λ λ INTJ cana-1744 219 81 × × NOUN cana-1744 219 82 ( ( PUNCT cana-1744 219 83 1 1 NUM cana-1744 219 84 + + CCONJ cana-1744 219 85 δ δ PROPN cana-1744 219 86 ) ) PUNCT cana-1744 219 87 µ µ NOUN cana-1744 219 88 ) ) PUNCT cana-1744 219 89 𝑍)𝑟 𝑍)𝑟 X cana-1744 219 90 − − PUNCT cana-1744 220 1 𝑅𝑟 𝑅𝑟 PROPN cana-1744 220 2 𝑅𝑟 𝑅𝑟 PROPN cana-1744 220 3 − − NOUN cana-1744 220 4 𝑍 𝑍 NOUN cana-1744 220 5 ∗ ∗ NOUN cana-1744 220 6 ( ( PUNCT cana-1744 220 7 𝑟 𝑟 NOUN cana-1744 220 8 + + CCONJ cana-1744 220 9 λ λ X cana-1744 220 10 × × NOUN cana-1744 220 11 ( ( PUNCT cana-1744 220 12 1 1 NUM cana-1744 220 13 + + CCONJ cana-1744 220 14 δ δ PROPN cana-1744 220 15 ) ) PUNCT cana-1744 220 16 µ µ NOUN cana-1744 220 17 − − PROPN cana-1744 221 1 ( ( PUNCT cana-1744 221 2 λ λ INTJ cana-1744 221 3 × × NOUN cana-1744 221 4 ( ( PUNCT cana-1744 221 5 1 1 NUM cana-1744 221 6 + + CCONJ cana-1744 221 7 δ δ PROPN cana-1744 221 8 ) ) PUNCT cana-1744 221 9 µ µ X cana-1744 221 10 ) ) PUNCT cana-1744 221 11 𝑍)𝑟 𝑍)𝑟 X cana-1744 221 12 ( ( PUNCT cana-1744 221 13 72 72 X cana-1744 221 14 ) ) PUNCT cana-1744 221 15 communications communication NOUN cana-1744 221 16 on on ADP cana-1744 221 17 applied apply VERB cana-1744 221 18 nonlinear nonlinear ADJ cana-1744 221 19 analysis analysis NOUN cana-1744 221 20 issn issn NOUN cana-1744 221 21 : : PUNCT cana-1744 221 22 1074 1074 NUM cana-1744 221 23 - - PUNCT cana-1744 221 24 133x 133x NUM cana-1744 221 25 vol vol NOUN cana-1744 221 26 32 32 NUM cana-1744 221 27 no no NOUN cana-1744 221 28 . . NOUN cana-1744 221 29 2 2 NUM cana-1744 221 30 ( ( PUNCT cana-1744 221 31 2025 2025 NUM cana-1744 221 32 ) ) PUNCT cana-1744 221 33 317 317 NUM cana-1744 221 34 https://internationalpubls.com https://internationalpubls.com X cana-1744 221 35 𝑃0(𝑍 𝑃0(𝑍 PROPN cana-1744 221 36 ) ) PUNCT cana-1744 221 37 = = VERB cana-1744 221 38 𝑝00 𝑝00 VERB cana-1744 221 39 1 1 NUM cana-1744 221 40 − − PROPN cana-1744 222 1 ( ( PUNCT cana-1744 222 2 λ λ INTJ cana-1744 222 3 × × NOUN cana-1744 222 4 ( ( PUNCT cana-1744 222 5 1 1 NUM cana-1744 222 6 + + CCONJ cana-1744 222 7 δ)𝑍 δ)𝑍 VERB cana-1744 222 8 𝜒 𝜒 X cana-1744 222 9 ) ) PUNCT cana-1744 222 10 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 222 11 ) ) PUNCT cana-1744 223 1 = = PRON cana-1744 223 2 𝑝00 𝑝00 VERB cana-1744 223 3 1 1 NUM cana-1744 223 4 − − PROPN cana-1744 223 5 ( ( PUNCT cana-1744 223 6 λ λ INTJ cana-1744 223 7 × × NOUN cana-1744 223 8 ( ( PUNCT cana-1744 223 9 1 1 NUM cana-1744 223 10 + + CCONJ cana-1744 223 11 δ)𝑍 δ)𝑍 NOUN cana-1744 223 12 𝜒 𝜒 X cana-1744 223 13 ) ) PUNCT cana-1744 223 14 ( ( PUNCT cana-1744 223 15 ( ( PUNCT cana-1744 223 16 𝑟 𝑟 X cana-1744 223 17 + + CCONJ cana-1744 223 18 λ λ X cana-1744 223 19 × × NOUN cana-1744 223 20 ( ( PUNCT cana-1744 223 21 1 1 NUM cana-1744 223 22 + + CCONJ cana-1744 223 23 δ δ PROPN cana-1744 223 24 ) ) PUNCT cana-1744 223 25 µ µ NOUN cana-1744 223 26 − − PROPN cana-1744 224 1 ( ( PUNCT cana-1744 224 2 λ λ INTJ cana-1744 224 3 × × NOUN cana-1744 224 4 ( ( PUNCT cana-1744 224 5 1 1 NUM cana-1744 224 6 + + CCONJ cana-1744 224 7 δ δ PROPN cana-1744 224 8 ) ) PUNCT cana-1744 224 9 µ µ NOUN cana-1744 224 10 ) ) PUNCT cana-1744 224 11 𝑍)𝑟 𝑍)𝑟 X cana-1744 224 12 − − PUNCT cana-1744 225 1 𝑅𝑟 𝑅𝑟 PROPN cana-1744 225 2 𝑅𝑟 𝑅𝑟 PROPN cana-1744 225 3 − − NOUN cana-1744 225 4 𝑍(𝑟 𝑍(𝑟 PUNCT cana-1744 226 1 + + NOUN cana-1744 226 2 λ λ X cana-1744 226 3 × × NOUN cana-1744 226 4 ( ( PUNCT cana-1744 226 5 1 1 NUM cana-1744 226 6 + + CCONJ cana-1744 226 7 δ δ PROPN cana-1744 226 8 ) ) PUNCT cana-1744 226 9 µ µ NOUN cana-1744 226 10 − − PROPN cana-1744 226 11 ( ( PUNCT cana-1744 226 12 λ λ INTJ cana-1744 226 13 × × NOUN cana-1744 226 14 ( ( PUNCT cana-1744 226 15 1 1 NUM cana-1744 226 16 + + CCONJ cana-1744 226 17 δ δ PROPN cana-1744 226 18 ) ) PUNCT cana-1744 226 19 µ µ X cana-1744 226 20 ) ) PUNCT cana-1744 226 21 𝑍)𝑟 𝑍)𝑟 X cana-1744 226 22 ) ) PUNCT cana-1744 226 23 ( ( PUNCT cana-1744 226 24 73 73 NUM cana-1744 226 25 ) ) PUNCT cana-1744 226 26 hereafter hereafter ADV cana-1744 226 27 the the DET cana-1744 226 28 solution solution NOUN cana-1744 226 29 of of ADP cana-1744 226 30 equation equation NOUN cana-1744 226 31 ( ( PUNCT cana-1744 226 32 73 73 NUM cana-1744 226 33 ) ) PUNCT cana-1744 226 34 , , PUNCT cana-1744 226 35 we we PRON cana-1744 226 36 obtain obtain VERB cana-1744 226 37 𝑃0(𝑍 𝑃0(𝑍 PRON cana-1744 226 38 ) ) PUNCT cana-1744 226 39 = = PUNCT cana-1744 227 1 𝑃00∗(1−𝑍∗(1 𝑃00∗(1−𝑍∗(1 X cana-1744 227 2 + + NUM cana-1744 227 3 1 1 NUM cana-1744 227 4 𝑅 𝑅 PROPN cana-1744 227 5 ∗ ∗ NOUN cana-1744 227 6 ( ( PUNCT cana-1744 227 7 λ×(1+δ λ×(1+δ NOUN cana-1744 227 8 ) ) PUNCT cana-1744 227 9 µ µ NOUN cana-1744 227 10 − − PROPN cana-1744 227 11 ( ( PUNCT cana-1744 227 12 λ×(1+δ λ×(1+δ NOUN cana-1744 227 13 ) ) PUNCT cana-1744 227 14 µ µ X cana-1744 227 15 ) ) PUNCT cana-1744 227 16 ∗𝑍 ∗𝑍 NOUN cana-1744 227 17 ) ) PUNCT cana-1744 227 18 ) ) PUNCT cana-1744 227 19 𝑟 𝑟 NOUN cana-1744 227 20 ) ) PUNCT cana-1744 227 21 1+𝑍 1+𝑍 NUM cana-1744 227 22 ( ( PUNCT cana-1744 227 23 λ×(1+δ λ×(1+δ PROPN cana-1744 227 24 ) ) PUNCT cana-1744 227 25 𝜒 𝜒 NOUN cana-1744 227 26 − − PROPN cana-1744 227 27 𝜌1 𝜌1 NOUN cana-1744 227 28 𝜌 𝜌 X cana-1744 227 29 ( ( PUNCT cana-1744 227 30 1 1 NUM cana-1744 227 31 + + SYM cana-1744 227 32 1 1 NUM cana-1744 227 33 𝑟 𝑟 NOUN cana-1744 227 34 ( ( PUNCT cana-1744 227 35 𝜌−𝜌𝑍 𝜌−𝜌𝑍 PROPN cana-1744 227 36 ) ) PUNCT cana-1744 227 37 ) ) PUNCT cana-1744 227 38 𝑟 𝑟 X cana-1744 227 39 ) ) PUNCT cana-1744 227 40 where where SCONJ cana-1744 227 41 𝜌 𝜌 ADP cana-1744 227 42 = = SYM cana-1744 227 43 λ λ X cana-1744 227 44 × × NOUN cana-1744 227 45 ( ( PUNCT cana-1744 227 46 1 1 NUM cana-1744 227 47 + + CCONJ cana-1744 227 48 δ δ PROPN cana-1744 227 49 ) ) PUNCT cana-1744 227 50 ∗ ∗ NOUN cana-1744 227 51 𝐸(𝑌 𝐸(𝑌 PROPN cana-1744 227 52 ) ) PUNCT cana-1744 227 53 and and CCONJ cana-1744 227 54 𝜌1 𝜌1 NOUN cana-1744 227 55 = = SYM cana-1744 227 56 λ×(1+δ)∗(λ×(1+δ)+𝜒 λ×(1+δ)∗(λ×(1+δ)+𝜒 NOUN cana-1744 227 57 ) ) PUNCT cana-1744 227 58 𝜒 𝜒 NOUN cana-1744 227 59 ∗ ∗ NOUN cana-1744 227 60 𝐸(𝑋 𝐸(𝑋 NOUN cana-1744 227 61 ) ) PUNCT cana-1744 227 62 ( ( PUNCT cana-1744 227 63 74 74 NUM cana-1744 227 64 ) ) PUNCT cana-1744 227 65 the the DET cana-1744 227 66 eqn eqn NOUN cana-1744 227 67 ( ( PUNCT cana-1744 227 68 74 74 NUM cana-1744 227 69 ) ) PUNCT cana-1744 227 70 means mean VERB cana-1744 227 71 the the DET cana-1744 227 72 number number NOUN cana-1744 227 73 of of ADP cana-1744 227 74 patrons patron NOUN cana-1744 227 75 in in ADP cana-1744 227 76 the the DET cana-1744 227 77 group group NOUN cana-1744 227 78 , , PUNCT cana-1744 227 79 and and CCONJ cana-1744 227 80 the the DET cana-1744 227 81 server server NOUN cana-1744 227 82 is be AUX cana-1744 227 83 free free ADJ cana-1744 227 84 . . PUNCT cana-1744 228 1 𝑃1(𝑍 𝑃1(𝑍 NOUN cana-1744 228 2 ) ) PUNCT cana-1744 228 3 = = SYM cana-1744 228 4 𝑃00 𝑃00 PROPN cana-1744 228 5 ( ( PUNCT cana-1744 228 6 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 228 7 ) ) PUNCT cana-1744 228 8 1 1 NUM cana-1744 228 9 − − PROPN cana-1744 228 10 ( ( PUNCT cana-1744 228 11 λ λ INTJ cana-1744 228 12 × × NOUN cana-1744 228 13 ( ( PUNCT cana-1744 228 14 1 1 NUM cana-1744 228 15 + + CCONJ cana-1744 228 16 δ)𝑍 δ)𝑍 VERB cana-1744 228 17 𝜒 𝜒 X cana-1744 228 18 ) ) PUNCT cana-1744 228 19 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 228 20 ) ) PUNCT cana-1744 228 21 ) ) PUNCT cana-1744 229 1 = = SYM cana-1744 229 2 𝑃00 𝑃00 PROPN cana-1744 229 3 ( ( PUNCT cana-1744 229 4 ( ( PUNCT cana-1744 229 5 𝑟 𝑟 NOUN cana-1744 229 6 + + CCONJ cana-1744 229 7 𝜌 𝜌 X cana-1744 229 8 − − PROPN cana-1744 229 9 𝜌𝑍)𝑟 𝜌𝑍)𝑟 PROPN cana-1744 229 10 − − PROPN cana-1744 229 11 𝑟𝑟 𝑟𝑟 INTJ cana-1744 229 12 𝑟𝑟 𝑟𝑟 ADP cana-1744 229 13 − − PROPN cana-1744 229 14 𝑍(𝑟 𝑍(𝑟 X cana-1744 229 15 + + CCONJ cana-1744 229 16 𝜌 𝜌 X cana-1744 229 17 − − PROPN cana-1744 229 18 𝜌𝑍)𝑟 𝜌𝑍)𝑟 PROPN cana-1744 229 19 1 1 NUM cana-1744 229 20 − − PROPN cana-1744 229 21 ( ( PUNCT cana-1744 229 22 λ λ INTJ cana-1744 229 23 × × NOUN cana-1744 229 24 ( ( PUNCT cana-1744 229 25 1 1 NUM cana-1744 229 26 + + CCONJ cana-1744 229 27 δ)𝑍 δ)𝑍 NOUN cana-1744 229 28 𝜒 𝜒 X cana-1744 229 29 ) ) PUNCT cana-1744 229 30 ( ( PUNCT cana-1744 229 31 ( ( PUNCT cana-1744 229 32 𝑟 𝑟 NOUN cana-1744 229 33 + + CCONJ cana-1744 229 34 𝜌 𝜌 X cana-1744 229 35 − − NOUN cana-1744 229 36 𝜌𝑧)𝑘 𝜌𝑧)𝑘 PROPN cana-1744 229 37 − − NOUN cana-1744 230 1 𝑟𝑟 𝑟𝑟 INTJ cana-1744 230 2 𝑟𝑟 𝑟𝑟 ADP cana-1744 230 3 − − PROPN cana-1744 230 4 𝑍(𝑟 𝑍(𝑟 X cana-1744 231 1 + + CCONJ cana-1744 231 2 𝜌 𝜌 X cana-1744 231 3 − − PROPN cana-1744 231 4 𝜌𝑍)𝑟 𝜌𝑍)𝑟 PROPN cana-1744 231 5 ) ) PUNCT cana-1744 231 6 ) ) PUNCT cana-1744 232 1 ( ( PUNCT cana-1744 232 2 75 75 X cana-1744 232 3 ) ) PUNCT cana-1744 232 4 hereafter hereafter ADV cana-1744 232 5 the the DET cana-1744 232 6 solution solution NOUN cana-1744 232 7 of of ADP cana-1744 232 8 equation equation NOUN cana-1744 232 9 ( ( PUNCT cana-1744 232 10 75 75 NUM cana-1744 232 11 ) ) PUNCT cana-1744 232 12 , , PUNCT cana-1744 232 13 we we PRON cana-1744 232 14 obtain obtain VERB cana-1744 232 15 𝑃1(𝑍 𝑃1(𝑍 PROPN cana-1744 232 16 ) ) PUNCT cana-1744 232 17 = = SYM cana-1744 232 18 𝑃00 𝑃00 PROPN cana-1744 232 19 ∗ ∗ NOUN cana-1744 232 20 ( ( PUNCT cana-1744 232 21 ( ( PUNCT cana-1744 232 22 1 1 NUM cana-1744 232 23 + + SYM cana-1744 232 24 1 1 NUM cana-1744 232 25 𝑟 𝑟 NOUN cana-1744 232 26 ∗ ∗ NOUN cana-1744 232 27 ( ( PUNCT cana-1744 232 28 𝜌 𝜌 X cana-1744 232 29 − − ADP cana-1744 232 30 𝜌 𝜌 ADP cana-1744 232 31 ∗ ∗ X cana-1744 232 32 𝑍 𝑍 NOUN cana-1744 232 33 ) ) PUNCT cana-1744 232 34 ) ) PUNCT cana-1744 232 35 𝑟 𝑟 X cana-1744 233 1 − − NOUN cana-1744 233 2 1 1 NUM cana-1744 233 3 1 1 NUM cana-1744 233 4 + + NUM cana-1744 233 5 𝑍 𝑍 PROPN cana-1744 233 6 ∗ ∗ NOUN cana-1744 233 7 ( ( PUNCT cana-1744 233 8 λ λ X cana-1744 233 9 × × NOUN cana-1744 233 10 ( ( PUNCT cana-1744 233 11 1 1 NUM cana-1744 233 12 + + CCONJ cana-1744 233 13 δ δ PROPN cana-1744 233 14 ) ) PUNCT cana-1744 233 15 𝜒 𝜒 PART cana-1744 233 16 − − PROPN cana-1744 233 17 𝜌1 𝜌1 NOUN cana-1744 233 18 𝜌 𝜌 X cana-1744 233 19 ( ( PUNCT cana-1744 233 20 1 1 NUM cana-1744 233 21 + + SYM cana-1744 233 22 1 1 NUM cana-1744 233 23 𝑟 𝑟 NOUN cana-1744 233 24 ( ( PUNCT cana-1744 233 25 𝜌 𝜌 X cana-1744 233 26 − − ADP cana-1744 233 27 𝜌𝑍 𝜌𝑍 NOUN cana-1744 233 28 ) ) PUNCT cana-1744 233 29 ) ) PUNCT cana-1744 233 30 𝑟 𝑟 NOUN cana-1744 233 31 ) ) PUNCT cana-1744 233 32 ) ) PUNCT cana-1744 234 1 ( ( PUNCT cana-1744 234 2 76 76 NUM cana-1744 234 3 ) ) PUNCT cana-1744 234 4 the the DET cana-1744 234 5 eqn eqn NOUN cana-1744 234 6 ( ( PUNCT cana-1744 234 7 76 76 NUM cana-1744 234 8 ) ) PUNCT cana-1744 234 9 means mean VERB cana-1744 234 10 the the DET cana-1744 234 11 number number NOUN cana-1744 234 12 of of ADP cana-1744 234 13 patrons patron NOUN cana-1744 234 14 in in ADP cana-1744 234 15 the the DET cana-1744 234 16 group group NOUN cana-1744 234 17 , , PUNCT cana-1744 234 18 and and CCONJ cana-1744 234 19 the the DET cana-1744 234 20 server server NOUN cana-1744 234 21 is be AUX cana-1744 234 22 engaged engage VERB cana-1744 234 23 . . PUNCT cana-1744 235 1 communications communication NOUN cana-1744 235 2 on on ADP cana-1744 235 3 applied apply VERB cana-1744 235 4 nonlinear nonlinear ADJ cana-1744 235 5 analysis analysis NOUN cana-1744 235 6 issn issn NOUN cana-1744 235 7 : : PUNCT cana-1744 235 8 1074 1074 NUM cana-1744 235 9 - - PUNCT cana-1744 235 10 133x 133x NUM cana-1744 235 11 vol vol NOUN cana-1744 235 12 32 32 NUM cana-1744 235 13 no no NOUN cana-1744 235 14 . . NOUN cana-1744 235 15 2 2 NUM cana-1744 235 16 ( ( PUNCT cana-1744 235 17 2025 2025 NUM cana-1744 235 18 ) ) PUNCT cana-1744 235 19 318 318 NUM cana-1744 235 20 https://internationalpubls.com https://internationalpubls.com X cana-1744 235 21 l𝑞 l𝑞 VERB cana-1744 235 22 = = SYM cana-1744 235 23 1 1 NUM cana-1744 235 24 ( ( PUNCT cana-1744 235 25 1 1 NUM cana-1744 235 26 − − PROPN cana-1744 235 27 𝜌1 𝜌1 NOUN cana-1744 235 28 ) ) PUNCT cana-1744 235 29 ∗ ∗ NOUN cana-1744 235 30 ( ( PUNCT cana-1744 235 31 ( ( PUNCT cana-1744 235 32 λ λ INTJ cana-1744 235 33 × × NOUN cana-1744 235 34 ( ( PUNCT cana-1744 235 35 1 1 NUM cana-1744 236 1 + + NUM cana-1744 236 2 δ))2 δ))2 PROPN cana-1744 236 3 ∗ ∗ NOUN cana-1744 236 4 𝐸(𝑌2 𝐸(𝑌2 SYM cana-1744 236 5 ) ) PUNCT cana-1744 236 6 2 2 NUM cana-1744 236 7 ∗ ∗ NOUN cana-1744 236 8 ( ( PUNCT cana-1744 236 9 1 1 NUM cana-1744 236 10 + + NUM cana-1744 236 11 λ λ PROPN cana-1744 236 12 × × NOUN cana-1744 236 13 ( ( PUNCT cana-1744 236 14 1 1 NUM cana-1744 236 15 + + CCONJ cana-1744 236 16 δ δ PROPN cana-1744 236 17 ) ) PUNCT cana-1744 236 18 𝜒 𝜒 NOUN cana-1744 236 19 ) ) PUNCT cana-1744 237 1 + + CCONJ cana-1744 237 2 λ λ X cana-1744 237 3 × × NOUN cana-1744 237 4 ( ( PUNCT cana-1744 237 5 1 1 NUM cana-1744 237 6 + + NUM cana-1744 237 7 δ δ PROPN cana-1744 237 8 ) ) PUNCT cana-1744 237 9 ∗ ∗ VERB cana-1744 237 10 𝜌 𝜌 X cana-1744 237 11 𝜒 𝜒 X cana-1744 237 12 ) ) PUNCT cana-1744 237 13 = = SYM cana-1744 237 14 1 1 NUM cana-1744 237 15 ( ( PUNCT cana-1744 237 16 1 1 NUM cana-1744 237 17 − − PROPN cana-1744 237 18 𝜌1 𝜌1 NOUN cana-1744 237 19 ) ) PUNCT cana-1744 237 20 ( ( PUNCT cana-1744 237 21 ( ( PUNCT cana-1744 237 22 λ λ INTJ cana-1744 237 23 × × NOUN cana-1744 237 24 ( ( PUNCT cana-1744 237 25 1 1 NUM cana-1744 237 26 + + NUM cana-1744 237 27 δ))2 δ))2 PROPN cana-1744 237 28 ( ( PUNCT cana-1744 237 29 𝑟(𝑟 𝑟(𝑟 NOUN cana-1744 237 30 + + NOUN cana-1744 237 31 1 1 X cana-1744 237 32 ) ) PUNCT cana-1744 237 33 𝜇2 𝜇2 NOUN cana-1744 237 34 ) ) PUNCT cana-1744 237 35 2 2 NUM cana-1744 237 36 ( ( PUNCT cana-1744 237 37 1 1 NUM cana-1744 238 1 + + NUM cana-1744 238 2 λ λ PROPN cana-1744 238 3 × × NOUN cana-1744 238 4 ( ( PUNCT cana-1744 238 5 1 1 NUM cana-1744 238 6 + + CCONJ cana-1744 238 7 δ δ PROPN cana-1744 238 8 ) ) PUNCT cana-1744 238 9 𝜒 𝜒 NOUN cana-1744 238 10 ) ) PUNCT cana-1744 239 1 + + CCONJ cana-1744 239 2 λ λ X cana-1744 239 3 × × NOUN cana-1744 239 4 ( ( PUNCT cana-1744 239 5 1 1 NUM cana-1744 239 6 + + CCONJ cana-1744 239 7 δ)𝜌 δ)𝜌 X cana-1744 239 8 𝜒 𝜒 X cana-1744 239 9 ) ) PUNCT cana-1744 239 10 ( ( PUNCT cana-1744 239 11 77 77 X cana-1744 239 12 ) ) PUNCT cana-1744 239 13 hereafter hereafter NOUN cana-1744 239 14 the the DET cana-1744 239 15 solution solution NOUN cana-1744 239 16 of of ADP cana-1744 239 17 equation equation NOUN cana-1744 239 18 ( ( PUNCT cana-1744 239 19 77 77 NUM cana-1744 239 20 ) ) PUNCT cana-1744 239 21 , , PUNCT cana-1744 239 22 we we PRON cana-1744 239 23 obtain obtain VERB cana-1744 239 24 l𝑞 l𝑞 PRON cana-1744 239 25 = = SYM cana-1744 239 26 1 1 NUM cana-1744 239 27 ( ( PUNCT cana-1744 239 28 1 1 NUM cana-1744 239 29 − − PROPN cana-1744 239 30 𝜌1 𝜌1 NOUN cana-1744 239 31 ) ) PUNCT cana-1744 239 32 ( ( PUNCT cana-1744 239 33 𝜆2 𝜆2 NOUN cana-1744 239 34 ( ( PUNCT cana-1744 239 35 𝑟(𝑟 𝑟(𝑟 PROPN cana-1744 239 36 + + NOUN cana-1744 239 37 1 1 X cana-1744 239 38 ) ) PUNCT cana-1744 239 39 𝜇2 𝜇2 NOUN cana-1744 239 40 ) ) PUNCT cana-1744 239 41 2 2 NUM cana-1744 239 42 ( ( PUNCT cana-1744 239 43 1 1 NUM cana-1744 239 44 + + NUM cana-1744 239 45 λ λ PROPN cana-1744 239 46 × × NOUN cana-1744 239 47 ( ( PUNCT cana-1744 239 48 1 1 NUM cana-1744 239 49 + + CCONJ cana-1744 239 50 δ δ PROPN cana-1744 239 51 ) ) PUNCT cana-1744 239 52 𝜒 𝜒 NOUN cana-1744 239 53 ) ) PUNCT cana-1744 240 1 + + CCONJ cana-1744 240 2 𝜆𝜌 𝜆𝜌 X cana-1744 240 3 𝜒 𝜒 X cana-1744 240 4 ) ) PUNCT cana-1744 240 5 ( ( PUNCT cana-1744 240 6 78 78 NUM cana-1744 240 7 ) ) PUNCT cana-1744 240 8 the the DET cana-1744 240 9 eqn eqn NOUN cana-1744 240 10 ( ( PUNCT cana-1744 240 11 78 78 NUM cana-1744 240 12 ) ) PUNCT cana-1744 240 13 means mean VERB cana-1744 240 14 the the DET cana-1744 240 15 number number NOUN cana-1744 240 16 of of ADP cana-1744 240 17 patrons patron NOUN cana-1744 240 18 in in ADP cana-1744 240 19 the the DET cana-1744 240 20 group group NOUN cana-1744 240 21 . . PUNCT cana-1744 241 1 l𝑠 l𝑠 PROPN cana-1744 241 2 = = PUNCT cana-1744 241 3 l𝑞 l𝑞 PROPN cana-1744 241 4 + + X cana-1744 241 5 𝜌 𝜌 X cana-1744 241 6 = = SYM cana-1744 241 7 1 1 NUM cana-1744 241 8 ( ( PUNCT cana-1744 241 9 1 1 NUM cana-1744 241 10 − − PROPN cana-1744 241 11 𝜌1 𝜌1 NOUN cana-1744 241 12 ) ) PUNCT cana-1744 241 13 ( ( PUNCT cana-1744 241 14 ( ( PUNCT cana-1744 241 15 λ λ INTJ cana-1744 241 16 × × NOUN cana-1744 241 17 ( ( PUNCT cana-1744 241 18 1 1 NUM cana-1744 241 19 + + NUM cana-1744 241 20 δ))2 δ))2 PROPN cana-1744 241 21 ( ( PUNCT cana-1744 241 22 𝑟(𝑟 𝑟(𝑟 NOUN cana-1744 241 23 + + NOUN cana-1744 241 24 1 1 X cana-1744 241 25 ) ) PUNCT cana-1744 241 26 𝜇2 𝜇2 NOUN cana-1744 241 27 ) ) PUNCT cana-1744 241 28 2 2 NUM cana-1744 241 29 ( ( PUNCT cana-1744 241 30 1 1 NUM cana-1744 242 1 + + NUM cana-1744 242 2 λ λ PROPN cana-1744 242 3 × × NOUN cana-1744 242 4 ( ( PUNCT cana-1744 242 5 1 1 NUM cana-1744 242 6 + + CCONJ cana-1744 242 7 δ δ PROPN cana-1744 242 8 ) ) PUNCT cana-1744 242 9 𝜒 𝜒 NOUN cana-1744 242 10 ) ) PUNCT cana-1744 243 1 + + CCONJ cana-1744 243 2 λ λ X cana-1744 243 3 × × NOUN cana-1744 243 4 ( ( PUNCT cana-1744 243 5 1 1 NUM cana-1744 243 6 + + CCONJ cana-1744 243 7 δ)𝜌 δ)𝜌 X cana-1744 243 8 𝜒 𝜒 X cana-1744 243 9 ) ) PUNCT cana-1744 243 10 + + CCONJ cana-1744 243 11 𝜌 𝜌 X cana-1744 243 12 ( ( PUNCT cana-1744 243 13 79 79 NUM cana-1744 243 14 ) ) PUNCT cana-1744 243 15 the the DET cana-1744 243 16 eqn eqn NOUN cana-1744 243 17 ( ( PUNCT cana-1744 243 18 79 79 NUM cana-1744 243 19 ) ) PUNCT cana-1744 243 20 means mean VERB cana-1744 243 21 the the DET cana-1744 243 22 number number NOUN cana-1744 243 23 of of ADP cana-1744 243 24 patrons patron NOUN cana-1744 243 25 in in ADP cana-1744 243 26 the the DET cana-1744 243 27 system system NOUN cana-1744 243 28 . . PUNCT cana-1744 244 1 privilege-3 privilege-3 NOUN cana-1744 244 2 : : PUNCT cana-1744 244 3 as as ADP cana-1744 244 4 𝜒 𝜒 X cana-1744 244 5 → → SYM cana-1744 244 6 ∞ ∞ PROPN cana-1744 244 7 , , PUNCT cana-1744 244 8 single single ADJ cana-1744 244 9 server server NOUN cana-1744 244 10 markovian markovian PROPN cana-1744 244 11 general general PROPN cana-1744 244 12 service service PROPN cana-1744 244 13 encouraged encourage VERB cana-1744 244 14 arrival arrival NOUN cana-1744 244 15 queuing queuing NOUN cana-1744 244 16 model model NOUN cana-1744 244 17 the the DET cana-1744 244 18 number number NOUN cana-1744 244 19 of of ADP cana-1744 244 20 patrons patron NOUN cana-1744 244 21 in in ADP cana-1744 244 22 the the DET cana-1744 244 23 system system NOUN cana-1744 244 24 is be AUX cana-1744 244 25 provided provide VERB cana-1744 244 26 by by ADP cana-1744 244 27 𝑃(𝑍 𝑃(𝑍 NOUN cana-1744 244 28 ) ) PUNCT cana-1744 244 29 = = SYM cana-1744 244 30 𝑃0(𝑍 𝑃0(𝑍 ADV cana-1744 244 31 ) ) PUNCT cana-1744 245 1 + + CCONJ cana-1744 245 2 𝑍 𝑍 PROPN cana-1744 245 3 ∗ ∗ NOUN cana-1744 245 4 𝑃1(𝑍 𝑃1(𝑍 PROPN cana-1744 245 5 ) ) PUNCT cana-1744 246 1 = = PRON cana-1744 246 2 𝑝00 𝑝00 VERB cana-1744 246 3 1 1 NUM cana-1744 246 4 − − PROPN cana-1744 246 5 ( ( PUNCT cana-1744 246 6 λ λ INTJ cana-1744 246 7 × × NOUN cana-1744 246 8 ( ( PUNCT cana-1744 246 9 1 1 NUM cana-1744 246 10 + + CCONJ cana-1744 246 11 δ)𝑍 δ)𝑍 VERB cana-1744 246 12 𝜒 𝜒 X cana-1744 246 13 ) ) PUNCT cana-1744 246 14 ∗ ∗ NOUN cana-1744 246 15 𝛿(𝑍 𝛿(𝑍 NUM cana-1744 246 16 ) ) PUNCT cana-1744 247 1 + + CCONJ cana-1744 247 2 𝑍 𝑍 PROPN cana-1744 247 3 ∗ ∗ NOUN cana-1744 247 4 𝑃00 𝑃00 PROPN cana-1744 247 5 ( ( PUNCT cana-1744 247 6 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 247 7 ) ) PUNCT cana-1744 247 8 1 1 NUM cana-1744 247 9 − − PROPN cana-1744 247 10 ( ( PUNCT cana-1744 247 11 λ λ INTJ cana-1744 247 12 × × NOUN cana-1744 247 13 ( ( PUNCT cana-1744 247 14 1 1 NUM cana-1744 247 15 + + CCONJ cana-1744 247 16 δ)𝑍 δ)𝑍 VERB cana-1744 247 17 𝜒 𝜒 X cana-1744 247 18 ) ) PUNCT cana-1744 247 19 𝛿(𝑍 𝛿(𝑍 PROPN cana-1744 247 20 ) ) PUNCT cana-1744 247 21 ) ) PUNCT cana-1744 247 22 ( ( PUNCT cana-1744 247 23 80 80 NUM cana-1744 247 24 ) ) PUNCT cana-1744 247 25 as as ADP cana-1744 247 26 𝜒 𝜒 X cana-1744 247 27 → → SYM cana-1744 247 28 ∞ ∞ PROPN cana-1744 247 29 , , PUNCT cana-1744 247 30 the the DET cana-1744 247 31 equation equation NOUN cana-1744 247 32 ( ( PUNCT cana-1744 247 33 80 80 NUM cana-1744 247 34 ) ) PUNCT cana-1744 247 35 , , PUNCT cana-1744 247 36 we we PRON cana-1744 247 37 have have VERB cana-1744 247 38 communications communication NOUN cana-1744 247 39 on on ADP cana-1744 247 40 applied apply VERB cana-1744 247 41 nonlinear nonlinear ADJ cana-1744 247 42 analysis analysis NOUN cana-1744 247 43 issn issn NOUN cana-1744 247 44 : : PUNCT cana-1744 247 45 1074 1074 NUM cana-1744 247 46 - - PUNCT cana-1744 247 47 133x 133x NUM cana-1744 247 48 vol vol NOUN cana-1744 247 49 32 32 NUM cana-1744 248 1 no no NOUN cana-1744 248 2 . . NOUN cana-1744 248 3 2 2 NUM cana-1744 248 4 ( ( PUNCT cana-1744 248 5 2025 2025 NUM cana-1744 248 6 ) ) PUNCT cana-1744 248 7 319 319 NUM cana-1744 248 8 https://internationalpubls.com https://internationalpubls.com X cana-1744 248 9 𝑃(𝑍 𝑃(𝑍 NUM cana-1744 248 10 ) ) PUNCT cana-1744 248 11 = = PUNCT cana-1744 248 12 𝑃0(𝑍 𝑃0(𝑍 ADV cana-1744 248 13 ) ) PUNCT cana-1744 249 1 + + CCONJ cana-1744 249 2 𝑍 𝑍 PROPN cana-1744 249 3 ∗ ∗ NOUN cana-1744 249 4 𝑃1(𝑍 𝑃1(𝑍 PROPN cana-1744 249 5 ) ) PUNCT cana-1744 249 6 = = SYM cana-1744 249 7 𝑃00 𝑃00 PROPN cana-1744 249 8 ∗ ∗ NOUN cana-1744 249 9 ( ( PUNCT cana-1744 249 10 1 1 NUM cana-1744 249 11 + + CCONJ cana-1744 249 12 𝑍𝛿(𝑍 𝑍𝛿(𝑍 NOUN cana-1744 249 13 ) ) PUNCT cana-1744 249 14 ) ) PUNCT cana-1744 250 1 = = SYM cana-1744 250 2 𝑃00 𝑃00 PROPN cana-1744 250 3 ∗ ∗ NOUN cana-1744 250 4 ( ( PUNCT cana-1744 250 5 1 1 NUM cana-1744 250 6 + + CCONJ cana-1744 250 7 𝑍 𝑍 PROPN cana-1744 250 8 ( ( PUNCT cana-1744 250 9 1 1 NUM cana-1744 250 10 − − NOUN cana-1744 250 11 𝑎‾ 𝑎‾ ADV cana-1744 250 12 𝑎‾ 𝑎‾ NOUN cana-1744 250 13 − − PROPN cana-1744 250 14 𝑍 𝑍 PROPN cana-1744 250 15 ) ) PUNCT cana-1744 250 16 ) ) PUNCT cana-1744 250 17 𝑃00 𝑃00 PROPN cana-1744 250 18 ∗ ∗ NOUN cana-1744 250 19 ( ( PUNCT cana-1744 250 20 1 1 NUM cana-1744 250 21 + + CCONJ cana-1744 250 22 𝑍 𝑍 PROPN cana-1744 250 23 ( ( PUNCT cana-1744 250 24 1 1 NUM cana-1744 250 25 − − NOUN cana-1744 250 26 𝑎‾ 𝑎‾ ADV cana-1744 250 27 𝑎‾ 𝑎‾ NOUN cana-1744 250 28 − − PROPN cana-1744 250 29 𝑍 𝑍 PROPN cana-1744 250 30 ) ) PUNCT cana-1744 250 31 ) ) PUNCT cana-1744 251 1 = = SYM cana-1744 251 2 𝑃00 𝑃00 X cana-1744 251 3 𝑎‾(1 𝑎‾(1 ADV cana-1744 251 4 − − PROPN cana-1744 251 5 𝑍 𝑍 NOUN cana-1744 251 6 ) ) PUNCT cana-1744 251 7 𝑎‾ 𝑎‾ ADV cana-1744 251 8 − − PROPN cana-1744 251 9 𝑍 𝑍 PROPN cana-1744 251 10 𝑃00 𝑃00 NOUN cana-1744 251 11 = = SYM cana-1744 251 12 1 1 NUM cana-1744 251 13 − − PROPN cana-1744 252 1 λ λ INTJ cana-1744 252 2 × × NOUN cana-1744 252 3 ( ( PUNCT cana-1744 252 4 1 1 NUM cana-1744 252 5 + + NUM cana-1744 252 6 δ δ NOUN cana-1744 252 7 ) ) PUNCT cana-1744 252 8 ( ( PUNCT cana-1744 252 9 ( ( PUNCT cana-1744 252 10 λ λ INTJ cana-1744 252 11 × × NOUN cana-1744 252 12 ( ( PUNCT cana-1744 252 13 1 1 NUM cana-1744 252 14 + + CCONJ cana-1744 252 15 δ δ NOUN cana-1744 252 16 ) ) PUNCT cana-1744 252 17 ) ) PUNCT cana-1744 253 1 + + CCONJ cana-1744 253 2 𝜎 𝜎 X cana-1744 253 3 ) ) PUNCT cana-1744 253 4 𝜒 𝜒 NOUN cana-1744 253 5 ∗ ∗ NOUN cana-1744 253 6 𝐸(𝑌 𝐸(𝑌 NOUN cana-1744 253 7 ) ) PUNCT cana-1744 253 8 = = SYM cana-1744 254 1 1 1 NUM cana-1744 254 2 − − NOUN cana-1744 255 1 λ λ INTJ cana-1744 256 1 × × NOUN cana-1744 257 1 ( ( PUNCT cana-1744 258 1 1 1 NUM cana-1744 258 2 + + NUM cana-1744 258 3 δ)𝐸(𝑌 δ)𝐸(𝑌 NOUN cana-1744 258 4 ) ) PUNCT cana-1744 258 5 ( ( PUNCT cana-1744 258 6 81 81 NUM cana-1744 258 7 ) ) PUNCT cana-1744 258 8 𝑃(𝑍 𝑃(𝑍 NUM cana-1744 258 9 ) ) PUNCT cana-1744 258 10 = = PUNCT cana-1744 259 1 ( ( PUNCT cana-1744 259 2 1 1 NUM cana-1744 259 3 − − PROPN cana-1744 259 4 λ λ INTJ cana-1744 259 5 × × NOUN cana-1744 259 6 ( ( PUNCT cana-1744 259 7 1 1 NUM cana-1744 259 8 + + NUM cana-1744 259 9 δ)𝐸(𝑌))(1 δ)𝐸(𝑌))(1 NOUN cana-1744 260 1 − − ADP cana-1744 260 2 𝑍)𝑎‾(λ 𝑍)𝑎‾(λ PROPN cana-1744 260 3 × × NOUN cana-1744 260 4 ( ( PUNCT cana-1744 260 5 1 1 NUM cana-1744 260 6 + + NUM cana-1744 260 7 δ δ NOUN cana-1744 260 8 ) ) PUNCT cana-1744 260 9 − − PROPN cana-1744 261 1 λ λ INTJ cana-1744 261 2 × × NOUN cana-1744 261 3 ( ( PUNCT cana-1744 261 4 1 1 NUM cana-1744 261 5 + + CCONJ cana-1744 261 6 δ δ PROPN cana-1744 261 7 ) ) PUNCT cana-1744 261 8 ∗ ∗ NOUN cana-1744 261 9 𝑍 𝑍 PROPN cana-1744 261 10 ) ) PUNCT cana-1744 261 11 𝑎‾(λ 𝑎‾(λ PROPN cana-1744 261 12 × × NOUN cana-1744 261 13 ( ( PUNCT cana-1744 261 14 1 1 NUM cana-1744 261 15 + + NUM cana-1744 261 16 δ δ NOUN cana-1744 261 17 ) ) PUNCT cana-1744 261 18 − − PROPN cana-1744 262 1 λ λ INTJ cana-1744 262 2 × × NOUN cana-1744 262 3 ( ( PUNCT cana-1744 262 4 1 1 NUM cana-1744 262 5 + + CCONJ cana-1744 262 6 δ δ PROPN cana-1744 262 7 ) ) PUNCT cana-1744 262 8 ∗ ∗ NOUN cana-1744 262 9 𝑍 𝑍 PROPN cana-1744 262 10 ) ) PUNCT cana-1744 262 11 − − NOUN cana-1744 262 12 𝑍 𝑍 PROPN cana-1744 262 13 ( ( PUNCT cana-1744 262 14 82 82 NUM cana-1744 262 15 ) ) PUNCT cana-1744 262 16 the the DET cana-1744 262 17 eqn eqn NOUN cana-1744 262 18 ( ( PUNCT cana-1744 262 19 82 82 NUM cana-1744 262 20 ) ) PUNCT cana-1744 262 21 means mean VERB cana-1744 262 22 the the DET cana-1744 262 23 pollaczek pollaczek ADJ cana-1744 262 24 khinchine khinchine ADJ cana-1744 262 25 equation equation NOUN cana-1744 262 26 for for ADP cana-1744 262 27 single single ADJ cana-1744 262 28 server server NOUN cana-1744 262 29 markovian markovian PROPN cana-1744 262 30 general general PROPN cana-1744 262 31 service service PROPN cana-1744 262 32 encouraged encourage VERB cana-1744 262 33 arrival arrival NOUN cana-1744 262 34 queuing queue VERB cana-1744 262 35 model model NOUN cana-1744 262 36 l𝑞 l𝑞 PROPN cana-1744 262 37 = = SYM cana-1744 262 38 𝑃00 𝑃00 PROPN cana-1744 262 39 ( ( PUNCT cana-1744 262 40 1 1 NUM cana-1744 262 41 − − NUM cana-1744 262 42 𝜌1)2 𝜌1)2 NUM cana-1744 262 43 ( ( PUNCT cana-1744 262 44 ( ( PUNCT cana-1744 262 45 λ λ INTJ cana-1744 262 46 × × NOUN cana-1744 262 47 ( ( PUNCT cana-1744 262 48 1 1 NUM cana-1744 262 49 + + NUM cana-1744 262 50 δ))2𝐸(𝑌2 δ))2𝐸(𝑌2 ADJ cana-1744 262 51 ) ) PUNCT cana-1744 262 52 2 2 NUM cana-1744 262 53 ( ( PUNCT cana-1744 262 54 1 1 NUM cana-1744 262 55 + + NUM cana-1744 262 56 λ λ PROPN cana-1744 262 57 × × NOUN cana-1744 262 58 ( ( PUNCT cana-1744 262 59 1 1 NUM cana-1744 262 60 + + CCONJ cana-1744 262 61 δ δ PROPN cana-1744 262 62 ) ) PUNCT cana-1744 262 63 𝜒 𝜒 NOUN cana-1744 262 64 ) ) PUNCT cana-1744 263 1 + + CCONJ cana-1744 264 1 λ λ X cana-1744 264 2 × × NOUN cana-1744 264 3 ( ( PUNCT cana-1744 264 4 1 1 NUM cana-1744 264 5 + + CCONJ cana-1744 264 6 δ)𝜌 δ)𝜌 X cana-1744 264 7 𝜒 𝜒 X cana-1744 264 8 ) ) PUNCT cana-1744 264 9 = = SYM cana-1744 264 10 ( ( PUNCT cana-1744 264 11 λ λ INTJ cana-1744 264 12 × × NOUN cana-1744 264 13 ( ( PUNCT cana-1744 264 14 1 1 NUM cana-1744 264 15 + + NUM cana-1744 264 16 δ))2𝐸(𝑌2 δ))2𝐸(𝑌2 NUM cana-1744 264 17 ) ) PUNCT cana-1744 264 18 2(1 2(1 NUM cana-1744 264 19 − − NOUN cana-1744 264 20 𝜌 𝜌 NOUN cana-1744 264 21 ) ) PUNCT cana-1744 264 22 ( ( PUNCT cana-1744 264 23 83 83 NUM cana-1744 264 24 ) ) PUNCT cana-1744 264 25 the the DET cana-1744 264 26 eqn eqn NOUN cana-1744 264 27 ( ( PUNCT cana-1744 264 28 83 83 NUM cana-1744 264 29 ) ) PUNCT cana-1744 264 30 means mean VERB cana-1744 264 31 the the DET cana-1744 264 32 mean mean ADJ cana-1744 264 33 number number NOUN cana-1744 264 34 of of ADP cana-1744 264 35 patrons patron NOUN cana-1744 264 36 in in ADP cana-1744 264 37 the the DET cana-1744 264 38 line line NOUN cana-1744 264 39 . . PUNCT cana-1744 265 1 6 6 X cana-1744 265 2 . . X cana-1744 265 3 numerical numerical PROPN cana-1744 265 4 study study PROPN cana-1744 265 5 the the DET cana-1744 265 6 parameters parameter NOUN cana-1744 265 7 λ λ X cana-1744 265 8 × × NOUN cana-1744 265 9 ( ( PUNCT cana-1744 265 10 1 1 NUM cana-1744 265 11 + + CCONJ cana-1744 265 12 δ δ PROPN cana-1744 265 13 ) ) PUNCT cana-1744 265 14 , , PUNCT cana-1744 265 15 𝜇 𝜇 ADP cana-1744 265 16 and and CCONJ cana-1744 265 17 𝜒 𝜒 NOUN cana-1744 265 18 will will AUX cana-1744 265 19 be be AUX cana-1744 265 20 verified verify VERB cana-1744 265 21 the the DET cana-1744 265 22 stability stability NOUN cana-1744 265 23 condition condition NOUN cana-1744 265 24 . . PUNCT cana-1744 266 1 the the DET cana-1744 266 2 performance performance NOUN cana-1744 266 3 metrics metric NOUN cana-1744 266 4 of of ADP cana-1744 266 5 this this PRON cana-1744 266 6 are be AUX cana-1744 266 7 expressed express VERB cana-1744 266 8 in in ADP cana-1744 266 9 tables table NOUN cana-1744 266 10 for for ADP cana-1744 266 11 different different ADJ cana-1744 266 12 service service NOUN cana-1744 266 13 distributions distribution NOUN cana-1744 266 14 . . PUNCT cana-1744 267 1 λ λ X cana-1744 267 2 δ δ X cana-1744 267 3 λ λ X cana-1744 267 4 × × NOUN cana-1744 267 5 ( ( PUNCT cana-1744 267 6 1 1 NUM cana-1744 267 7 + + NUM cana-1744 267 8 δ δ NOUN cana-1744 267 9 ) ) PUNCT cana-1744 267 10 𝜇 𝜇 ADP cana-1744 267 11 𝜒 𝜒 X cana-1744 267 12 5 5 NUM cana-1744 267 13 0.1 0.1 NUM cana-1744 267 14 5.5 5.5 NUM cana-1744 267 15 10 10 NUM cana-1744 267 16 10,30,50,70, 10,30,50,70, NUM cana-1744 267 17 … … SYM cana-1744 267 18 5000 5000 NUM cana-1744 267 19 table table NOUN cana-1744 267 20 1 1 NUM cana-1744 267 21 : : PUNCT cana-1744 267 22 performance performance NOUN cana-1744 267 23 metrics metric NOUN cana-1744 267 24 for for ADP cana-1744 267 25 λ λ PROPN cana-1744 267 26 × × NOUN cana-1744 267 27 ( ( PUNCT cana-1744 267 28 1 1 NUM cana-1744 267 29 + + CCONJ cana-1744 267 30 δ δ X cana-1744 267 31 ) ) PUNCT cana-1744 267 32 = = SYM cana-1744 267 33 5.5 5.5 NUM cana-1744 267 34 and and CCONJ cana-1744 267 35 𝜇 𝜇 X cana-1744 267 36 = = NOUN cana-1744 267 37 10 10 NUM cana-1744 267 38 for for ADP cana-1744 267 39 different different ADJ cana-1744 267 40 parameters parameter NOUN cana-1744 267 41 of of ADP cana-1744 267 42 𝜒. 𝜒. NOUN cana-1744 267 43 𝜒 𝜒 SYM cana-1744 267 44 p0 p0 NOUN cana-1744 267 45 p1 p1 NOUN cana-1744 267 46 lq lq VERB cana-1744 267 47 ls ls PROPN cana-1744 267 48 wq wq PROPN cana-1744 267 49 ws ws PROPN cana-1744 267 50 10 10 NUM cana-1744 267 51 0.5 0.5 NUM cana-1744 267 52 0.5 0.5 NUM cana-1744 267 53 5.2297 5.2297 NUM cana-1744 267 54 5.7797 5.7797 NUM cana-1744 267 55 0.9508 0.9508 NUM cana-1744 267 56 1.0508 1.0508 NUM cana-1744 267 57 30 30 NUM cana-1744 267 58 0.5 0.5 NUM cana-1744 267 59 0.5 0.5 NUM cana-1744 267 60 1.0174 1.0174 NUM cana-1744 267 61 1.8640 1.8640 NUM cana-1744 267 62 0.2389 0.2389 NUM cana-1744 267 63 0.3389 0.3389 NUM cana-1744 267 64 50 50 NUM cana-1744 267 65 0.5 0.5 NUM cana-1744 267 66 0.5 0.5 NUM cana-1744 267 67 1.0174 1.0174 NUM cana-1744 267 68 1.5674 1.5674 NUM cana-1744 267 69 0.1851 0.1851 NUM cana-1744 267 70 0 0 NUM cana-1744 267 71 .. .. SYM cana-1744 267 72 2850 2850 NUM cana-1744 267 73 70 70 NUM cana-1744 267 74 0.5 0.5 NUM cana-1744 267 75 0.5 0.5 NUM cana-1744 267 76 0.9083 0.9083 NUM cana-1744 267 77 1.4583 1.4583 NUM cana-1744 267 78 0.1651 0.1651 NUM cana-1744 267 79 0.2651 0.2651 NUM cana-1744 267 80 90 90 NUM cana-1744 267 81 0.5 0.5 NUM cana-1744 267 82 0.5 0.5 NUM cana-1744 267 83 0.8516 0.8516 NUM cana-1744 267 84 1.4016 1.4016 NUM cana-1744 267 85 0.1548 0.1548 NUM cana-1744 267 86 0.2548 0.2548 NUM cana-1744 267 87 100 100 NUM cana-1744 267 88 0.5 0.5 NUM cana-1744 267 89 0.5 0.5 NUM cana-1744 267 90 0.8324 0.8324 NUM cana-1744 267 91 1.3834 1.3834 NUM cana-1744 267 92 0.1513 0.1513 NUM cana-1744 267 93 0.2513 0.2513 NUM cana-1744 267 94 300 300 NUM cana-1744 267 95 0.5 0.5 NUM cana-1744 267 96 0.5 0.5 NUM cana-1744 267 97 0.7232 0.7232 NUM cana-1744 267 98 1.2732 1.2732 NUM cana-1744 267 99 0.1315 0.1315 NUM cana-1744 267 100 0.2315 0.2315 NUM cana-1744 267 101 500 500 NUM cana-1744 267 102 0.5 0.5 NUM cana-1744 267 103 0.5 0.5 NUM cana-1744 267 104 0.7025 0.7025 NUM cana-1744 267 105 1.2525 1.2525 NUM cana-1744 267 106 0.1277 0.1277 NUM cana-1744 267 107 0.2277 0.2277 NUM cana-1744 267 108 communications communication NOUN cana-1744 267 109 on on ADP cana-1744 267 110 applied apply VERB cana-1744 267 111 nonlinear nonlinear ADJ cana-1744 267 112 analysis analysis NOUN cana-1744 267 113 issn issn NOUN cana-1744 267 114 : : PUNCT cana-1744 267 115 1074 1074 NUM cana-1744 267 116 - - PUNCT cana-1744 267 117 133x 133x NUM cana-1744 267 118 vol vol NOUN cana-1744 267 119 32 32 NUM cana-1744 267 120 no no NOUN cana-1744 267 121 . . NOUN cana-1744 267 122 2 2 NUM cana-1744 267 123 ( ( PUNCT cana-1744 267 124 2025 2025 NUM cana-1744 267 125 ) ) PUNCT cana-1744 267 126 320 320 NUM cana-1744 267 127 https://internationalpubls.com https://internationalpubls.com X cana-1744 267 128 700 700 NUM cana-1744 267 129 0.5 0.5 NUM cana-1744 267 130 0.5 0.5 NUM cana-1744 267 131 0.6938 0.6938 NUM cana-1744 267 132 1.2438 1.2438 NUM cana-1744 267 133 0.1261 0.1261 NUM cana-1744 267 134 0.2261 0.2261 NUM cana-1744 267 135 900 900 NUM cana-1744 267 136 0.5 0.5 NUM cana-1744 267 137 0.5 0.5 NUM cana-1744 267 138 0.6889 0.6889 NUM cana-1744 267 139 1.2389 1.2389 NUM cana-1744 267 140 0.1253 0.1253 NUM cana-1744 267 141 0.2253 0.2253 NUM cana-1744 267 142 1000 1000 NUM cana-1744 267 143 0.5 0.5 NUM cana-1744 267 144 0.5 0.5 NUM cana-1744 267 145 0.6873 0.6873 NUM cana-1744 267 146 1.2373 1.2373 NUM cana-1744 267 147 0.1250 0.1250 NUM cana-1744 267 148 0.2250 0.2250 NUM cana-1744 267 149 3000 3000 NUM cana-1744 267 150 0.5 0.5 NUM cana-1744 267 151 0.5 0.5 NUM cana-1744 267 152 0.6772 0.6772 NUM cana-1744 267 153 1.2272 1.2272 NUM cana-1744 267 154 0.1231 0.1231 NUM cana-1744 267 155 0.2231 0.2231 NUM cana-1744 267 156 5000 5000 NUM cana-1744 267 157 0.5 0.5 NUM cana-1744 267 158 0.5 0.5 NUM cana-1744 267 159 0.6752 0.6752 NUM cana-1744 267 160 1.2252 1.2252 NUM cana-1744 267 161 0.1228 0.1228 NUM cana-1744 267 162 0.2228 0.2228 NUM cana-1744 267 163 remarks:1 remarks:1 NOUN cana-1744 267 164 given give VERB cana-1744 267 165 an an DET cana-1744 267 166 exponential exponential ADJ cana-1744 267 167 distribution distribution NOUN cana-1744 267 168 for for ADP cana-1744 267 169 the the DET cana-1744 267 170 service service NOUN cana-1744 267 171 distribution distribution NOUN cana-1744 267 172 , , PUNCT cana-1744 267 173 table table NOUN cana-1744 267 174 1 1 NUM cana-1744 267 175 illustrates illustrate VERB cana-1744 267 176 the the DET cana-1744 267 177 effect effect NOUN cana-1744 267 178 of of ADP cana-1744 267 179 χ χ NOUN cana-1744 267 180 on on ADP cana-1744 267 181 the the DET cana-1744 267 182 average average ADJ cana-1744 267 183 number number NOUN cana-1744 267 184 of of ADP cana-1744 267 185 patrons patron NOUN cana-1744 267 186 in in ADP cana-1744 267 187 a a DET cana-1744 267 188 group group NOUN cana-1744 267 189 . . PUNCT cana-1744 268 1 additionally additionally ADV cana-1744 268 2 , , PUNCT cana-1744 268 3 the the DET cana-1744 268 4 following follow VERB cana-1744 268 5 is be AUX cana-1744 268 6 implied imply VERB cana-1744 268 7 : : PUNCT cana-1744 268 8 • • ADP cana-1744 268 9 the the DET cana-1744 268 10 average average ADJ cana-1744 268 11 number number NOUN cana-1744 268 12 of of ADP cana-1744 268 13 patrons patron NOUN cana-1744 268 14 in in ADP cana-1744 268 15 the the DET cana-1744 268 16 group group NOUN cana-1744 268 17 reduces reduce VERB cana-1744 268 18 the the DET cana-1744 268 19 retrial retrial ADJ cana-1744 268 20 rate rate NOUN cana-1744 268 21 𝜒 𝜒 NOUN cana-1744 268 22 maximizes maximize NOUN cana-1744 268 23 and and CCONJ cana-1744 268 24 then then ADV cana-1744 268 25 applies apply VERB cana-1744 268 26 the the DET cana-1744 268 27 encouraged encouraged ADJ cana-1744 268 28 arrival arrival NOUN cana-1744 268 29 concept concept NOUN cana-1744 268 30 for for ADP cana-1744 268 31 this this DET cana-1744 268 32 model model NOUN cana-1744 268 33 to to PART cana-1744 268 34 increase increase VERB cana-1744 268 35 the the DET cana-1744 268 36 arrival arrival NOUN cana-1744 268 37 rates rate NOUN cana-1744 268 38 . . PUNCT cana-1744 269 1 this this DET cana-1744 269 2 method method NOUN cana-1744 269 3 using use VERB cana-1744 269 4 a a DET cana-1744 269 5 single single ADJ cana-1744 269 6 server server NOUN cana-1744 269 7 encouraged encouraged ADJ cana-1744 269 8 arrival arrival NOUN cana-1744 269 9 queuing queue VERB cana-1744 269 10 system system NOUN cana-1744 269 11 if if SCONJ cana-1744 269 12 𝜒 𝜒 NOUN cana-1744 269 13 is be AUX cana-1744 269 14 maximum maximum ADJ cana-1744 269 15 . . PUNCT cana-1744 269 16 table table NOUN cana-1744 269 17 2 2 NUM cana-1744 269 18 : : PUNCT cana-1744 269 19 performance performance NOUN cana-1744 269 20 metrics metric NOUN cana-1744 269 21 for for ADP cana-1744 269 22 λ λ PROPN cana-1744 269 23 × × NOUN cana-1744 269 24 ( ( PUNCT cana-1744 269 25 1 1 NUM cana-1744 269 26 + + CCONJ cana-1744 269 27 δ δ NOUN cana-1744 269 28 ) ) PUNCT cana-1744 269 29 , , PUNCT cana-1744 269 30 = = NOUN cana-1744 269 31 5.5 5.5 NUM cana-1744 269 32 , , PUNCT cana-1744 269 33 𝜇 𝜇 ADP cana-1744 269 34 = = NOUN cana-1744 269 35 50 50 NUM cana-1744 269 36 and and CCONJ cana-1744 269 37 𝑟 𝑟 NOUN cana-1744 269 38 = = SYM cana-1744 269 39 3 3 NUM cana-1744 269 40 for for ADP cana-1744 269 41 different different ADJ cana-1744 269 42 points point NOUN cana-1744 269 43 of of ADP cana-1744 269 44 𝜒. 𝜒. NOUN cana-1744 269 45 𝜒 𝜒 SYM cana-1744 269 46 p0 p0 NOUN cana-1744 269 47 p1 p1 NOUN cana-1744 269 48 lq lq VERB cana-1744 269 49 ls ls PROPN cana-1744 269 50 wq wq PROPN cana-1744 269 51 ws ws PROPN cana-1744 269 52 10 10 NUM cana-1744 269 53 0.7 0.7 NUM cana-1744 269 54 0.3 0.3 NUM cana-1744 269 55 0.2086 0.2086 NUM cana-1744 269 56 0.3186 0.3186 NUM cana-1744 269 57 0.0379 0.0379 NUM cana-1744 269 58 0.0579 0.0579 NUM cana-1744 269 59 30 30 NUM cana-1744 269 60 0.7 0.7 NUM cana-1744 269 61 0.3 0.3 NUM cana-1744 270 1 0.1220 0.1220 NUM cana-1744 270 2 0.2320 0.2320 NUM cana-1744 270 3 0.0222 0.0222 NUM cana-1744 270 4 0.0422 0.0422 NUM cana-1744 270 5 50 50 NUM cana-1744 270 6 0.7 0.7 NUM cana-1744 270 7 0.3 0.3 NUM cana-1744 270 8 0.1056 0.1056 NUM cana-1744 270 9 0.2156 0.2156 NUM cana-1744 270 10 0.0192 0.0192 NUM cana-1744 270 11 0.0392 0.0392 NUM cana-1744 270 12 70 70 NUM cana-1744 270 13 0.7 0.7 NUM cana-1744 270 14 0.3 0.3 NUM cana-1744 270 15 0.0987 0.0987 NUM cana-1744 270 16 0.2087 0.2087 NUM cana-1744 270 17 0.0179 0.0179 NUM cana-1744 270 18 0.0379 0.0379 NUM cana-1744 270 19 90 90 NUM cana-1744 270 20 0.7 0.7 NUM cana-1744 270 21 0.3 0.3 NUM cana-1744 270 22 0.0948 0.0948 NUM cana-1744 270 23 0.2048 0.2048 NUM cana-1744 270 24 0.0172 0.0172 NUM cana-1744 270 25 0.0372 0.0372 NUM cana-1744 270 26 100 100 NUM cana-1744 270 27 0.7 0.7 NUM cana-1744 270 28 0.3 0.3 NUM cana-1744 270 29 0.0935 0.0935 NUM cana-1744 270 30 0.2035 0.2035 NUM cana-1744 270 31 0.0170 0.0170 NUM cana-1744 270 32 0.0370 0.0370 NUM cana-1744 270 33 300 300 NUM cana-1744 270 34 0.7 0.7 NUM cana-1744 270 35 0.3 0.3 NUM cana-1744 270 36 0.0855 0.0855 NUM cana-1744 270 37 0.1955 0.1955 NUM cana-1744 270 38 0.0156 0.0156 NUM cana-1744 270 39 0.0356 0.0356 NUM cana-1744 270 40 500 500 NUM cana-1744 270 41 0.7 0.7 NUM cana-1744 270 42 0.3 0.3 NUM cana-1744 270 43 0.0839 0.0839 NUM cana-1744 270 44 0.1939 0.1939 NUM cana-1744 270 45 0.0153 0.0153 NUM cana-1744 270 46 0.0353 0.0353 NUM cana-1744 270 47 700 700 NUM cana-1744 270 48 0.7 0.7 NUM cana-1744 270 49 0.3 0.3 NUM cana-1744 270 50 0.0833 0.0833 NUM cana-1744 270 51 0.1933 0.1933 NUM cana-1744 270 52 0.0151 0.0151 NUM cana-1744 270 53 0.0351 0.0351 NUM cana-1744 270 54 900 900 NUM cana-1744 270 55 0.7 0.7 NUM cana-1744 270 56 0.3 0.3 NUM cana-1744 270 57 0.0829 0.0829 NUM cana-1744 270 58 0.1929 0.1929 NUM cana-1744 270 59 0.0151 0.0151 NUM cana-1744 270 60 0.0351 0.0351 NUM cana-1744 270 61 1000 1000 NUM cana-1744 270 62 0.7 0.7 NUM cana-1744 270 63 0.3 0.3 NUM cana-1744 270 64 0.0828 0.0828 NUM cana-1744 270 65 01928 01928 NUM cana-1744 270 66 0.0150 0.0150 NUM cana-1744 270 67 0.0350 0.0350 NUM cana-1744 270 68 3000 3000 NUM cana-1744 270 69 0.7 0.7 NUM cana-1744 270 70 0.3 0.3 NUM cana-1744 270 71 0.0820 0.0820 NUM cana-1744 270 72 0.1920 0.1920 NUM cana-1744 270 73 0.0149 0.0149 NUM cana-1744 270 74 0.0349 0.0349 NUM cana-1744 270 75 5000 5000 NUM cana-1744 270 76 0.7 0.7 NUM cana-1744 270 77 0.3 0.3 NUM cana-1744 270 78 0.0818 0.0818 NUM cana-1744 270 79 0.1918 0.1918 NUM cana-1744 270 80 0.0149 0.0149 NUM cana-1744 270 81 0.0.349 0.0.349 NUM cana-1744 270 82 communications communication NOUN cana-1744 270 83 on on ADP cana-1744 270 84 applied apply VERB cana-1744 270 85 nonlinear nonlinear ADJ cana-1744 270 86 analysis analysis NOUN cana-1744 270 87 issn issn NOUN cana-1744 270 88 : : PUNCT cana-1744 270 89 1074 1074 NUM cana-1744 270 90 - - PUNCT cana-1744 270 91 133x 133x NUM cana-1744 270 92 vol vol NOUN cana-1744 270 93 32 32 NUM cana-1744 270 94 no no NOUN cana-1744 270 95 . . NOUN cana-1744 270 96 2 2 NUM cana-1744 270 97 ( ( PUNCT cana-1744 270 98 2025 2025 NUM cana-1744 270 99 ) ) PUNCT cana-1744 270 100 321 321 NUM cana-1744 270 101 https://internationalpubls.com https://internationalpubls.com X cana-1744 270 102 table table NOUN cana-1744 270 103 3 3 NUM cana-1744 270 104 : : PUNCT cana-1744 270 105 performance performance NOUN cana-1744 270 106 metrics metric NOUN cana-1744 270 107 for for ADP cana-1744 270 108 λ λ PROPN cana-1744 270 109 × × NOUN cana-1744 270 110 ( ( PUNCT cana-1744 270 111 1 1 NUM cana-1744 270 112 + + CCONJ cana-1744 270 113 δ δ X cana-1744 270 114 ) ) PUNCT cana-1744 270 115 = = SYM cana-1744 270 116 8.8 8.8 NUM cana-1744 270 117 , , PUNCT cana-1744 270 118 𝜇 𝜇 X cana-1744 270 119 = = NOUN cana-1744 270 120 50 50 NUM cana-1744 270 121 and and CCONJ cana-1744 270 122 r r NOUN cana-1744 270 123 = = SYM cana-1744 270 124 3 3 NUM cana-1744 270 125 for for ADP cana-1744 270 126 different different ADJ cana-1744 270 127 points point NOUN cana-1744 270 128 of of ADP cana-1744 270 129 𝜒. 𝜒. NOUN cana-1744 270 130 𝜒 𝜒 SYM cana-1744 270 131 p0 p0 NOUN cana-1744 270 132 p1 p1 NOUN cana-1744 270 133 lq lq VERB cana-1744 270 134 ls ls PROPN cana-1744 270 135 wq wq PROPN cana-1744 270 136 ws ws PROPN cana-1744 270 137 10 10 NUM cana-1744 270 138 0.52 0.52 NUM cana-1744 270 139 0.48 0.48 NUM cana-1744 270 140 0.7537 0.7537 NUM cana-1744 270 141 0.9297 0.9297 NUM cana-1744 270 142 0.0856 0.0856 NUM cana-1744 270 143 0.1056 0.1056 NUM cana-1744 270 144 30 30 NUM cana-1744 271 1 0.52 0.52 NUM cana-1744 271 2 0.48 0.48 NUM cana-1744 271 3 0.3781 0.3781 NUM cana-1744 271 4 0.5541 0.5541 NUM cana-1744 271 5 0.0430 0.0430 NUM cana-1744 271 6 0.0.630 0.0.630 NUM cana-1744 271 7 50 50 NUM cana-1744 271 8 0.52 0.52 NUM cana-1744 271 9 0.48 0.48 NUM cana-1744 271 10 0.3147 0.3147 NUM cana-1744 271 11 0.4907 0.4907 NUM cana-1744 271 12 0.0358 0.0358 NUM cana-1744 271 13 0.0558 0.0558 NUM cana-1744 271 14 70 70 NUM cana-1744 271 15 0.52 0.52 NUM cana-1744 271 16 0.48 0.48 NUM cana-1744 271 17 0.2885 0.2885 NUM cana-1744 271 18 0.4645 0.4645 NUM cana-1744 271 19 0.0328 0.0328 NUM cana-1744 271 20 0.0528 0.0528 NUM cana-1744 271 21 90 90 NUM cana-1744 271 22 0.52 0.52 NUM cana-1744 271 23 0.48 0.48 NUM cana-1744 271 24 0.2742 0.2742 NUM cana-1744 272 1 0.4502 0.4502 NUM cana-1744 272 2 0.0312 0.0312 NUM cana-1744 272 3 0.0512 0.0512 NUM cana-1744 272 4 100 100 NUM cana-1744 272 5 0.52 0.52 NUM cana-1744 272 6 0.48 0.48 NUM cana-1744 272 7 0.2693 0.2693 NUM cana-1744 272 8 0.4453 0.4453 NUM cana-1744 272 9 0.0306 0.0306 NUM cana-1744 272 10 0.0506 0.0506 NUM cana-1744 272 11 300 300 NUM cana-1744 272 12 0.52 0.52 NUM cana-1744 272 13 0.48 0.48 NUM cana-1744 272 14 0.2399 0.2399 NUM cana-1744 272 15 0.4159 0.4159 NUM cana-1744 272 16 0.0273 0.0273 NUM cana-1744 272 17 0.0473 0.0473 NUM cana-1744 272 18 500 500 NUM cana-1744 272 19 0.52 0.52 NUM cana-1744 272 20 0.48 0.48 NUM cana-1744 272 21 0.2342 0.2342 NUM cana-1744 272 22 0.4102 0.4102 NUM cana-1744 272 23 0.0266 0.0266 NUM cana-1744 272 24 0.0466 0.0466 NUM cana-1744 272 25 700 700 NUM cana-1744 272 26 0.52 0.52 NUM cana-1744 272 27 0.48 0.48 NUM cana-1744 272 28 0.2317 0.2317 NUM cana-1744 272 29 0.4077 0.4077 NUM cana-1744 272 30 0.0263 0.0263 NUM cana-1744 272 31 0.0463 0.0463 NUM cana-1744 272 32 900 900 NUM cana-1744 272 33 0.52 0.52 NUM cana-1744 272 34 0.48 0.48 NUM cana-1744 272 35 0.2303 0.2303 NUM cana-1744 272 36 0.4063 0.4063 NUM cana-1744 272 37 0.0262 0.0262 NUM cana-1744 272 38 0.0462 0.0462 NUM cana-1744 272 39 1000 1000 NUM cana-1744 272 40 0.52 0.52 NUM cana-1744 272 41 0.48 0.48 NUM cana-1744 272 42 0.2298 0.2298 NUM cana-1744 272 43 0.4058 0.4058 NUM cana-1744 272 44 0.0261 0.0261 NUM cana-1744 272 45 0.0461 0.0461 NUM cana-1744 272 46 3000 3000 NUM cana-1744 272 47 0.52 0.52 NUM cana-1744 272 48 0.48 0.48 NUM cana-1744 272 49 0.2270 0.2270 NUM cana-1744 272 50 0.4030 0.4030 NUM cana-1744 272 51 0.0258 0.0258 NUM cana-1744 272 52 0.0458 0.0458 NUM cana-1744 272 53 5000 5000 NUM cana-1744 272 54 0.52 0.52 NUM cana-1744 272 55 0.48 0.48 NUM cana-1744 272 56 0.2264 0.2264 NUM cana-1744 272 57 0.4024 0.4024 NUM cana-1744 272 58 0.0257 0.0257 NUM cana-1744 272 59 0.0457 0.0457 NUM cana-1744 272 60 remark:2 remark:2 NOUN cana-1744 272 61 given give VERB cana-1744 272 62 an an DET cana-1744 272 63 erlang erlang NOUN cana-1744 272 64 distribution distribution NOUN cana-1744 272 65 for for ADP cana-1744 272 66 the the DET cana-1744 272 67 service service NOUN cana-1744 272 68 distribution distribution NOUN cana-1744 272 69 , , PUNCT cana-1744 272 70 table table NOUN cana-1744 272 71 2&3 2&3 NUM cana-1744 272 72 illustrates illustrate VERB cana-1744 272 73 the the DET cana-1744 272 74 effect effect NOUN cana-1744 272 75 of of ADP cana-1744 272 76 χ χ NOUN cana-1744 272 77 on on ADP cana-1744 272 78 the the DET cana-1744 272 79 average average ADJ cana-1744 272 80 number number NOUN cana-1744 272 81 of of ADP cana-1744 272 82 patrons patron NOUN cana-1744 272 83 in in ADP cana-1744 272 84 a a DET cana-1744 272 85 group group NOUN cana-1744 272 86 . . PUNCT cana-1744 273 1 additionally additionally ADV cana-1744 273 2 , , PUNCT cana-1744 273 3 the the DET cana-1744 273 4 following follow VERB cana-1744 273 5 is be AUX cana-1744 273 6 implied imply VERB cana-1744 273 7 : : PUNCT cana-1744 273 8 the the DET cana-1744 273 9 average average ADJ cana-1744 273 10 number number NOUN cana-1744 273 11 of of ADP cana-1744 273 12 patrons patron NOUN cana-1744 273 13 in in ADP cana-1744 273 14 the the DET cana-1744 273 15 group group NOUN cana-1744 273 16 increases increase VERB cana-1744 273 17 the the DET cana-1744 273 18 retrial retrial ADJ cana-1744 273 19 rate rate NOUN cana-1744 273 20 𝜒 𝜒 NOUN cana-1744 273 21 maximizes maximize NOUN cana-1744 273 22 and and CCONJ cana-1744 273 23 then then ADV cana-1744 273 24 applies apply VERB cana-1744 273 25 the the DET cana-1744 273 26 encouraged encouraged ADJ cana-1744 273 27 arrival arrival NOUN cana-1744 273 28 concept concept NOUN cana-1744 273 29 for for ADP cana-1744 273 30 this this DET cana-1744 273 31 model model NOUN cana-1744 273 32 to to PART cana-1744 273 33 increase increase VERB cana-1744 273 34 the the DET cana-1744 273 35 arrival arrival NOUN cana-1744 273 36 rates rate NOUN cana-1744 273 37 . . PUNCT cana-1744 274 1 this this DET cana-1744 274 2 method method NOUN cana-1744 274 3 using use VERB cana-1744 274 4 a a DET cana-1744 274 5 single single ADJ cana-1744 274 6 server server NOUN cana-1744 274 7 encouraged encouraged ADJ cana-1744 274 8 arrival arrival NOUN cana-1744 274 9 queuing queue VERB cana-1744 274 10 system system NOUN cana-1744 274 11 if if SCONJ cana-1744 274 12 𝜒 𝜒 NOUN cana-1744 274 13 is be AUX cana-1744 274 14 maximum maximum ADJ cana-1744 274 15 7 7 NUM cana-1744 274 16 . . PUNCT cana-1744 274 17 economic economic ADJ cana-1744 274 18 cost cost NOUN cana-1744 274 19 to to PART cana-1744 274 20 optimize optimize VERB cana-1744 274 21 the the DET cana-1744 274 22 system system NOUN cana-1744 274 23 ’s ’s PART cana-1744 274 24 operating operate VERB cana-1744 274 25 cost cost NOUN cana-1744 274 26 , , PUNCT cana-1744 274 27 we we PRON cana-1744 274 28 established establish VERB cana-1744 274 29 a a DET cana-1744 274 30 cost cost NOUN cana-1744 274 31 analysis.in analysis.in PRON cana-1744 274 32 single single ADJ cana-1744 274 33 server server NOUN cana-1744 274 34 markovian markovian NOUN cana-1744 274 35 encouraged encourage VERB cana-1744 274 36 arrival arrival NOUN cana-1744 274 37 queuing queue VERB cana-1744 274 38 system system NOUN cana-1744 274 39 . . PUNCT cana-1744 275 1 we we PRON cana-1744 275 2 find find VERB cana-1744 275 3 out out ADP cana-1744 275 4 the the DET cana-1744 275 5 following follow VERB cana-1744 275 6 costs cost NOUN cana-1744 275 7 , , PUNCT cana-1744 275 8 • • ADV cana-1744 275 9 waiting wait VERB cana-1744 275 10 cost= cost= PROPN cana-1744 275 11 ( ( PUNCT cana-1744 275 12 c c X cana-1744 275 13 ) ) PUNCT cana-1744 275 14 * * PUNCT cana-1744 275 15 ( ( PUNCT cana-1744 275 16 wait wait VERB cana-1744 275 17 time time NOUN cana-1744 275 18 ) ) PUNCT cana-1744 275 19 • • NUM cana-1744 275 20 operating operate VERB cana-1744 275 21 cost= cost= PROPN cana-1744 275 22 ( ( PUNCT cana-1744 275 23 r)*(server r)*(server NOUN cana-1744 275 24 charge charge NOUN cana-1744 275 25 per per ADP cana-1744 275 26 time time NOUN cana-1744 275 27 duration duration NOUN cana-1744 275 28 ) ) PUNCT cana-1744 275 29 • • NUM cana-1744 275 30 estimated estimate VERB cana-1744 275 31 total total ADJ cana-1744 275 32 cost cost NOUN cana-1744 275 33 ( ( PUNCT cana-1744 275 34 etc)= etc)= NOUN cana-1744 275 35 operating operating NOUN cana-1744 275 36 cost cost NOUN cana-1744 275 37 + + CCONJ cana-1744 275 38 waiting wait VERB cana-1744 275 39 cost cost NOUN cana-1744 275 40 λ λ PROPN cana-1744 275 41 δ δ PROPN cana-1744 275 42 λ λ X cana-1744 275 43 × × NOUN cana-1744 275 44 ( ( PUNCT cana-1744 275 45 1 1 NUM cana-1744 275 46 + + CCONJ cana-1744 275 47 δ δ NOUN cana-1744 275 48 ) ) PUNCT cana-1744 275 49 𝜇 𝜇 SCONJ cana-1744 275 50 r r NOUN cana-1744 275 51 𝜒 𝜒 NOUN cana-1744 275 52 5 5 NUM cana-1744 275 53 0.1 0.1 NUM cana-1744 275 54 5.5 5.5 NUM cana-1744 275 55 10 10 NUM cana-1744 275 56 3 3 NUM cana-1744 275 57 10,30,50,70, 10,30,50,70, NUM cana-1744 275 58 … … SYM cana-1744 275 59 5000 5000 NUM cana-1744 275 60 communications communication NOUN cana-1744 275 61 on on ADP cana-1744 275 62 applied apply VERB cana-1744 275 63 nonlinear nonlinear ADJ cana-1744 275 64 analysis analysis NOUN cana-1744 275 65 issn issn NOUN cana-1744 275 66 : : PUNCT cana-1744 275 67 1074 1074 NUM cana-1744 275 68 - - PUNCT cana-1744 275 69 133x 133x NUM cana-1744 275 70 vol vol NOUN cana-1744 275 71 32 32 NUM cana-1744 275 72 no no NOUN cana-1744 275 73 . . NOUN cana-1744 275 74 2 2 NUM cana-1744 275 75 ( ( PUNCT cana-1744 275 76 2025 2025 NUM cana-1744 275 77 ) ) PUNCT cana-1744 275 78 322 322 NUM cana-1744 275 79 https://internationalpubls.com https://internationalpubls.com X cana-1744 275 80 table table NOUN cana-1744 275 81 4 4 NUM cana-1744 275 82 : : PUNCT cana-1744 275 83 𝜒 𝜒 NUM cana-1744 275 84 waiting waiting NOUN cana-1744 275 85 time time NOUN cana-1744 275 86 ( ( PUNCT cana-1744 275 87 wq wq NOUN cana-1744 275 88 ) ) PUNCT cana-1744 275 89 waiting wait VERB cana-1744 275 90 cost cost NOUN cana-1744 275 91 operating operating NOUN cana-1744 275 92 cost cost NOUN cana-1744 275 93 total total NOUN cana-1744 275 94 cost cost NOUN cana-1744 275 95 10 10 NUM cana-1744 275 96 0.0379 0.0379 NUM cana-1744 275 97 0.3793 0.3793 NUM cana-1744 275 98 150 150 NUM cana-1744 275 99 150.3793 150.3793 NUM cana-1744 275 100 30 30 NUM cana-1744 275 101 0.0222 0.0222 NUM cana-1744 275 102 0.2217 0.2217 NUM cana-1744 275 103 150 150 NUM cana-1744 275 104 150.2217 150.2217 NUM cana-1744 275 105 50 50 NUM cana-1744 275 106 0.0192 0.0192 NUM cana-1744 275 107 0.1920 0.1920 NUM cana-1744 275 108 150 150 NUM cana-1744 275 109 150.1920 150.1920 NUM cana-1744 275 110 70 70 NUM cana-1744 275 111 0.0179 0.0179 NUM cana-1744 275 112 0.1794 0.1794 NUM cana-1744 276 1 150 150 NUM cana-1744 276 2 150.1794 150.1794 NUM cana-1744 276 3 90 90 NUM cana-1744 276 4 0.0172 0.0172 NUM cana-1744 276 5 0.1724 0.1724 NUM cana-1744 276 6 150 150 NUM cana-1744 276 7 150.1724 150.1724 NUM cana-1744 276 8 100 100 NUM cana-1744 276 9 0.0170 0.0170 NUM cana-1744 276 10 0.1700 0.1700 NUM cana-1744 276 11 150 150 NUM cana-1744 276 12 150.1700 150.1700 NUM cana-1744 276 13 300 300 NUM cana-1744 276 14 0.0156 0.0156 NUM cana-1744 276 15 0.1555 0.1555 NUM cana-1744 276 16 150 150 NUM cana-1744 276 17 150.1555 150.1555 NUM cana-1744 276 18 500 500 NUM cana-1744 276 19 0.0153 0.0153 NUM cana-1744 276 20 0.1526 0.1526 NUM cana-1744 276 21 150 150 NUM cana-1744 276 22 150.1526 150.1526 NUM cana-1744 276 23 700 700 NUM cana-1744 276 24 0.0151 0.0151 NUM cana-1744 276 25 0.1514 0.1514 NUM cana-1744 276 26 150 150 NUM cana-1744 276 27 150.1514 150.1514 NUM cana-1744 276 28 900 900 NUM cana-1744 276 29 0.0151 0.0151 NUM cana-1744 276 30 0.1507 0.1507 NUM cana-1744 276 31 150 150 NUM cana-1744 276 32 150.1507 150.1507 NUM cana-1744 276 33 1000 1000 NUM cana-1744 276 34 0.0150 0.0150 NUM cana-1744 276 35 0.1505 0.1505 NUM cana-1744 276 36 150 150 NUM cana-1744 276 37 150.1505 150.1505 NUM cana-1744 276 38 3000 3000 NUM cana-1744 276 39 0.0149 0.0149 NUM cana-1744 276 40 0.1490 0.1490 NUM cana-1744 276 41 150 150 NUM cana-1744 276 42 150.1490 150.1490 NUM cana-1744 276 43 5000 5000 NUM cana-1744 276 44 0.0149 0.0149 NUM cana-1744 276 45 0.1487 0.1487 NUM cana-1744 276 46 150 150 NUM cana-1744 276 47 150.1487 150.1487 NUM cana-1744 276 48 table table NOUN cana-1744 276 49 5 5 NUM cana-1744 276 50 : : PUNCT cana-1744 276 51 λ λ PROPN cana-1744 276 52 δ δ PROPN cana-1744 276 53 λ λ X cana-1744 276 54 × × NOUN cana-1744 276 55 ( ( PUNCT cana-1744 276 56 1 1 NUM cana-1744 276 57 + + CCONJ cana-1744 276 58 δ δ NOUN cana-1744 276 59 ) ) PUNCT cana-1744 276 60 𝜇 𝜇 ADP cana-1744 276 61 r r NOUN cana-1744 276 62 𝜒 𝜒 NOUN cana-1744 276 63 8 8 NUM cana-1744 276 64 0.1 0.1 NUM cana-1744 276 65 8.8 8.8 NUM cana-1744 276 66 10 10 NUM cana-1744 276 67 3 3 NUM cana-1744 276 68 10,30,50,70, 10,30,50,70, NUM cana-1744 276 69 … … SYM cana-1744 276 70 5000 5000 NUM cana-1744 276 71 𝜒 𝜒 NOUN cana-1744 276 72 waiting waiting NOUN cana-1744 276 73 time time NOUN cana-1744 276 74 ( ( PUNCT cana-1744 276 75 wq wq NOUN cana-1744 276 76 ) ) PUNCT cana-1744 276 77 waiting wait VERB cana-1744 276 78 cost cost NOUN cana-1744 276 79 operating operating NOUN cana-1744 276 80 cost cost NOUN cana-1744 276 81 total total NOUN cana-1744 276 82 cost cost NOUN cana-1744 276 83 10 10 NUM cana-1744 276 84 0.0856 0.0856 NUM cana-1744 276 85 0.8564 0.8564 NUM cana-1744 276 86 150 150 NUM cana-1744 276 87 150.8564 150.8564 NUM cana-1744 276 88 30 30 NUM cana-1744 276 89 0.0430 0.0430 NUM cana-1744 276 90 0.8463 0.8463 NUM cana-1744 276 91 150 150 NUM cana-1744 276 92 150.8463 150.8463 NUM cana-1744 276 93 50 50 NUM cana-1744 276 94 0.0358 0.0358 NUM cana-1744 276 95 0.4296 0.4296 NUM cana-1744 276 96 150 150 NUM cana-1744 276 97 150.4296 150.4296 NUM cana-1744 276 98 70 70 NUM cana-1744 276 99 0.0328 0.0328 NUM cana-1744 276 100 0.3576 0.3576 NUM cana-1744 276 101 150 150 NUM cana-1744 276 102 150.3576 150.3576 NUM cana-1744 276 103 90 90 NUM cana-1744 276 104 0.0312 0.0312 NUM cana-1744 276 105 0.3278 0.3278 NUM cana-1744 276 106 150 150 NUM cana-1744 276 107 150.3278 150.3278 NUM cana-1744 276 108 100 100 NUM cana-1744 276 109 0.0306 0.0306 NUM cana-1744 276 110 0.3116 0.3116 NUM cana-1744 276 111 150 150 NUM cana-1744 276 112 150.3116 150.3116 NUM cana-1744 276 113 300 300 NUM cana-1744 276 114 0.0273 0.0273 NUM cana-1744 276 115 0.3060 0.3060 NUM cana-1744 276 116 150 150 NUM cana-1744 276 117 150.3060 150.3060 NUM cana-1744 276 118 500 500 NUM cana-1744 276 119 0.0266 0.0266 NUM cana-1744 276 120 0.2727 0.2727 NUM cana-1744 276 121 150 150 NUM cana-1744 276 122 150.2727 150.2727 NUM cana-1744 276 123 700 700 NUM cana-1744 276 124 0.0263 0.0263 NUM cana-1744 276 125 0.2661 0.2661 NUM cana-1744 276 126 150 150 NUM cana-1744 276 127 150.2661 150.2661 NUM cana-1744 276 128 900 900 NUM cana-1744 276 129 0.0262 0.0262 NUM cana-1744 276 130 0.2633 0.2633 NUM cana-1744 276 131 150 150 NUM cana-1744 276 132 150.2633 150.2633 NUM cana-1744 276 133 1000 1000 NUM cana-1744 276 134 0.0261 0.0261 NUM cana-1744 276 135 0.2617 0.2617 NUM cana-1744 276 136 150 150 NUM cana-1744 276 137 150.2617 150.2617 NUM cana-1744 276 138 3000 3000 NUM cana-1744 276 139 0.0258 0.0258 NUM cana-1744 276 140 0.2612 0.2612 NUM cana-1744 276 141 150 150 NUM cana-1744 276 142 150.2612 150.2612 NUM cana-1744 276 143 5000 5000 NUM cana-1744 276 144 0.0257 0.0257 NUM cana-1744 276 145 0.2579 0.2579 NUM cana-1744 276 146 150 150 NUM cana-1744 276 147 150.2579 150.2579 NUM cana-1744 276 148 communications communication NOUN cana-1744 276 149 on on ADP cana-1744 276 150 applied apply VERB cana-1744 276 151 nonlinear nonlinear ADJ cana-1744 276 152 analysis analysis NOUN cana-1744 276 153 issn issn NOUN cana-1744 276 154 : : PUNCT cana-1744 276 155 1074 1074 NUM cana-1744 276 156 - - PUNCT cana-1744 276 157 133x 133x NUM cana-1744 276 158 vol vol NOUN cana-1744 276 159 32 32 NUM cana-1744 276 160 no no NOUN cana-1744 276 161 . . NOUN cana-1744 276 162 2 2 NUM cana-1744 276 163 ( ( PUNCT cana-1744 276 164 2025 2025 NUM cana-1744 276 165 ) ) PUNCT cana-1744 276 166 323 323 NUM cana-1744 276 167 https://internationalpubls.com https://internationalpubls.com SYM cana-1744 276 168 8 8 NUM cana-1744 276 169 . . PUNCT cana-1744 277 1 conclusion conclusion NOUN cana-1744 277 2 the the DET cana-1744 277 3 single single ADJ cana-1744 277 4 server server NOUN cana-1744 277 5 markovian markovian PROPN cana-1744 277 6 general general PROPN cana-1744 277 7 service service NOUN cana-1744 277 8 retrial retrial NOUN cana-1744 277 9 encouraged encourage VERB cana-1744 277 10 arrival arrival NOUN cana-1744 277 11 queuing queue VERB cana-1744 277 12 model model NOUN cana-1744 277 13 under under ADP cana-1744 277 14 the the DET cana-1744 277 15 persistent persistent NOUN cana-1744 277 16 with with SCONJ cana-1744 277 17 retrial retrial ADJ cana-1744 277 18 policy policy NOUN cana-1744 277 19 is be AUX cana-1744 277 20 calculated calculate VERB cana-1744 277 21 using use VERB cana-1744 277 22 the the DET cana-1744 277 23 exponential exponential NOUN cana-1744 277 24 and and CCONJ cana-1744 277 25 erlang erlang NOUN cana-1744 277 26 distribution distribution NOUN cana-1744 277 27 method method NOUN cana-1744 277 28 . . PUNCT cana-1744 278 1 hereafter hereafter ADV cana-1744 278 2 we we PRON cana-1744 278 3 find find VERB cana-1744 278 4 out out ADP cana-1744 278 5 the the DET cana-1744 278 6 number number NOUN cana-1744 278 7 of of ADP cana-1744 278 8 patrons patron NOUN cana-1744 278 9 in in ADP cana-1744 278 10 the the DET cana-1744 278 11 group group NOUN cana-1744 278 12 , , PUNCT cana-1744 278 13 the the DET cana-1744 278 14 server server NOUN cana-1744 278 15 is be AUX cana-1744 278 16 a a DET cana-1744 278 17 free free ADJ cana-1744 278 18 / / SYM cana-1744 278 19 engaged engaged ADJ cana-1744 278 20 concept concept NOUN cana-1744 278 21 of of ADP cana-1744 278 22 this this DET cana-1744 278 23 model model NOUN cana-1744 278 24 . . PUNCT cana-1744 279 1 this this DET cana-1744 279 2 method method NOUN cana-1744 279 3 using use VERB cana-1744 279 4 a a DET cana-1744 279 5 single single ADJ cana-1744 279 6 server server NOUN cana-1744 279 7 encouraged encouraged ADJ cana-1744 279 8 arrival arrival NOUN cana-1744 279 9 queuing queue VERB cana-1744 279 10 system system NOUN cana-1744 279 11 if if SCONJ cana-1744 279 12 𝜒 𝜒 PRON cana-1744 279 13 value value NOUN cana-1744 279 14 is be AUX cana-1744 279 15 maximum maximum ADJ cana-1744 279 16 . . PUNCT cana-1744 280 1 additionally additionally ADV cana-1744 280 2 , , PUNCT cana-1744 280 3 we we PRON cana-1744 280 4 calculated calculate VERB cana-1744 280 5 the the DET cana-1744 280 6 economic economic ADJ cana-1744 280 7 cost cost NOUN cana-1744 280 8 analysis analysis NOUN cana-1744 280 9 for for ADP cana-1744 280 10 this this DET cana-1744 280 11 model model NOUN cana-1744 280 12 . . PUNCT cana-1744 281 1 applies apply VERB cana-1744 281 2 the the DET cana-1744 281 3 encouraged encourage VERB cana-1744 281 4 arrival arrival NOUN cana-1744 281 5 concept concept NOUN cana-1744 281 6 for for ADP cana-1744 281 7 this this DET cana-1744 281 8 model model NOUN cana-1744 281 9 , , PUNCT cana-1744 281 10 more more ADV cana-1744 281 11 efficient efficient ADJ cana-1744 281 12 results result NOUN cana-1744 281 13 get get VERB cana-1744 281 14 it it PRON cana-1744 281 15 compare compare VERB cana-1744 281 16 of of ADP cana-1744 281 17 the the DET cana-1744 281 18 poisson poisson PROPN cana-1744 281 19 arrival arrival PROPN cana-1744 281 20 model model PROPN cana-1744 281 21 . . PUNCT cana-1744 282 1 different different ADJ cana-1744 282 2 special special ADJ cana-1744 282 3 privileges privilege NOUN cana-1744 282 4 are be AUX cana-1744 282 5 done do VERB cana-1744 282 6 by by ADP cana-1744 282 7 various various ADJ cana-1744 282 8 service service NOUN cana-1744 282 9 time time NOUN cana-1744 282 10 distributions distribution NOUN cana-1744 282 11 . . PUNCT cana-1744 283 1 declaration declaration NOUN cana-1744 283 2 : : PUNCT cana-1744 283 3 no no DET cana-1744 283 4 conflict conflict NOUN cana-1744 283 5 of of ADP cana-1744 283 6 interest interest NOUN cana-1744 283 7 references reference NOUN cana-1744 283 8 [ [ X cana-1744 283 9 1 1 NUM cana-1744 283 10 ] ] X cana-1744 283 11 artalejo artalejo ADJ cana-1744 283 12 . . PUNCT cana-1744 284 1 j.r j.r PROPN cana-1744 284 2 and and CCONJ cana-1744 284 3 g.i.falin g.i.falin PROPN cana-1744 284 4 ( ( PUNCT cana-1744 284 5 2002 2002 NUM cana-1744 284 6 ) ) PUNCT cana-1744 284 7 . . PUNCT cana-1744 285 1 standard standard ADJ cana-1744 285 2 and and CCONJ cana-1744 285 3 retrial retrial ADJ cana-1744 285 4 queueing queueing NOUN cana-1744 285 5 systems system NOUN cana-1744 285 6 . . PUNCT cana-1744 286 1 a a DET cana-1744 286 2 comparative comparative ADJ cana-1744 286 3 analysis analysis NOUN cana-1744 286 4 , , PUNCT cana-1744 286 5 revista revista PROPN cana-1744 286 6 , , PUNCT cana-1744 286 7 matematica matematica PROPN cana-1744 286 8 , , PUNCT cana-1744 286 9 complutense complutense NOUN cana-1744 286 10 , , PUNCT cana-1744 286 11 15 15 NUM cana-1744 286 12 , , PUNCT cana-1744 286 13 pp pp ADV cana-1744 286 14 101 101 NUM cana-1744 286 15 - - SYM cana-1744 286 16 129 129 NUM cana-1744 286 17 [ [ X cana-1744 286 18 2 2 NUM cana-1744 286 19 ] ] X cana-1744 286 20 artalejo artalejo PROPN cana-1744 286 21 j.r j.r PROPN cana-1744 286 22 and and CCONJ cana-1744 286 23 a. a. PROPN cana-1744 286 24 gomez gomez PROPN cana-1744 286 25 - - PUNCT cana-1744 286 26 corral corral PROPN cana-1744 286 27 ( ( PUNCT cana-1744 286 28 2008 2008 NUM cana-1744 286 29 ) ) PUNCT cana-1744 286 30 . . PUNCT cana-1744 287 1 retrial retrial ADJ cana-1744 287 2 queueing queue VERB cana-1744 287 3 systems system NOUN cana-1744 287 4 - - PUNCT cana-1744 287 5 a a DET cana-1744 287 6 computational computational ADJ cana-1744 287 7 approach approach NOUN cana-1744 287 8 , , PUNCT cana-1744 287 9 springer springer NOUN cana-1744 287 10 . . PUNCT cana-1744 288 1 [ [ X cana-1744 288 2 3 3 NUM cana-1744 288 3 ] ] X cana-1744 288 4 falin falin PROPN cana-1744 288 5 g.i g.i PROPN cana-1744 288 6 ( ( PUNCT cana-1744 288 7 1990 1990 NUM cana-1744 288 8 ) ) PUNCT cana-1744 288 9 . . PUNCT cana-1744 289 1 a a DET cana-1744 289 2 survey survey NOUN cana-1744 289 3 of of ADP cana-1744 289 4 retrial retrial ADJ cana-1744 289 5 queues queue NOUN cana-1744 289 6 . . PUNCT cana-1744 290 1 queueing queue VERB cana-1744 290 2 systems system NOUN cana-1744 290 3 7 7 NUM cana-1744 290 4 , , PUNCT cana-1744 290 5 no.2 no.2 PROPN cana-1744 290 6 , , PUNCT cana-1744 290 7 pp pp ADV cana-1744 290 8 127 127 NUM cana-1744 290 9 - - SYM cana-1744 290 10 167 167 NUM cana-1744 290 11 . . PUNCT cana-1744 291 1 [ [ X cana-1744 291 2 4 4 NUM cana-1744 291 3 ] ] X cana-1744 291 4 farahmand farahmand NOUN cana-1744 291 5 . . PUNCT cana-1744 292 1 k k X cana-1744 292 2 ( ( PUNCT cana-1744 292 3 1990 1990 NUM cana-1744 292 4 ) ) PUNCT cana-1744 292 5 . . PUNCT cana-1744 293 1 single single ADJ cana-1744 293 2 line line NOUN cana-1744 293 3 queue queue NOUN cana-1744 293 4 with with ADP cana-1744 293 5 repeated repeat VERB cana-1744 293 6 demands demand NOUN cana-1744 293 7 , , PUNCT cana-1744 293 8 queueing queue VERB cana-1744 293 9 systems system NOUN cana-1744 293 10 , , PUNCT cana-1744 293 11 6 6 NUM cana-1744 293 12 , , PUNCT cana-1744 293 13 no.2 no.2 PROPN cana-1744 293 14 , , PUNCT cana-1744 293 15 pp pp ADP cana-1744 293 16 223 223 NUM cana-1744 293 17 - - SYM cana-1744 293 18 228 228 NUM cana-1744 293 19 . . PUNCT cana-1744 294 1 [ [ X cana-1744 294 2 5 5 X cana-1744 294 3 ] ] PUNCT cana-1744 294 4 kulkarni kulkarni PROPN cana-1744 294 5 v.g v.g PROPN cana-1744 294 6 ( ( PUNCT cana-1744 294 7 1983 1983 NUM cana-1744 294 8 ) ) PUNCT cana-1744 294 9 . . PUNCT cana-1744 295 1 on on ADP cana-1744 295 2 queueing queue VERB cana-1744 295 3 systems system NOUN cana-1744 295 4 with with ADP cana-1744 295 5 retrials retrial NOUN cana-1744 295 6 . . PUNCT cana-1744 296 1 journal journal NOUN cana-1744 296 2 of of ADP cana-1744 296 3 applied apply VERB cana-1744 296 4 probability probability NOUN cana-1744 296 5 20 20 NUM cana-1744 296 6 , , PUNCT cana-1744 296 7 no.2 no.2 PROPN cana-1744 296 8 , , PUNCT cana-1744 296 9 pp pp ADJ cana-1744 296 10 380 380 NUM cana-1744 296 11 - - SYM cana-1744 296 12 389 389 NUM cana-1744 296 13 . . PUNCT cana-1744 297 1 [ [ X cana-1744 297 2 6 6 NUM cana-1744 297 3 ] ] X cana-1744 297 4 templeton templeton PROPN cana-1744 297 5 j.g.c j.g.c PROPN cana-1744 297 6 ( ( PUNCT cana-1744 297 7 1990 1990 NUM cana-1744 297 8 ) ) PUNCT cana-1744 297 9 . . PUNCT cana-1744 298 1 retrial retrial ADJ cana-1744 298 2 queues queue NOUN cana-1744 298 3 , , PUNCT cana-1744 298 4 queueing queue VERB cana-1744 298 5 systems system NOUN cana-1744 298 6 7 7 NUM cana-1744 298 7 , , PUNCT cana-1744 298 8 no.2 no.2 PROPN cana-1744 298 9 , , PUNCT cana-1744 298 10 pp pp ADV cana-1744 298 11 125 125 NUM cana-1744 298 12 - - SYM cana-1744 298 13 227 227 NUM cana-1744 298 14 . . PUNCT cana-1744 299 1 [ [ X cana-1744 299 2 7 7 X cana-1744 299 3 ] ] X cana-1744 299 4 yang yang PROPN cana-1744 299 5 t t PROPN cana-1744 299 6 and and CCONJ cana-1744 299 7 templeton templeton PROPN cana-1744 299 8 j.g.c j.g.c PROPN cana-1744 299 9 ( ( PUNCT cana-1744 299 10 1987 1987 NUM cana-1744 299 11 ) ) PUNCT cana-1744 299 12 . . PUNCT cana-1744 300 1 a a DET cana-1744 300 2 survey survey NOUN cana-1744 300 3 on on ADP cana-1744 300 4 retrial retrial ADJ cana-1744 300 5 queues queue NOUN cana-1744 300 6 . . PUNCT cana-1744 301 1 queueing queue VERB cana-1744 301 2 systems system NOUN cana-1744 301 3 , , PUNCT cana-1744 301 4 2 2 NUM cana-1744 301 5 , , PUNCT cana-1744 301 6 pp pp ADV cana-1744 301 7 201 201 NUM cana-1744 301 8 - - SYM cana-1744 301 9 233 233 NUM cana-1744 301 10 . . PUNCT cana-1744 302 1 [ [ X cana-1744 302 2 8 8 NUM cana-1744 302 3 ] ] X cana-1744 302 4 choudhury choudhury PROPN cana-1744 302 5 , , PUNCT cana-1744 302 6 g.(2003 g.(2003 PROPN cana-1744 302 7 ) ) PUNCT cana-1744 302 8 . . PUNCT cana-1744 303 1 some some DET cana-1744 303 2 aspects aspect NOUN cana-1744 303 3 of of ADP cana-1744 303 4 m m NOUN cana-1744 303 5 / / SYM cana-1744 303 6 g/1 g/1 NOUN cana-1744 303 7 queueing queue VERB cana-1744 303 8 system system NOUN cana-1744 303 9 with with ADP cana-1744 303 10 optional optional ADJ cana-1744 303 11 second second ADJ cana-1744 303 12 service service NOUN cana-1744 303 13 : : PUNCT cana-1744 303 14 top top ADJ cana-1744 303 15 , , PUNCT cana-1744 303 16 vol.11 vol.11 ADJ cana-1744 303 17 , , PUNCT cana-1744 303 18 141 141 NUM cana-1744 303 19 - - SYM cana-1744 303 20 150 150 NUM cana-1744 303 21 . . PUNCT cana-1744 304 1 [ [ X cana-1744 304 2 9 9 NUM cana-1744 304 3 ] ] X cana-1744 304 4 choudhury choudhury PROPN cana-1744 304 5 , , PUNCT cana-1744 304 6 g. g. PROPN cana-1744 304 7 ( ( PUNCT cana-1744 304 8 2005 2005 NUM cana-1744 304 9 ) ) PUNCT cana-1744 304 10 . . PUNCT cana-1744 305 1 an an DET cana-1744 305 2 m m NOUN cana-1744 305 3 / / SYM cana-1744 305 4 g/1 g/1 NOUN cana-1744 305 5 queueing queue VERB cana-1744 305 6 system system NOUN cana-1744 305 7 with with ADP cana-1744 305 8 two two NUM cana-1744 305 9 phase phase NOUN cana-1744 305 10 service service NOUN cana-1744 305 11 under under ADP cana-1744 305 12 d d NOUN cana-1744 305 13 - - NOUN cana-1744 305 14 policy policy NOUN cana-1744 305 15 : : PUNCT cana-1744 305 16 information information NOUN cana-1744 305 17 and and CCONJ cana-1744 305 18 management management NOUN cana-1744 305 19 sciences science NOUN cana-1744 305 20 . . PUNCT cana-1744 306 1 vol.16 vol.16 PROPN cana-1744 306 2 , , PUNCT cana-1744 306 3 no no INTJ cana-1744 306 4 . . NOUN cana-1744 306 5 4 4 NUM cana-1744 306 6 , , PUNCT cana-1744 306 7 1 1 NUM cana-1744 306 8 - - SYM cana-1744 306 9 17 17 NUM cana-1744 306 10 . . PUNCT cana-1744 307 1 [ [ X cana-1744 307 2 10 10 NUM cana-1744 307 3 ] ] X cana-1744 307 4 artalejo artalejo PROPN cana-1744 307 5 , , PUNCT cana-1744 307 6 j.r j.r PROPN cana-1744 307 7 . . PROPN cana-1744 307 8 and and CCONJ cana-1744 307 9 choudhury choudhury PROPN cana-1744 307 10 , , PUNCT cana-1744 307 11 g. g. PROPN cana-1744 307 12 2004 2004 NUM cana-1744 307 13 . . PUNCT cana-1744 308 1 steady steady ADJ cana-1744 308 2 state state NOUN cana-1744 308 3 analysis analysis NOUN cana-1744 308 4 of of ADP cana-1744 308 5 an an DET cana-1744 308 6 m m NOUN cana-1744 308 7 / / SYM cana-1744 308 8 g/1 g/1 NOUN cana-1744 308 9 queue queue NOUN cana-1744 308 10 with with ADP cana-1744 308 11 repeated repeat VERB cana-1744 308 12 attempts attempt NOUN cana-1744 308 13 and and CCONJ cana-1744 308 14 two two NUM cana-1744 308 15 - - PUNCT cana-1744 308 16 phase phase NOUN cana-1744 308 17 service service NOUN cana-1744 308 18 : : PUNCT cana-1744 308 19 quality quality NOUN cana-1744 308 20 technology technology NOUN cana-1744 308 21 and and CCONJ cana-1744 308 22 quantitative quantitative ADJ cana-1744 308 23 management management NOUN cana-1744 308 24 , , PUNCT cana-1744 308 25 vol.1 vol.1 PROPN cana-1744 308 26 , , PUNCT cana-1744 308 27 189 189 NUM cana-1744 308 28 - - SYM cana-1744 308 29 199 199 NUM cana-1744 308 30 . . PUNCT cana-1744 309 1 [ [ X cana-1744 309 2 11 11 NUM cana-1744 309 3 ] ] X cana-1744 309 4 jehad jehad PROPN cana-1744 309 5 al al PROPN cana-1744 309 6 - - PUNCT cana-1744 309 7 jararha jararha PROPN cana-1744 309 8 kailash kailash PROPN cana-1744 309 9 c. c. PROPN cana-1744 309 10 madan madan PROPN cana-1744 309 11 2003 2003 NUM cana-1744 309 12 . . PUNCT cana-1744 310 1 an an DET cana-1744 310 2 m m NOUN cana-1744 310 3 / / SYM cana-1744 310 4 g/1 g/1 NOUN cana-1744 310 5 queue queue NOUN cana-1744 310 6 with with ADP cana-1744 310 7 second second ADJ cana-1744 310 8 optional optional ADJ cana-1744 310 9 service service NOUN cana-1744 310 10 with with ADP cana-1744 310 11 general general ADJ cana-1744 310 12 service service NOUN cana-1744 310 13 time time NOUN cana-1744 310 14 distribution distribution NOUN cana-1744 310 15 : : PUNCT cana-1744 310 16 information information NOUN cana-1744 310 17 and and CCONJ cana-1744 310 18 management management NOUN cana-1744 310 19 sciences science NOUN cana-1744 310 20 , , PUNCT cana-1744 310 21 vol.14 vol.14 NOUN cana-1744 310 22 , , PUNCT cana-1744 310 23 no.2 no.2 PROPN cana-1744 310 24 , , PUNCT cana-1744 310 25 47 47 NUM cana-1744 310 26 - - SYM cana-1744 310 27 56 56 NUM cana-1744 310 28 . . PUNCT cana-1744 311 1 [ [ X cana-1744 311 2 12 12 NUM cana-1744 311 3 ] ] X cana-1744 311 4 madan madan PROPN cana-1744 311 5 , , PUNCT cana-1744 311 6 k.c k.c PROPN cana-1744 311 7 . . PROPN cana-1744 311 8 , , PUNCT cana-1744 311 9 abu abu PROPN cana-1744 311 10 - - PUNCT cana-1744 311 11 dayyeh dayyeh PROPN cana-1744 311 12 , , PUNCT cana-1744 311 13 w. w. PROPN cana-1744 311 14 and and CCONJ cana-1744 311 15 saleh saleh PROPN cana-1744 311 16 , , PUNCT cana-1744 311 17 m.f.2002 m.f.2002 PROPN cana-1744 311 18 . . PUNCT cana-1744 312 1 an an DET cana-1744 312 2 m m NOUN cana-1744 312 3 / / SYM cana-1744 312 4 g/1 g/1 NOUN cana-1744 312 5 queue queue NOUN cana-1744 312 6 with with ADP cana-1744 312 7 second second ADJ cana-1744 312 8 optional optional ADJ cana-1744 312 9 service service NOUN cana-1744 312 10 and and CCONJ cana-1744 312 11 bernoulli bernoulli NOUN cana-1744 312 12 schedule schedule NOUN cana-1744 312 13 server server NOUN cana-1744 312 14 vacations vacation NOUN cana-1744 312 15 : : PUNCT cana-1744 312 16 systems system NOUN cana-1744 312 17 science science NOUN cana-1744 312 18 , , PUNCT cana-1744 312 19 vol.28 vol.28 NOUN cana-1744 312 20 , , PUNCT cana-1744 312 21 51 51 NUM cana-1744 312 22 - - SYM cana-1744 312 23 62 62 NUM cana-1744 312 24 . . PUNCT cana-1744 313 1 [ [ X cana-1744 313 2 13 13 NUM cana-1744 313 3 ] ] X cana-1744 313 4 som som X cana-1744 313 5 bk bk PROPN cana-1744 313 6 , , PUNCT cana-1744 313 7 seth seth PROPN cana-1744 313 8 s. s. PROPN cana-1744 313 9 an an DET cana-1744 313 10 m m PROPN cana-1744 313 11 / / SYM cana-1744 313 12 m/1 m/1 NOUN cana-1744 313 13 / / SYM cana-1744 313 14 n n NOUN cana-1744 313 15 queuing queue VERB cana-1744 313 16 system system NOUN cana-1744 313 17 with with ADP cana-1744 313 18 encouraged encouraged ADJ cana-1744 313 19 arrivals arrival NOUN cana-1744 313 20 . . PUNCT cana-1744 314 1 global global ADJ cana-1744 314 2 journal journal PROPN cana-1744 314 3 of of ADP cana-1744 314 4 pure pure ADJ cana-1744 314 5 and and CCONJ cana-1744 314 6 applied applied ADJ cana-1744 314 7 mathematics mathematic NOUN cana-1744 314 8 . . PUNCT cana-1744 315 1 2017 2017 NUM cana-1744 315 2 ; ; PUNCT cana-1744 315 3 13 13 NUM cana-1744 315 4 : : SYM cana-1744 315 5 3443 3443 NUM cana-1744 315 6 - - SYM cana-1744 315 7 3453 3453 NUM cana-1744 315 8 . . PUNCT cana-1744 316 1 [ [ X cana-1744 316 2 14 14 NUM cana-1744 316 3 ] ] X cana-1744 316 4 khan khan PROPN cana-1744 316 5 ie ie X cana-1744 316 6 , , PUNCT cana-1744 316 7 paramasivam paramasivam VERB cana-1744 316 8 r. r. NOUN cana-1744 316 9 reduction reduction NOUN cana-1744 316 10 in in ADP cana-1744 316 11 waiting wait VERB cana-1744 316 12 time time NOUN cana-1744 316 13 in in ADP cana-1744 316 14 an an PRON cana-1744 316 15 m m NOUN cana-1744 316 16 / / SYM cana-1744 316 17 m/1 m/1 NOUN cana-1744 316 18 / / SYM cana-1744 316 19 n n CCONJ cana-1744 316 20 encouraged encourage VERB cana-1744 316 21 arrival arrival NOUN cana-1744 316 22 queue queue NOUN cana-1744 316 23 with with ADP cana-1744 316 24 feedback feedback NOUN cana-1744 316 25 , , PUNCT cana-1744 316 26 balking balk VERB cana-1744 316 27 and and CCONJ cana-1744 316 28 maintaining maintain VERB cana-1744 316 29 of of ADP cana-1744 316 30 reneged renege VERB cana-1744 316 31 customers customer NOUN cana-1744 316 32 . . PUNCT cana-1744 316 33 symmetry symmetry NOUN cana-1744 316 34 . . PUNCT cana-1744 317 1 2022 2022 NUM cana-1744 317 2 ; ; PUNCT cana-1744 317 3 [ [ X cana-1744 317 4 15 15 NUM cana-1744 317 5 ] ] X cana-1744 317 6 khan khan PROPN cana-1744 317 7 ie ie X cana-1744 317 8 , , PUNCT cana-1744 317 9 paramasivam paramasivam VERB cana-1744 317 10 r r NOUN cana-1744 317 11 , , PUNCT cana-1744 317 12 performance performance NOUN cana-1744 317 13 study study NOUN cana-1744 317 14 of of ADP cana-1744 317 15 an an DET cana-1744 317 16 m m PROPN cana-1744 317 17 / / SYM cana-1744 317 18 m/1 m/1 NOUN cana-1744 317 19 retrial retrial NOUN cana-1744 317 20 queueing queueing NOUN cana-1744 317 21 system system NOUN cana-1744 317 22 with with ADP cana-1744 317 23 balking balk VERB cana-1744 317 24 , , PUNCT cana-1744 317 25 dissatisfied dissatisfied ADJ cana-1744 317 26 customers customer NOUN cana-1744 317 27 , , PUNCT cana-1744 317 28 and and CCONJ cana-1744 317 29 server server NOUN cana-1744 317 30 vacations vacation NOUN cana-1744 317 31 , , PUNCT cana-1744 317 32 contemporary contemporary ADJ cana-1744 317 33 mathematics mathematic NOUN cana-1744 317 34 , , PUNCT cana-1744 317 35 volume volume NOUN cana-1744 317 36 4 4 NUM cana-1744 317 37 issue issue NOUN cana-1744 317 38 3 3 NUM cana-1744 317 39 ( ( PUNCT cana-1744 317 40 2023 2023 NUM cana-1744 317 41 ) ) PUNCT cana-1744 317 42 , , PUNCT cana-1744 317 43 379 379 NUM cana-1744 317 44 - - SYM cana-1744 317 45 619 619 NUM cana-1744 317 46 . . PUNCT cana-1744 318 1 https://ojs.wiserpub.com/index.php/cm/article/view/3117 https://ojs.wiserpub.com/index.php/cm/article/view/3117 PRON cana-1744 318 2 https://ojs.wiserpub.com/index.php/cm/article/view/3117 https://ojs.wiserpub.com/index.php/cm/article/view/3117 ADV cana-1744 318 3 https://ojs.wiserpub.com/index.php/cm/issue/view/cm.v4i32023.379-619 https://ojs.wiserpub.com/index.php/cm/issue/view/cm.v4i32023.379-619 ADP