id sid tid token lemma pos cana-1902 1 1 communications communication NOUN cana-1902 1 2 on on ADP cana-1902 1 3 applied apply VERB cana-1902 1 4 nonlinear nonlinear ADJ cana-1902 1 5 analysis analysis NOUN cana-1902 1 6 issn issn NOUN cana-1902 1 7 : : PUNCT cana-1902 1 8 1074 1074 NUM cana-1902 1 9 - - PUNCT cana-1902 1 10 133x 133x NUM cana-1902 1 11 vol vol NOUN cana-1902 1 12 32 32 NUM cana-1902 1 13 no no NOUN cana-1902 1 14 . . NOUN cana-1902 1 15 3 3 NUM cana-1902 1 16 ( ( PUNCT cana-1902 1 17 2025 2025 NUM cana-1902 1 18 ) ) PUNCT cana-1902 1 19 1 1 NUM cana-1902 1 20 https://internationalpubls.com https://internationalpubls.com X cana-1902 1 21 a a DET cana-1902 1 22 study study NOUN cana-1902 1 23 on on ADP cana-1902 1 24 catastrophic catastrophic ADJ cana-1902 1 25 retrial retrial ADJ cana-1902 1 26 feedback feedback NOUN cana-1902 1 27 queueing queue VERB cana-1902 1 28 network network NOUN cana-1902 1 29 model model NOUN cana-1902 1 30 with with ADP cana-1902 1 31 three three NUM cana-1902 1 32 nodes node NOUN cana-1902 1 33 in in ADP cana-1902 1 34 steady steady ADJ cana-1902 1 35 state state NOUN cana-1902 1 36 s. s. PROPN cana-1902 1 37 shanmugasundaram1 shanmugasundaram1 PROPN cana-1902 1 38 , , PUNCT cana-1902 1 39 c. c. PROPN cana-1902 1 40 baby2 baby2 NOUN cana-1902 1 41 1associate 1associate NUM cana-1902 1 42 professor professor NOUN cana-1902 1 43 of of ADP cana-1902 1 44 mathematics mathematic NOUN cana-1902 1 45 , , PUNCT cana-1902 1 46 government government NOUN cana-1902 1 47 arts arts PROPN cana-1902 1 48 college college PROPN cana-1902 1 49 ( ( PUNCT cana-1902 1 50 autonomous autonomous ADJ cana-1902 1 51 ) ) PUNCT cana-1902 1 52 , , PUNCT cana-1902 1 53 salem salem NOUN cana-1902 1 54 – – PUNCT cana-1902 1 55 636007 636007 NUM cana-1902 1 56 , , PUNCT cana-1902 1 57 tamil tamil PROPN cana-1902 1 58 nadu nadu PROPN cana-1902 1 59 , , PUNCT cana-1902 2 1 india india PROPN cana-1902 2 2 . . PUNCT cana-1902 2 3 email email NOUN cana-1902 2 4 : : PUNCT cana-1902 3 1 sundaramsss@hotmail.com sundaramsss@hotmail.com X cana-1902 3 2 2ph.d 2ph.d NUM cana-1902 3 3 research research NOUN cana-1902 3 4 scholar scholar NOUN cana-1902 3 5 ( ( PUNCT cana-1902 3 6 part part NOUN cana-1902 3 7 time time NOUN cana-1902 3 8 ) ) PUNCT cana-1902 3 9 , , PUNCT cana-1902 3 10 department department NOUN cana-1902 3 11 of of ADP cana-1902 3 12 mathematics mathematic NOUN cana-1902 3 13 , , PUNCT cana-1902 3 14 government government NOUN cana-1902 3 15 arts arts PROPN cana-1902 3 16 college college PROPN cana-1902 3 17 ( ( PUNCT cana-1902 3 18 autonomous autonomous ADJ cana-1902 3 19 ) ) PUNCT cana-1902 3 20 , , PUNCT cana-1902 3 21 salem salem NOUN cana-1902 3 22 – – PUNCT cana-1902 3 23 636007 636007 NUM cana-1902 3 24 , , PUNCT cana-1902 3 25 tamil tamil PROPN cana-1902 3 26 nadu nadu PROPN cana-1902 3 27 , , PUNCT cana-1902 3 28 india india PROPN cana-1902 3 29 . . PUNCT cana-1902 3 30 email email NOUN cana-1902 3 31 : : PUNCT cana-1902 3 32 babyakcika2015@gmail.com babyakcika2015@gmail.com X cana-1902 3 33 article article NOUN cana-1902 3 34 history history NOUN cana-1902 3 35 : : PUNCT cana-1902 3 36 received receive VERB cana-1902 3 37 : : PUNCT cana-1902 3 38 19 19 NUM cana-1902 3 39 - - PUNCT cana-1902 3 40 07 07 NUM cana-1902 3 41 - - PUNCT cana-1902 3 42 2024 2024 NUM cana-1902 3 43 revised revise VERB cana-1902 3 44 : : PUNCT cana-1902 3 45 09 09 NUM cana-1902 3 46 - - SYM cana-1902 3 47 09 09 NUM cana-1902 3 48 - - PUNCT cana-1902 3 49 2024 2024 NUM cana-1902 3 50 accepted accept VERB cana-1902 3 51 : : PUNCT cana-1902 3 52 29 29 NUM cana-1902 3 53 - - SYM cana-1902 3 54 09 09 NUM cana-1902 3 55 - - PUNCT cana-1902 3 56 2024 2024 NUM cana-1902 3 57 abstract abstract ADJ cana-1902 3 58 queueing queue VERB cana-1902 3 59 networks network NOUN cana-1902 3 60 , , PUNCT cana-1902 3 61 which which PRON cana-1902 3 62 are be AUX cana-1902 3 63 effectively effectively ADV cana-1902 3 64 used use VERB cana-1902 3 65 for for ADP cana-1902 3 66 performance performance NOUN cana-1902 3 67 analysis analysis NOUN cana-1902 3 68 of of ADP cana-1902 3 69 various various ADJ cana-1902 3 70 systems system NOUN cana-1902 3 71 , , PUNCT cana-1902 3 72 including include VERB cana-1902 3 73 computer computer NOUN cana-1902 3 74 , , PUNCT cana-1902 3 75 communications communication NOUN cana-1902 3 76 , , PUNCT cana-1902 3 77 transportation transportation NOUN cana-1902 3 78 networks network NOUN cana-1902 3 79 , , PUNCT cana-1902 3 80 and and CCONJ cana-1902 3 81 manufacturing manufacturing NOUN cana-1902 3 82 , , PUNCT cana-1902 3 83 are be AUX cana-1902 3 84 discussed discuss VERB cana-1902 3 85 in in ADP cana-1902 3 86 this this DET cana-1902 3 87 article article NOUN cana-1902 3 88 . . PUNCT cana-1902 4 1 under under ADP cana-1902 4 2 the the DET cana-1902 4 3 catastrophic catastrophic ADJ cana-1902 4 4 condition condition NOUN cana-1902 4 5 , , PUNCT cana-1902 4 6 we we PRON cana-1902 4 7 evaluate evaluate VERB cana-1902 4 8 a a DET cana-1902 4 9 queueing queue VERB cana-1902 4 10 network network NOUN cana-1902 4 11 with with ADP cana-1902 4 12 feedback feedback NOUN cana-1902 4 13 and and CCONJ cana-1902 4 14 retrial retrial NOUN cana-1902 4 15 for for ADP cana-1902 4 16 single single ADJ cana-1902 4 17 server server NOUN cana-1902 4 18 . . PUNCT cana-1902 5 1 in in ADP cana-1902 5 2 the the DET cana-1902 5 3 third third ADJ cana-1902 5 4 node node NOUN cana-1902 5 5 the the DET cana-1902 5 6 customer customer NOUN cana-1902 5 7 can can AUX cana-1902 5 8 decide decide VERB cana-1902 5 9 whether whether SCONJ cana-1902 5 10 feedback feedback VERB cana-1902 5 11 or or CCONJ cana-1902 5 12 leave leave VERB cana-1902 5 13 the the DET cana-1902 5 14 system system NOUN cana-1902 5 15 with with ADP cana-1902 5 16 probabilities probability NOUN cana-1902 5 17 t t PROPN cana-1902 5 18 , , PUNCT cana-1902 5 19 u u NOUN cana-1902 5 20 and and CCONJ cana-1902 5 21 1 1 PROPN cana-1902 5 22 - - SYM cana-1902 5 23 tu tu PROPN cana-1902 5 24 . . PUNCT cana-1902 5 25 also also ADV cana-1902 5 26 using use VERB cana-1902 5 27 little little ADJ cana-1902 5 28 's 's PART cana-1902 5 29 formula formula NOUN cana-1902 5 30 , , PUNCT cana-1902 5 31 we we PRON cana-1902 5 32 are be AUX cana-1902 5 33 determining determine VERB cana-1902 5 34 the the DET cana-1902 5 35 likelihood likelihood NOUN cana-1902 5 36 of of ADP cana-1902 5 37 having have VERB cana-1902 5 38 idle idle ADJ cana-1902 5 39 customers customer NOUN cana-1902 5 40 and and CCONJ cana-1902 5 41 determining determine VERB cana-1902 5 42 n n DET cana-1902 5 43 number number NOUN cana-1902 5 44 of of ADP cana-1902 5 45 customers customer NOUN cana-1902 5 46 in in ADP cana-1902 5 47 the the DET cana-1902 5 48 system system NOUN cana-1902 5 49 . . PUNCT cana-1902 6 1 we we PRON cana-1902 6 2 are be AUX cana-1902 6 3 deriving derive VERB cana-1902 6 4 πΏπ‘ž πΏπ‘ž PROPN cana-1902 6 5 , , PUNCT cana-1902 6 6 𝐿𝑠 𝐿𝑠 PROPN cana-1902 6 7 , , PUNCT cana-1902 6 8 π‘Šπ‘ž π‘Šπ‘ž PROPN cana-1902 6 9 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ cana-1902 6 10 π‘Šπ‘  π‘Šπ‘  PROPN cana-1902 6 11 for for ADP cana-1902 6 12 the the DET cana-1902 6 13 above above ADJ cana-1902 6 14 model model NOUN cana-1902 6 15 . . PUNCT cana-1902 7 1 the the DET cana-1902 7 2 purpose purpose NOUN cana-1902 7 3 of of ADP cana-1902 7 4 the the DET cana-1902 7 5 numerical numerical ADJ cana-1902 7 6 example example NOUN cana-1902 7 7 gives give VERB cana-1902 7 8 the the DET cana-1902 7 9 richness richness NOUN cana-1902 7 10 of of ADP cana-1902 7 11 our our PRON cana-1902 7 12 result result NOUN cana-1902 7 13 and and CCONJ cana-1902 7 14 the the DET cana-1902 7 15 feasibility feasibility NOUN cana-1902 7 16 of of ADP cana-1902 7 17 this this DET cana-1902 7 18 concept concept NOUN cana-1902 7 19 . . PUNCT cana-1902 8 1 keywords keyword NOUN cana-1902 8 2 : : PUNCT cana-1902 8 3 queueing queue VERB cana-1902 8 4 network network NOUN cana-1902 8 5 , , PUNCT cana-1902 8 6 feedback feedback NOUN cana-1902 8 7 , , PUNCT cana-1902 8 8 retrial retrial NOUN cana-1902 8 9 , , PUNCT cana-1902 8 10 catastrophes catastrophe NOUN cana-1902 8 11 . . PUNCT cana-1902 9 1 1 1 X cana-1902 9 2 . . X cana-1902 9 3 introduction introduction NOUN cana-1902 9 4 queues queue NOUN cana-1902 9 5 form form VERB cana-1902 9 6 when when SCONJ cana-1902 9 7 there there PRON cana-1902 9 8 is be VERB cana-1902 9 9 a a DET cana-1902 9 10 current current ADJ cana-1902 9 11 demand demand NOUN cana-1902 9 12 for for ADP cana-1902 9 13 a a DET cana-1902 9 14 certain certain ADJ cana-1902 9 15 service service NOUN cana-1902 9 16 that that PRON cana-1902 9 17 exceeds exceed VERB cana-1902 9 18 supply supply NOUN cana-1902 9 19 . . PUNCT cana-1902 10 1 if if SCONJ cana-1902 10 2 the the DET cana-1902 10 3 customer customer NOUN cana-1902 10 4 's 's PART cana-1902 10 5 requested request VERB cana-1902 10 6 service service NOUN cana-1902 10 7 is be AUX cana-1902 10 8 not not PART cana-1902 10 9 immediately immediately ADV cana-1902 10 10 available available ADJ cana-1902 10 11 , , PUNCT cana-1902 10 12 a a DET cana-1902 10 13 queue queue NOUN cana-1902 10 14 will will AUX cana-1902 10 15 emerge emerge VERB cana-1902 10 16 . . PUNCT cana-1902 11 1 our our PRON cana-1902 11 2 everyday everyday ADJ cana-1902 11 3 lives life NOUN cana-1902 11 4 involve involve VERB cana-1902 11 5 waiting wait VERB cana-1902 11 6 in in ADP cana-1902 11 7 line line NOUN cana-1902 11 8 for for ADP cana-1902 11 9 services service NOUN cana-1902 11 10 ; ; PUNCT cana-1902 11 11 examples example NOUN cana-1902 11 12 include include VERB cana-1902 11 13 waiting wait VERB cana-1902 11 14 at at ADP cana-1902 11 15 hotels hotel NOUN cana-1902 11 16 , , PUNCT cana-1902 11 17 at at ADP cana-1902 11 18 train train NOUN cana-1902 11 19 reservation reservation NOUN cana-1902 11 20 counters counter NOUN cana-1902 11 21 , , PUNCT cana-1902 11 22 and and CCONJ cana-1902 11 23 at at ADP cana-1902 11 24 banks bank NOUN cana-1902 11 25 . . PUNCT cana-1902 12 1 other other ADJ cana-1902 12 2 scenarios scenario NOUN cana-1902 12 3 involve involve VERB cana-1902 12 4 waiting wait VERB cana-1902 12 5 , , PUNCT cana-1902 12 6 such such ADJ cana-1902 12 7 as as ADP cana-1902 12 8 tasks task NOUN cana-1902 12 9 that that PRON cana-1902 12 10 require require VERB cana-1902 12 11 a a DET cana-1902 12 12 machine machine NOUN cana-1902 12 13 to to PART cana-1902 12 14 complete complete VERB cana-1902 12 15 , , PUNCT cana-1902 12 16 aircraft aircraft NOUN cana-1902 12 17 that that PRON cana-1902 12 18 must must AUX cana-1902 12 19 circle circle VERB cana-1902 12 20 in in ADP cana-1902 12 21 the the DET cana-1902 12 22 air air NOUN cana-1902 12 23 before before ADP cana-1902 12 24 landing landing NOUN cana-1902 12 25 and and CCONJ cana-1902 12 26 vehicles vehicle NOUN cana-1902 12 27 that that PRON cana-1902 12 28 must must AUX cana-1902 12 29 stop stop VERB cana-1902 12 30 at at ADP cana-1902 12 31 traffic traffic NOUN cana-1902 12 32 signals signal NOUN cana-1902 12 33 , , PUNCT cana-1902 12 34 among among ADP cana-1902 12 35 others other NOUN cana-1902 12 36 . . PUNCT cana-1902 13 1 erlang erlang PROPN cana-1902 14 1 [ [ X cana-1902 14 2 4 4 NUM cana-1902 14 3 ] ] PUNCT cana-1902 14 4 , , PUNCT cana-1902 14 5 a a DET cana-1902 14 6 danish danish ADJ cana-1902 14 7 mathematician mathematician NOUN cana-1902 14 8 and and CCONJ cana-1902 14 9 engineer engineer NOUN cana-1902 14 10 , , PUNCT cana-1902 14 11 initially initially ADV cana-1902 14 12 contributed contribute VERB cana-1902 14 13 in in ADP cana-1902 14 14 queueing queue VERB cana-1902 14 15 theory theory NOUN cana-1902 14 16 , , PUNCT cana-1902 14 17 which which PRON cana-1902 14 18 formed form VERB cana-1902 14 19 the the DET cana-1902 14 20 foundation foundation NOUN cana-1902 14 21 of of ADP cana-1902 14 22 the the DET cana-1902 14 23 system system NOUN cana-1902 14 24 . . PUNCT cana-1902 15 1 when when SCONJ cana-1902 15 2 the the DET cana-1902 15 3 behaviour behaviour NOUN cana-1902 15 4 of of ADP cana-1902 15 5 the the DET cana-1902 15 6 system system NOUN cana-1902 15 7 depends depend VERB cana-1902 15 8 on on ADP cana-1902 15 9 time time NOUN cana-1902 15 10 , , PUNCT cana-1902 15 11 it it PRON cana-1902 15 12 is be AUX cana-1902 15 13 said say VERB cana-1902 15 14 to to PART cana-1902 15 15 be be AUX cana-1902 15 16 in in ADP cana-1902 15 17 a a DET cana-1902 15 18 transient transient ADJ cana-1902 15 19 state state NOUN cana-1902 15 20 . . PUNCT cana-1902 16 1 when when SCONJ cana-1902 16 2 the the DET cana-1902 16 3 operational operational ADJ cana-1902 16 4 characteristics characteristic NOUN cana-1902 16 5 do do AUX cana-1902 16 6 not not PART cana-1902 16 7 depent depent VERB cana-1902 16 8 on on ADP cana-1902 16 9 time time NOUN cana-1902 16 10 , , PUNCT cana-1902 16 11 they they PRON cana-1902 16 12 are be AUX cana-1902 16 13 said say VERB cana-1902 16 14 to to PART cana-1902 16 15 be be AUX cana-1902 16 16 in in ADP cana-1902 16 17 a a DET cana-1902 16 18 steady steady ADJ cana-1902 16 19 state state NOUN cana-1902 16 20 . . PUNCT cana-1902 17 1 1.1 1.1 NUM cana-1902 17 2 queueing queue VERB cana-1902 17 3 network network NOUN cana-1902 17 4 a a DET cana-1902 17 5 collection collection NOUN cana-1902 17 6 of of ADP cana-1902 17 7 nodes node NOUN cana-1902 17 8 , , PUNCT cana-1902 17 9 with with ADP cana-1902 17 10 each each DET cana-1902 17 11 one one NOUN cana-1902 17 12 representing represent VERB cana-1902 17 13 a a DET cana-1902 17 14 different different ADJ cana-1902 17 15 service service NOUN cana-1902 17 16 facility facility NOUN cana-1902 17 17 , , PUNCT cana-1902 17 18 forms form VERB cana-1902 17 19 a a DET cana-1902 17 20 queuing queue VERB cana-1902 17 21 network network NOUN cana-1902 17 22 . . PUNCT cana-1902 18 1 in in ADP cana-1902 18 2 1957 1957 NUM cana-1902 18 3 , , PUNCT cana-1902 18 4 jackson jackson PROPN cana-1902 19 1 [ [ X cana-1902 19 2 7 7 NUM cana-1902 19 3 ] ] PUNCT cana-1902 19 4 first first ADV cana-1902 19 5 proposed propose VERB cana-1902 19 6 the the DET cana-1902 19 7 application application NOUN cana-1902 19 8 of of ADP cana-1902 19 9 queueing queue VERB cana-1902 19 10 networks network NOUN cana-1902 19 11 . . PUNCT cana-1902 20 1 for for ADP cana-1902 20 2 the the DET cana-1902 20 3 queueing queue VERB cana-1902 20 4 network network NOUN cana-1902 20 5 , , PUNCT cana-1902 20 6 jackson jackson PROPN cana-1902 20 7 's 's PART cana-1902 20 8 network network NOUN cana-1902 20 9 [ [ X cana-1902 20 10 8 8 NUM cana-1902 20 11 ] ] PUNCT cana-1902 20 12 has have AUX cana-1902 20 13 contributed contribute VERB cana-1902 20 14 the the DET cana-1902 20 15 initial initial ADJ cana-1902 20 16 model model NOUN cana-1902 20 17 which which PRON cana-1902 20 18 is be AUX cana-1902 20 19 still still ADV cana-1902 20 20 considering consider VERB cana-1902 20 21 till till SCONJ cana-1902 20 22 date date NOUN cana-1902 20 23 . . PUNCT cana-1902 21 1 queuing queue VERB cana-1902 21 2 network network NOUN cana-1902 21 3 models model NOUN cana-1902 21 4 have have AUX cana-1902 21 5 been be AUX cana-1902 21 6 utilized utilize VERB cana-1902 21 7 in in ADP cana-1902 21 8 a a DET cana-1902 21 9 wide wide ADJ cana-1902 21 10 range range NOUN cana-1902 21 11 of of ADP cana-1902 21 12 businesses business NOUN cana-1902 21 13 and and CCONJ cana-1902 21 14 environments environment NOUN cana-1902 21 15 , , PUNCT cana-1902 21 16 including include VERB cana-1902 21 17 airport airport NOUN cana-1902 21 18 terminals terminal NOUN cana-1902 21 19 , , PUNCT cana-1902 21 20 healthcare healthcare NOUN cana-1902 21 21 systems system NOUN cana-1902 21 22 , , PUNCT cana-1902 21 23 flexible flexible ADJ cana-1902 21 24 manufacturing manufacturing NOUN cana-1902 21 25 and and CCONJ cana-1902 21 26 production production NOUN cana-1902 21 27 systems system NOUN cana-1902 21 28 , , PUNCT cana-1902 21 29 computer computer NOUN cana-1902 21 30 networks network NOUN cana-1902 21 31 , , PUNCT cana-1902 21 32 and and CCONJ cana-1902 21 33 networks network NOUN cana-1902 21 34 for for ADP cana-1902 21 35 communication communication NOUN cana-1902 21 36 . . PUNCT cana-1902 22 1 queuing queue VERB cana-1902 22 2 networks network NOUN cana-1902 22 3 fall fall VERB cana-1902 22 4 into into ADP cana-1902 22 5 three three NUM cana-1902 22 6 categories category NOUN cana-1902 22 7 : : PUNCT cana-1902 22 8 mixed mixed ADJ cana-1902 22 9 , , PUNCT cana-1902 22 10 closed closed ADJ cana-1902 22 11 , , PUNCT cana-1902 22 12 and and CCONJ cana-1902 22 13 open open ADJ cana-1902 22 14 networks network NOUN cana-1902 22 15 . . PUNCT cana-1902 23 1 an an DET cana-1902 23 2 arrival arrival NOUN cana-1902 23 3 enters enter VERB cana-1902 23 4 the the DET cana-1902 23 5 system system NOUN cana-1902 23 6 get get VERB cana-1902 23 7 service service NOUN cana-1902 23 8 and and CCONJ cana-1902 23 9 leaves leave VERB cana-1902 23 10 the the DET cana-1902 23 11 system system NOUN cana-1902 23 12 in in ADP cana-1902 23 13 the the DET cana-1902 23 14 open open ADJ cana-1902 23 15 network network NOUN cana-1902 23 16 . . PUNCT cana-1902 24 1 in in ADP cana-1902 24 2 closed closed ADJ cana-1902 24 3 networks network NOUN cana-1902 24 4 , , PUNCT cana-1902 24 5 the the DET cana-1902 24 6 number number NOUN cana-1902 24 7 of of ADP cana-1902 24 8 users user NOUN cana-1902 24 9 is be AUX cana-1902 24 10 fixed fix VERB cana-1902 24 11 , , PUNCT cana-1902 24 12 and and CCONJ cana-1902 24 13 they they PRON cana-1902 24 14 never never ADV cana-1902 24 15 leave leave VERB cana-1902 24 16 the the DET cana-1902 24 17 system system NOUN cana-1902 24 18 , , PUNCT cana-1902 24 19 they they PRON cana-1902 24 20 just just ADV cana-1902 24 21 switch switch VERB cana-1902 24 22 between between ADP cana-1902 24 23 queues queue NOUN cana-1902 24 24 . . PUNCT cana-1902 25 1 mixed mixed ADJ cana-1902 25 2 networks network NOUN cana-1902 25 3 allow allow VERB cana-1902 25 4 certain certain ADJ cana-1902 25 5 kinds kind NOUN cana-1902 25 6 of of ADP cana-1902 25 7 users user NOUN cana-1902 25 8 in in ADP cana-1902 25 9 but but CCONJ cana-1902 25 10 prohibit prohibit VERB cana-1902 25 11 others other NOUN cana-1902 25 12 . . PUNCT cana-1902 26 1 1.2 1.2 NUM cana-1902 26 2 retrial retrial ADJ cana-1902 26 3 queue queue NOUN cana-1902 26 4 retrial retrial NOUN cana-1902 26 5 queueing queueing NOUN cana-1902 26 6 models model NOUN cana-1902 26 7 are be AUX cana-1902 26 8 predicated predicate VERB cana-1902 26 9 on on ADP cana-1902 26 10 the the DET cana-1902 26 11 idea idea NOUN cana-1902 26 12 that that SCONJ cana-1902 26 13 arriving arrive VERB cana-1902 26 14 customers customer NOUN cana-1902 26 15 do do AUX cana-1902 26 16 not not PART cana-1902 26 17 queue queue VERB cana-1902 26 18 up up ADV cana-1902 26 19 or or CCONJ cana-1902 26 20 move move VERB cana-1902 26 21 the the DET cana-1902 26 22 system system NOUN cana-1902 26 23 instantly instantly ADV cana-1902 26 24 when when SCONJ cana-1902 26 25 the the DET cana-1902 26 26 server server NOUN cana-1902 26 27 is be AUX cana-1902 26 28 crowded crowded ADJ cana-1902 26 29 . . PUNCT cana-1902 27 1 instead instead ADV cana-1902 27 2 , , PUNCT cana-1902 27 3 they they PRON cana-1902 27 4 visit visit VERB cana-1902 27 5 a a DET cana-1902 27 6 virtual virtual ADJ cana-1902 27 7 space space NOUN cana-1902 27 8 called call VERB cana-1902 27 9 orbit orbit NOUN cana-1902 27 10 and and CCONJ cana-1902 27 11 return return VERB cana-1902 27 12 later later ADV cana-1902 27 13 to to PART cana-1902 27 14 try try VERB cana-1902 27 15 their their PRON cana-1902 27 16 luck luck NOUN cana-1902 27 17 . . PUNCT cana-1902 28 1 many many ADJ cana-1902 28 2 computer computer NOUN cana-1902 28 3 systems system NOUN cana-1902 28 4 and and CCONJ cana-1902 28 5 communication communication NOUN cana-1902 28 6 networks network NOUN cana-1902 28 7 may may AUX cana-1902 28 8 be be AUX cana-1902 28 9 mailto:sundaramsss@hotmail.com mailto:sundaramsss@hotmail.com PROPN cana-1902 28 10 mailto:babyakcika2015@gmail.com mailto:babyakcika2015@gmail.com PROPN cana-1902 28 11 communications communication NOUN cana-1902 28 12 on on ADP cana-1902 28 13 applied apply VERB cana-1902 28 14 nonlinear nonlinear ADJ cana-1902 28 15 analysis analysis NOUN cana-1902 28 16 issn issn NOUN cana-1902 28 17 : : PUNCT cana-1902 28 18 1074 1074 NUM cana-1902 28 19 - - PUNCT cana-1902 28 20 133x 133x NUM cana-1902 28 21 vol vol NOUN cana-1902 28 22 32 32 NUM cana-1902 28 23 no no NOUN cana-1902 28 24 . . NOUN cana-1902 28 25 3 3 NUM cana-1902 28 26 ( ( PUNCT cana-1902 28 27 2025 2025 NUM cana-1902 28 28 ) ) PUNCT cana-1902 28 29 2 2 NUM cana-1902 28 30 https://internationalpubls.com https://internationalpubls.com X cana-1902 28 31 mathematically mathematically ADV cana-1902 28 32 modeled model VERB cana-1902 28 33 using use VERB cana-1902 28 34 retrial retrial ADJ cana-1902 28 35 queues queue NOUN cana-1902 28 36 , , PUNCT cana-1902 28 37 which which PRON cana-1902 28 38 are be AUX cana-1902 28 39 employed employ VERB cana-1902 28 40 with with ADP cana-1902 28 41 great great ADJ cana-1902 28 42 effectiveness effectiveness NOUN cana-1902 28 43 in in ADP cana-1902 28 44 these these DET cana-1902 28 45 applications application NOUN cana-1902 28 46 . . PUNCT cana-1902 29 1 kosten kosten PROPN cana-1902 30 1 [ [ X cana-1902 30 2 9 9 NUM cana-1902 30 3 ] ] PUNCT cana-1902 30 4 initially initially ADV cana-1902 30 5 presents present VERB cana-1902 30 6 the the DET cana-1902 30 7 retrial retrial ADJ cana-1902 30 8 queue queue NOUN cana-1902 30 9 in in ADP cana-1902 30 10 1947 1947 NUM cana-1902 30 11 . . PUNCT cana-1902 31 1 falin falin NOUN cana-1902 31 2 [ [ X cana-1902 31 3 5 5 NUM cana-1902 31 4 ] ] PUNCT cana-1902 31 5 examined examine VERB cana-1902 31 6 the the DET cana-1902 31 7 key key ADJ cana-1902 31 8 results result NOUN cana-1902 31 9 and and CCONJ cana-1902 31 10 methods method NOUN cana-1902 31 11 of of ADP cana-1902 31 12 retrial retrial ADJ cana-1902 31 13 queues queue NOUN cana-1902 31 14 theory theory NOUN cana-1902 31 15 in in ADP cana-1902 31 16 a a DET cana-1902 31 17 short short ADJ cana-1902 31 18 discussion discussion NOUN cana-1902 31 19 . . PUNCT cana-1902 32 1 shanmugasundaram shanmugasundaram PROPN cana-1902 32 2 et et PROPN cana-1902 32 3 al al PROPN cana-1902 32 4 . . PUNCT cana-1902 33 1 [ [ X cana-1902 33 2 12 12 NUM cana-1902 33 3 ] ] PUNCT cana-1902 33 4 examined examine VERB cana-1902 33 5 a a DET cana-1902 33 6 feedback feedback NOUN cana-1902 33 7 retrial retrial NOUN cana-1902 33 8 queueing queue VERB cana-1902 33 9 network network NOUN cana-1902 33 10 consisting consist VERB cana-1902 33 11 of of ADP cana-1902 33 12 three three NUM cana-1902 33 13 nodes node NOUN cana-1902 33 14 under under ADP cana-1902 33 15 catastrophic catastrophic ADJ cana-1902 33 16 circumstances circumstance NOUN cana-1902 33 17 . . PUNCT cana-1902 34 1 1.3 1.3 NUM cana-1902 34 2 feedback feedback NOUN cana-1902 34 3 queue queue NOUN cana-1902 34 4 in in ADP cana-1902 34 5 modern modern ADJ cana-1902 34 6 service service NOUN cana-1902 34 7 systems system NOUN cana-1902 34 8 , , PUNCT cana-1902 34 9 where where SCONJ cana-1902 34 10 specific specific ADJ cana-1902 34 11 activities activity NOUN cana-1902 34 12 may may AUX cana-1902 34 13 necessitate necessitate VERB cana-1902 34 14 repeated repeat VERB cana-1902 34 15 services service NOUN cana-1902 34 16 , , PUNCT cana-1902 34 17 the the DET cana-1902 34 18 feedback feedback NOUN cana-1902 34 19 queue queue NOUN cana-1902 34 20 is be AUX cana-1902 34 21 crucial crucial ADJ cana-1902 34 22 . . PUNCT cana-1902 35 1 feedback feedback NOUN cana-1902 35 2 queues queue NOUN cana-1902 35 3 are be AUX cana-1902 35 4 queuing queue VERB cana-1902 35 5 systems system NOUN cana-1902 35 6 that that PRON cana-1902 35 7 allow allow VERB cana-1902 35 8 customers customer NOUN cana-1902 35 9 to to PART cana-1902 35 10 return return VERB cana-1902 35 11 for for ADP cana-1902 35 12 extra extra ADJ cana-1902 35 13 services service NOUN cana-1902 35 14 or or CCONJ cana-1902 35 15 because because SCONJ cana-1902 35 16 they they PRON cana-1902 35 17 are be AUX cana-1902 35 18 dissatisfied dissatisfied ADJ cana-1902 35 19 with with ADP cana-1902 35 20 the the DET cana-1902 35 21 service service NOUN cana-1902 35 22 they they PRON cana-1902 35 23 received receive VERB cana-1902 35 24 . . PUNCT cana-1902 36 1 numerous numerous ADJ cana-1902 36 2 real real ADJ cana-1902 36 3 - - PUNCT cana-1902 36 4 world world NOUN cana-1902 36 5 scenarios scenario NOUN cana-1902 36 6 , , PUNCT cana-1902 36 7 including include VERB cana-1902 36 8 the the DET cana-1902 36 9 redesign redesign NOUN cana-1902 36 10 of of ADP cana-1902 36 11 manufacturing manufacturing NOUN cana-1902 36 12 systems system NOUN cana-1902 36 13 , , PUNCT cana-1902 36 14 communication communication NOUN cana-1902 36 15 networks network NOUN cana-1902 36 16 , , PUNCT cana-1902 36 17 and and CCONJ cana-1902 36 18 supermarkets supermarket NOUN cana-1902 36 19 , , PUNCT cana-1902 36 20 demonstrate demonstrate VERB cana-1902 36 21 the the DET cana-1902 36 22 feedback feedback NOUN cana-1902 36 23 phenomenon phenomenon NOUN cana-1902 36 24 . . PUNCT cana-1902 37 1 takacs takac NOUN cana-1902 37 2 introduced introduce VERB cana-1902 37 3 the the DET cana-1902 37 4 feedback feedback NOUN cana-1902 37 5 mechanism mechanism NOUN cana-1902 37 6 in in ADP cana-1902 37 7 1963 1963 NUM cana-1902 37 8 [ [ X cana-1902 37 9 15 15 NUM cana-1902 37 10 ] ] PUNCT cana-1902 37 11 . . PUNCT cana-1902 38 1 working work VERB cana-1902 38 2 vacations vacation NOUN cana-1902 38 3 , , PUNCT cana-1902 38 4 server server NOUN cana-1902 38 5 breakdowns breakdown NOUN cana-1902 38 6 , , PUNCT cana-1902 38 7 and and CCONJ cana-1902 38 8 single single ADJ cana-1902 38 9 - - PUNCT cana-1902 38 10 server server NOUN cana-1902 38 11 queues queue NOUN cana-1902 38 12 with with ADP cana-1902 38 13 instant instant ADJ cana-1902 38 14 feedback feedback NOUN cana-1902 38 15 have have AUX cana-1902 38 16 all all PRON cana-1902 38 17 been be AUX cana-1902 38 18 taken take VERB cana-1902 38 19 into into ADP cana-1902 38 20 consideration consideration NOUN cana-1902 38 21 by by ADP cana-1902 38 22 varalakshmi varalakshmi PROPN cana-1902 38 23 et et PROPN cana-1902 38 24 al al PROPN cana-1902 38 25 . . PUNCT cana-1902 39 1 [ [ X cana-1902 39 2 17 17 NUM cana-1902 39 3 ] ] SYM cana-1902 39 4 . . PUNCT cana-1902 40 1 1.4 1.4 NUM cana-1902 40 2 catastrophe catastrophe NOUN cana-1902 40 3 the the DET cana-1902 40 4 evolution evolution NOUN cana-1902 40 5 of of ADP cana-1902 40 6 networks network NOUN cana-1902 40 7 and and CCONJ cana-1902 40 8 communication communication NOUN cana-1902 40 9 systems system NOUN cana-1902 40 10 has have AUX cana-1902 40 11 resulted result VERB cana-1902 40 12 in in ADP cana-1902 40 13 increasing increase VERB cana-1902 40 14 attention attention NOUN cana-1902 40 15 to to ADP cana-1902 40 16 queueing queue VERB cana-1902 40 17 systems system NOUN cana-1902 40 18 with with ADP cana-1902 40 19 disasters disaster NOUN cana-1902 40 20 . . PUNCT cana-1902 41 1 the the DET cana-1902 41 2 subject subject NOUN cana-1902 41 3 of of ADP cana-1902 41 4 disaster disaster NOUN cana-1902 41 5 queues queue NOUN cana-1902 41 6 has have AUX cana-1902 41 7 been be AUX cana-1902 41 8 extensively extensively ADV cana-1902 41 9 researched research VERB cana-1902 41 10 by by ADP cana-1902 41 11 numerous numerous ADJ cana-1902 41 12 researchers researcher NOUN cana-1902 41 13 over over ADP cana-1902 41 14 the the DET cana-1902 41 15 past past ADJ cana-1902 41 16 20 20 NUM cana-1902 41 17 years year NOUN cana-1902 41 18 . . PUNCT cana-1902 42 1 every every DET cana-1902 42 2 customer customer NOUN cana-1902 42 3 ( ( PUNCT cana-1902 42 4 including include VERB cana-1902 42 5 the the DET cana-1902 42 6 one one NUM cana-1902 42 7 in in ADP cana-1902 42 8 service service NOUN cana-1902 42 9 ) ) PUNCT cana-1902 42 10 must must AUX cana-1902 42 11 exit exit VERB cana-1902 42 12 the the DET cana-1902 42 13 system system NOUN cana-1902 42 14 in in ADP cana-1902 42 15 the the DET cana-1902 42 16 case case NOUN cana-1902 42 17 of of ADP cana-1902 42 18 a a DET cana-1902 42 19 complete complete ADJ cana-1902 42 20 disaster disaster NOUN cana-1902 42 21 . . PUNCT cana-1902 43 1 there there PRON cana-1902 43 2 are be VERB cana-1902 43 3 numerous numerous ADJ cana-1902 43 4 applications application NOUN cana-1902 43 5 for for ADP cana-1902 43 6 these these DET cana-1902 43 7 kinds kind NOUN cana-1902 43 8 of of ADP cana-1902 43 9 queueing queue VERB cana-1902 43 10 systems system NOUN cana-1902 43 11 . . PUNCT cana-1902 44 1 for for ADP cana-1902 44 2 instance instance NOUN cana-1902 44 3 , , PUNCT cana-1902 44 4 every every DET cana-1902 44 5 customer customer NOUN cana-1902 44 6 are be AUX cana-1902 44 7 required require VERB cana-1902 44 8 to to PART cana-1902 44 9 vacate vacate VERB cana-1902 44 10 the the DET cana-1902 44 11 premises premise NOUN cana-1902 44 12 when when SCONJ cana-1902 44 13 an an DET cana-1902 44 14 atm atm NOUN cana-1902 44 15 defects defect NOUN cana-1902 44 16 in in ADP cana-1902 44 17 a a DET cana-1902 44 18 bank bank NOUN cana-1902 44 19 . . PUNCT cana-1902 45 1 moreover moreover ADV cana-1902 45 2 , , PUNCT cana-1902 45 3 viruses virus NOUN cana-1902 45 4 have have VERB cana-1902 45 5 the the DET cana-1902 45 6 ability ability NOUN cana-1902 45 7 to to PART cana-1902 45 8 erase erase VERB cana-1902 45 9 all all DET cana-1902 45 10 stored store VERB cana-1902 45 11 data datum NOUN cana-1902 45 12 from from ADP cana-1902 45 13 computer computer NOUN cana-1902 45 14 networks network NOUN cana-1902 45 15 during during ADP cana-1902 45 16 a a DET cana-1902 45 17 clearing clearing NOUN cana-1902 45 18 process process NOUN cana-1902 45 19 . . PUNCT cana-1902 46 1 gelenbe gelenbe PROPN cana-1902 47 1 [ [ X cana-1902 47 2 6 6 NUM cana-1902 47 3 ] ] PUNCT cana-1902 47 4 introduced introduce VERB cana-1902 47 5 the the DET cana-1902 47 6 concept concept NOUN cana-1902 47 7 of of ADP cana-1902 47 8 catastrophes catastrophe NOUN cana-1902 47 9 , , PUNCT cana-1902 47 10 furthermore furthermore ADV cana-1902 47 11 , , PUNCT cana-1902 47 12 chao chao PROPN cana-1902 48 1 [ [ X cana-1902 48 2 2 2 NUM cana-1902 48 3 ] ] PUNCT cana-1902 48 4 is be AUX cana-1902 48 5 motivated motivated ADJ cana-1902 48 6 to to PART cana-1902 48 7 assess assess VERB cana-1902 48 8 the the DET cana-1902 48 9 migration migration NOUN cana-1902 48 10 process process NOUN cana-1902 48 11 in in ADP cana-1902 48 12 the the DET cana-1902 48 13 context context NOUN cana-1902 48 14 of of ADP cana-1902 48 15 disasters disaster NOUN cana-1902 48 16 and and CCONJ cana-1902 48 17 virus virus NOUN cana-1902 48 18 - - PUNCT cana-1902 48 19 infected infect VERB cana-1902 48 20 computer computer NOUN cana-1902 48 21 networks network NOUN cana-1902 48 22 . . PUNCT cana-1902 49 1 krishna krishna PROPN cana-1902 49 2 kumar kumar PROPN cana-1902 49 3 et et PROPN cana-1902 49 4 al al PROPN cana-1902 49 5 . . PUNCT cana-1902 50 1 [ [ X cana-1902 50 2 10 10 NUM cana-1902 50 3 ] ] PUNCT cana-1902 50 4 considered consider VERB cana-1902 50 5 the the DET cana-1902 50 6 transient transient ADJ cana-1902 50 7 solution solution NOUN cana-1902 50 8 of of ADP cana-1902 50 9 the the DET cana-1902 50 10 system system NOUN cana-1902 50 11 size size NOUN cana-1902 50 12 in in ADP cana-1902 50 13 the the DET cana-1902 50 14 queuing queuing NOUN cana-1902 50 15 model model NOUN cana-1902 50 16 with with ADP cana-1902 50 17 the the DET cana-1902 50 18 possibility possibility NOUN cana-1902 50 19 of of ADP cana-1902 50 20 disasters disaster NOUN cana-1902 50 21 in in ADP cana-1902 50 22 a a DET cana-1902 50 23 service service NOUN cana-1902 50 24 station station NOUN cana-1902 50 25 . . PUNCT cana-1902 51 1 shanmugasundaram shanmugasundaram PROPN cana-1902 51 2 et et PROPN cana-1902 51 3 al al PROPN cana-1902 51 4 . . PUNCT cana-1902 52 1 [ [ X cana-1902 52 2 13 13 NUM cana-1902 52 3 ] ] PUNCT cana-1902 52 4 focused focus VERB cana-1902 52 5 on on ADP cana-1902 52 6 a a DET cana-1902 52 7 timedependent timedependent NOUN cana-1902 52 8 solution solution NOUN cana-1902 52 9 of of ADP cana-1902 52 10 an an DET cana-1902 52 11 arrival arrival NOUN cana-1902 52 12 of of ADP cana-1902 52 13 customer customer NOUN cana-1902 52 14 with with ADP cana-1902 52 15 retrial retrial ADJ cana-1902 52 16 customers customer NOUN cana-1902 52 17 and and CCONJ cana-1902 52 18 providing provide VERB cana-1902 52 19 feedback feedback NOUN cana-1902 52 20 to to ADP cana-1902 52 21 nonretrial nonretrial ADJ cana-1902 52 22 customers customer NOUN cana-1902 52 23 with with ADP cana-1902 52 24 disasters disaster NOUN cana-1902 52 25 . . PUNCT cana-1902 53 1 thangaraj thangaraj PROPN cana-1902 53 2 et et PROPN cana-1902 53 3 al al PROPN cana-1902 54 1 [ [ X cana-1902 54 2 16 16 NUM cana-1902 54 3 ] ] PUNCT cana-1902 54 4 studied study VERB cana-1902 54 5 the the DET cana-1902 54 6 analytically analytically ADV cana-1902 54 7 obtained obtain VERB cana-1902 54 8 transient transient ADJ cana-1902 54 9 solution solution NOUN cana-1902 54 10 using use VERB cana-1902 54 11 continuous continuous ADJ cana-1902 54 12 fractions fraction NOUN cana-1902 54 13 of of ADP cana-1902 54 14 the the DET cana-1902 54 15 feedback feedback NOUN cana-1902 54 16 queue queue NOUN cana-1902 54 17 under under ADP cana-1902 54 18 catastrophic catastrophic ADJ cana-1902 54 19 condition condition NOUN cana-1902 54 20 . . PUNCT cana-1902 55 1 shanmugasundaram shanmugasundaram PROPN cana-1902 55 2 et et PROPN cana-1902 55 3 al al PROPN cana-1902 55 4 . . PUNCT cana-1902 56 1 [ [ X cana-1902 56 2 14 14 NUM cana-1902 56 3 ] ] PUNCT cana-1902 56 4 have have AUX cana-1902 56 5 studied study VERB cana-1902 56 6 a a DET cana-1902 56 7 steady steady ADJ cana-1902 56 8 - - PUNCT cana-1902 56 9 state state NOUN cana-1902 56 10 single single ADJ cana-1902 56 11 server server NOUN cana-1902 56 12 retrial retrial NOUN cana-1902 56 13 queueing queue VERB cana-1902 56 14 network network NOUN cana-1902 56 15 with with ADP cana-1902 56 16 catastrophes catastrophe NOUN cana-1902 56 17 . . PUNCT cana-1902 57 1 using use VERB cana-1902 57 2 the the DET cana-1902 57 3 continuous continuous ADJ cana-1902 57 4 fractions fraction NOUN cana-1902 57 5 approach approach NOUN cana-1902 57 6 , , PUNCT cana-1902 57 7 chandrasekaran chandrasekaran VERB cana-1902 57 8 et et PROPN cana-1902 57 9 al al PROPN cana-1902 57 10 . . PUNCT cana-1902 58 1 [ [ X cana-1902 58 2 3 3 X cana-1902 58 3 ] ] PUNCT cana-1902 58 4 have have AUX cana-1902 58 5 examined examine VERB cana-1902 58 6 the the DET cana-1902 58 7 transient transient ADJ cana-1902 58 8 and and CCONJ cana-1902 58 9 reliable reliable ADJ cana-1902 58 10 nature nature NOUN cana-1902 58 11 of of ADP cana-1902 58 12 the the DET cana-1902 58 13 m m PROPN cana-1902 58 14 / / SYM cana-1902 58 15 m/1 m/1 NOUN cana-1902 58 16 feedback feedback NOUN cana-1902 58 17 queue queue NOUN cana-1902 58 18 in in ADP cana-1902 58 19 the the DET cana-1902 58 20 face face NOUN cana-1902 58 21 of of ADP cana-1902 58 22 disasters disaster NOUN cana-1902 58 23 , , PUNCT cana-1902 58 24 server server NOUN cana-1902 58 25 outages outage NOUN cana-1902 58 26 , , PUNCT cana-1902 58 27 and and CCONJ cana-1902 58 28 repairs repair NOUN cana-1902 58 29 . . PUNCT cana-1902 59 1 the the DET cana-1902 59 2 past past ADJ cana-1902 59 3 few few ADJ cana-1902 59 4 years year NOUN cana-1902 59 5 , , PUNCT cana-1902 59 6 investigation investigation NOUN cana-1902 59 7 have have AUX cana-1902 59 8 been be AUX cana-1902 59 9 done do VERB cana-1902 59 10 in in ADP cana-1902 59 11 disaster disaster NOUN cana-1902 59 12 - - PUNCT cana-1902 59 13 prone prone ADJ cana-1902 59 14 queueing queueing NOUN cana-1902 59 15 systems system NOUN cana-1902 59 16 by by ADP cana-1902 59 17 chowdhury chowdhury PROPN cana-1902 59 18 et et PROPN cana-1902 59 19 al al PROPN cana-1902 59 20 . . PUNCT cana-1902 60 1 [ [ X cana-1902 60 2 1 1 X cana-1902 60 3 ] ] PUNCT cana-1902 60 4 and and CCONJ cana-1902 60 5 kumar kumar PROPN cana-1902 60 6 et et PROPN cana-1902 60 7 al al PROPN cana-1902 60 8 . . PUNCT cana-1902 61 1 [ [ X cana-1902 61 2 11 11 NUM cana-1902 61 3 ] ] SYM cana-1902 61 4 2 2 NUM cana-1902 61 5 . . X cana-1902 61 6 description description NOUN cana-1902 61 7 of of ADP cana-1902 61 8 the the DET cana-1902 61 9 model model NOUN cana-1902 61 10 an an DET cana-1902 61 11 investigation investigation NOUN cana-1902 61 12 is be AUX cana-1902 61 13 conducted conduct VERB cana-1902 61 14 on on ADP cana-1902 61 15 a a DET cana-1902 61 16 queueing queue VERB cana-1902 61 17 network network NOUN cana-1902 61 18 consisting consist VERB cana-1902 61 19 of of ADP cana-1902 61 20 three three NUM cana-1902 61 21 nodes node NOUN cana-1902 61 22 , , PUNCT cana-1902 61 23 incorporating incorporate VERB cana-1902 61 24 retrial retrial NOUN cana-1902 61 25 , , PUNCT cana-1902 61 26 feedback feedback NOUN cana-1902 61 27 , , PUNCT cana-1902 61 28 and and CCONJ cana-1902 61 29 catastrophe catastrophe NOUN cana-1902 61 30 . . PUNCT cana-1902 62 1 external external ADJ cana-1902 62 2 customers customer NOUN cana-1902 62 3 access access VERB cana-1902 62 4 the the DET cana-1902 62 5 system system NOUN cana-1902 62 6 through through ADP cana-1902 62 7 a a DET cana-1902 62 8 poisson poisson NOUN cana-1902 62 9 process process NOUN cana-1902 62 10 with with ADP cana-1902 62 11 a a DET cana-1902 62 12 rate rate NOUN cana-1902 62 13 of of ADP cana-1902 62 14 arrival arrival NOUN cana-1902 62 15 πœ†. πœ†. NOUN cana-1902 63 1 if if SCONJ cana-1902 63 2 the the DET cana-1902 63 3 server server NOUN cana-1902 63 4 is be AUX cana-1902 63 5 not not PART cana-1902 63 6 busy busy ADJ cana-1902 63 7 , , PUNCT cana-1902 63 8 there there PRON cana-1902 63 9 is be VERB cana-1902 63 10 a a DET cana-1902 63 11 high high ADJ cana-1902 63 12 likelihood likelihood NOUN cana-1902 63 13 that that SCONJ cana-1902 63 14 incoming incoming ADJ cana-1902 63 15 customers customer NOUN cana-1902 63 16 will will AUX cana-1902 63 17 enter enter VERB cana-1902 63 18 the the DET cana-1902 63 19 queue queue NOUN cana-1902 63 20 with with ADP cana-1902 63 21 probability probability NOUN cana-1902 63 22 𝑠. 𝑠. NOUN cana-1902 63 23 customers customer NOUN cana-1902 63 24 have have VERB cana-1902 63 25 a a DET cana-1902 63 26 likelihood likelihood NOUN cana-1902 63 27 of of ADP cana-1902 63 28 1 1 NUM cana-1902 63 29 βˆ’ βˆ’ NOUN cana-1902 63 30 𝑠 𝑠 INTJ cana-1902 63 31 to to PART cana-1902 63 32 join join VERB cana-1902 63 33 the the DET cana-1902 63 34 orbit orbit NOUN cana-1902 63 35 when when SCONJ cana-1902 63 36 the the DET cana-1902 63 37 server server NOUN cana-1902 63 38 is be AUX cana-1902 63 39 occupied occupy VERB cana-1902 63 40 . . PUNCT cana-1902 64 1 it it PRON cana-1902 64 2 is be AUX cana-1902 64 3 considered consider VERB cana-1902 64 4 that that SCONJ cana-1902 64 5 the the DET cana-1902 64 6 capacity capacity NOUN cana-1902 64 7 is be AUX cana-1902 64 8 infinite infinite ADJ cana-1902 64 9 , , PUNCT cana-1902 64 10 and and CCONJ cana-1902 64 11 that that SCONJ cana-1902 64 12 the the DET cana-1902 64 13 only only ADJ cana-1902 64 14 person person NOUN cana-1902 64 15 allowed allow VERB cana-1902 64 16 to to PART cana-1902 64 17 get get VERB cana-1902 64 18 service service NOUN cana-1902 64 19 on on ADP cana-1902 64 20 a a DET cana-1902 64 21 first first ADJ cana-1902 64 22 - - PUNCT cana-1902 64 23 come come NOUN cana-1902 64 24 , , PUNCT cana-1902 64 25 first first ADV cana-1902 64 26 - - PUNCT cana-1902 64 27 served serve VERB cana-1902 64 28 basis basis NOUN cana-1902 64 29 is be AUX cana-1902 64 30 the the DET cana-1902 64 31 one one NUM cana-1902 64 32 at at ADP cana-1902 64 33 the the DET cana-1902 64 34 front front NOUN cana-1902 64 35 of of ADP cana-1902 64 36 the the DET cana-1902 64 37 line line NOUN cana-1902 64 38 . . PUNCT cana-1902 65 1 the the DET cana-1902 65 2 customer customer NOUN cana-1902 65 3 returns return VERB cana-1902 65 4 to to ADP cana-1902 65 5 the the DET cana-1902 65 6 orbit orbit NOUN cana-1902 65 7 , , PUNCT cana-1902 65 8 if if SCONJ cana-1902 65 9 the the DET cana-1902 65 10 server server NOUN cana-1902 65 11 is be AUX cana-1902 65 12 busy busy ADJ cana-1902 65 13 . . PUNCT cana-1902 66 1 this this DET cana-1902 66 2 procedure procedure NOUN cana-1902 66 3 persists persist VERB cana-1902 66 4 until until SCONJ cana-1902 66 5 the the DET cana-1902 66 6 customer customer NOUN cana-1902 66 7 observes observe VERB cana-1902 66 8 that that SCONJ cana-1902 66 9 the the DET cana-1902 66 10 server server NOUN cana-1902 66 11 on on ADP cana-1902 66 12 node node PROPN cana-1902 66 13 one one NUM cana-1902 66 14 is be AUX cana-1902 66 15 idle idle ADJ cana-1902 66 16 . . PUNCT cana-1902 67 1 during during ADP cana-1902 67 2 the the DET cana-1902 67 3 retrial retrial NOUN cana-1902 67 4 , , PUNCT cana-1902 67 5 both both PRON cana-1902 67 6 requested request VERB cana-1902 67 7 and and CCONJ cana-1902 67 8 required require VERB cana-1902 67 9 services service NOUN cana-1902 67 10 are be AUX cana-1902 67 11 provided provide VERB cana-1902 67 12 . . PUNCT cana-1902 68 1 if if SCONJ cana-1902 68 2 the the DET cana-1902 68 3 server server NOUN cana-1902 68 4 is be AUX cana-1902 68 5 busy busy ADJ cana-1902 68 6 , , PUNCT cana-1902 68 7 customers customer NOUN cana-1902 68 8 are be AUX cana-1902 68 9 required require VERB cana-1902 68 10 to to PART cana-1902 68 11 wait wait VERB cana-1902 68 12 in in ADP cana-1902 68 13 an an DET cana-1902 68 14 endless endless ADJ cana-1902 68 15 circle circle NOUN cana-1902 68 16 and and CCONJ cana-1902 68 17 repeat repeat VERB cana-1902 68 18 their their PRON cana-1902 68 19 communications communication NOUN cana-1902 68 20 on on ADP cana-1902 68 21 applied apply VERB cana-1902 68 22 nonlinear nonlinear ADJ cana-1902 68 23 analysis analysis NOUN cana-1902 68 24 issn issn NOUN cana-1902 68 25 : : PUNCT cana-1902 68 26 1074 1074 NUM cana-1902 68 27 - - PUNCT cana-1902 68 28 133x 133x NUM cana-1902 68 29 vol vol NOUN cana-1902 68 30 32 32 NUM cana-1902 68 31 no no NOUN cana-1902 68 32 . . NOUN cana-1902 68 33 3 3 NUM cana-1902 68 34 ( ( PUNCT cana-1902 68 35 2025 2025 NUM cana-1902 68 36 ) ) PUNCT cana-1902 68 37 3 3 NUM cana-1902 68 38 https://internationalpubls.com https://internationalpubls.com X cana-1902 68 39 request request NOUN cana-1902 68 40 after after ADP cana-1902 68 41 an an DET cana-1902 68 42 exponential exponential ADJ cana-1902 68 43 rate rate NOUN cana-1902 68 44 . . PUNCT cana-1902 69 1 after after ADP cana-1902 69 2 receiving receive VERB cana-1902 69 3 service service NOUN cana-1902 69 4 at at ADP cana-1902 69 5 node node PROPN cana-1902 69 6 one one NUM cana-1902 69 7 , , PUNCT cana-1902 69 8 they they PRON cana-1902 69 9 proceed proceed VERB cana-1902 69 10 to to PART cana-1902 69 11 node node VERB cana-1902 69 12 two two NUM cana-1902 69 13 and and CCONJ cana-1902 69 14 then then ADV cana-1902 69 15 to to PART cana-1902 69 16 node node VERB cana-1902 69 17 three three NUM cana-1902 69 18 . . PUNCT cana-1902 70 1 here here ADV cana-1902 70 2 , , PUNCT cana-1902 70 3 the the DET cana-1902 70 4 customer customer NOUN cana-1902 70 5 chooses choose VERB cana-1902 70 6 whether whether SCONJ cana-1902 70 7 or or CCONJ cana-1902 70 8 not not PART cana-1902 70 9 to to PART cana-1902 70 10 request request VERB cana-1902 70 11 feedback feedback NOUN cana-1902 70 12 . . PUNCT cana-1902 71 1 after after ADP cana-1902 71 2 receiving receive VERB cana-1902 71 3 service service NOUN cana-1902 71 4 in in ADP cana-1902 71 5 node node NOUN cana-1902 71 6 three three NUM cana-1902 71 7 with with ADP cana-1902 71 8 probability1 probability1 NOUN cana-1902 71 9 βˆ’ βˆ’ NOUN cana-1902 72 1 𝑑 𝑑 NOUN cana-1902 72 2 βˆ’ βˆ’ NOUN cana-1902 72 3 𝑒 𝑒 NOUN cana-1902 72 4 , , PUNCT cana-1902 72 5 if if SCONJ cana-1902 72 6 the the DET cana-1902 72 7 customer customer NOUN cana-1902 72 8 is be AUX cana-1902 72 9 happy happy ADJ cana-1902 72 10 with with ADP cana-1902 72 11 the the DET cana-1902 72 12 service service NOUN cana-1902 72 13 , , PUNCT cana-1902 72 14 they they PRON cana-1902 72 15 exit exit VERB cana-1902 72 16 the the DET cana-1902 72 17 system system NOUN cana-1902 72 18 . . PUNCT cana-1902 73 1 if if SCONJ cana-1902 73 2 the the DET cana-1902 73 3 customer customer NOUN cana-1902 73 4 is be AUX cana-1902 73 5 dissatisfied dissatisfied ADJ cana-1902 73 6 in in ADP cana-1902 73 7 node node PROPN cana-1902 73 8 three three NUM cana-1902 73 9 , , PUNCT cana-1902 73 10 they they PRON cana-1902 73 11 will will AUX cana-1902 73 12 either either CCONJ cana-1902 73 13 travel travel VERB cana-1902 73 14 to to PART cana-1902 73 15 node node VERB cana-1902 73 16 two two NUM cana-1902 73 17 for for ADP cana-1902 73 18 instant instant ADJ cana-1902 73 19 feedback feedback NOUN cana-1902 73 20 with with ADP cana-1902 73 21 a a DET cana-1902 73 22 probability probability NOUN cana-1902 73 23 of of ADP cana-1902 73 24 t t NOUN cana-1902 73 25 or or CCONJ cana-1902 73 26 to to PART cana-1902 73 27 node node VERB cana-1902 73 28 one one NUM cana-1902 73 29 for for ADP cana-1902 73 30 delayed delay VERB cana-1902 73 31 feedback feedback NOUN cana-1902 73 32 with with ADP cana-1902 73 33 a a DET cana-1902 73 34 probability probability NOUN cana-1902 73 35 of of ADP cana-1902 73 36 u. u. NOUN cana-1902 73 37 every every DET cana-1902 73 38 node node NOUN cana-1902 73 39 runs run VERB cana-1902 73 40 on on ADP cana-1902 73 41 an an DET cana-1902 73 42 m m NOUN cana-1902 73 43 / / SYM cana-1902 73 44 m/1 m/1 NOUN cana-1902 73 45 basis basis NOUN cana-1902 73 46 . . PUNCT cana-1902 74 1 the the DET cana-1902 74 2 service service NOUN cana-1902 74 3 rate rate NOUN cana-1902 74 4 for for ADP cana-1902 74 5 all all DET cana-1902 74 6 the the DET cana-1902 74 7 three three NUM cana-1902 74 8 nodes node NOUN cana-1902 74 9 are be AUX cana-1902 74 10 πœ‡1 πœ‡1 ADJ cana-1902 74 11 , , PUNCT cana-1902 74 12 πœ‡2 πœ‡2 VERB cana-1902 74 13 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ cana-1902 74 14 πœ‡3 πœ‡3 PROPN cana-1902 74 15 and and CCONJ cana-1902 74 16 are be AUX cana-1902 74 17 dispersed disperse VERB cana-1902 74 18 exponentially exponentially ADV cana-1902 74 19 . . PUNCT cana-1902 75 1 the the DET cana-1902 75 2 arrival arrival NOUN cana-1902 75 3 and and CCONJ cana-1902 75 4 service service NOUN cana-1902 75 5 processes process NOUN cana-1902 75 6 , , PUNCT cana-1902 75 7 which which PRON cana-1902 75 8 are be AUX cana-1902 75 9 followed follow VERB cana-1902 75 10 by by ADP cana-1902 75 11 the the DET cana-1902 75 12 poisson poisson NOUN cana-1902 75 13 process process NOUN cana-1902 75 14 with with ADP cana-1902 75 15 rate rate NOUN cana-1902 75 16 Ξ³ Ξ³ NOUN cana-1902 75 17 , , PUNCT cana-1902 75 18 are be AUX cana-1902 75 19 the the DET cana-1902 75 20 sources source NOUN cana-1902 75 21 of of ADP cana-1902 75 22 catastrophes catastrophe NOUN cana-1902 75 23 . . PUNCT cana-1902 76 1 the the DET cana-1902 76 2 server server NOUN cana-1902 76 3 is be AUX cana-1902 76 4 deactivated deactivate VERB cana-1902 76 5 , , PUNCT cana-1902 76 6 and and CCONJ cana-1902 76 7 all all DET cana-1902 76 8 available available ADJ cana-1902 76 9 customers customer NOUN cana-1902 76 10 are be AUX cana-1902 76 11 immediately immediately ADV cana-1902 76 12 destroyed destroy VERB cana-1902 76 13 in in ADP cana-1902 76 14 the the DET cana-1902 76 15 event event NOUN cana-1902 76 16 of of ADP cana-1902 76 17 a a DET cana-1902 76 18 catastrophic catastrophic ADJ cana-1902 76 19 system system NOUN cana-1902 76 20 catastrophe catastrophe NOUN cana-1902 76 21 . . PUNCT cana-1902 77 1 when when SCONJ cana-1902 77 2 someone someone PRON cana-1902 77 3 arrives arrive VERB cana-1902 77 4 , , PUNCT cana-1902 77 5 the the DET cana-1902 77 6 server server NOUN cana-1902 77 7 is be AUX cana-1902 77 8 ready ready ADJ cana-1902 77 9 to to PART cana-1902 77 10 serve serve VERB cana-1902 77 11 . . PUNCT cana-1902 78 1 in in ADP cana-1902 78 2 fig fig NOUN cana-1902 78 3 . . PUNCT cana-1902 79 1 1 1 NUM cana-1902 79 2 , , PUNCT cana-1902 79 3 this this DET cana-1902 79 4 mechanism mechanism NOUN cana-1902 79 5 is be AUX cana-1902 79 6 displayed display VERB cana-1902 79 7 . . PUNCT cana-1902 80 1 fig fig NOUN cana-1902 80 2 . . PUNCT cana-1902 80 3 1 1 NUM cana-1902 81 1 the the DET cana-1902 81 2 transient transient ADJ cana-1902 81 3 state state NOUN cana-1902 81 4 probability probability NOUN cana-1902 81 5 of of ADP cana-1902 81 6 the the DET cana-1902 81 7 system system NOUN cana-1902 81 8 having have VERB cana-1902 81 9 n n PRON cana-1902 81 10 customers customer NOUN cana-1902 81 11 at at ADP cana-1902 81 12 time time NOUN cana-1902 81 13 t t PROPN cana-1902 81 14 is be AUX cana-1902 81 15 represented represent VERB cana-1902 81 16 as as ADP cana-1902 81 17 𝑄𝑛(𝑑 𝑄𝑛(𝑑 X cana-1902 81 18 ) ) PUNCT cana-1902 81 19 = = SYM cana-1902 82 1 𝑄{𝑋(𝑑 𝑄{𝑋(𝑑 PROPN cana-1902 82 2 ) ) PUNCT cana-1902 82 3 = = SYM cana-1902 82 4 𝑛 𝑛 PROPN cana-1902 82 5 } } PUNCT cana-1902 82 6 , , PUNCT cana-1902 82 7 𝑛 𝑛 PROPN cana-1902 82 8 = = SYM cana-1902 82 9 0,1,2,3 0,1,2,3 NOUN cana-1902 82 10 … … PUNCT cana-1902 82 11 consider consider VERB cana-1902 82 12 q(x q(x NOUN cana-1902 82 13 , , PUNCT cana-1902 82 14 t t PROPN cana-1902 82 15 ) ) PUNCT cana-1902 82 16 as as ADP cana-1902 82 17 the the DET cana-1902 82 18 probability probability NOUN cana-1902 82 19 generating generating NOUN cana-1902 82 20 function function NOUN cana-1902 82 21 , , PUNCT cana-1902 82 22 𝑄(π‘₯ 𝑄(π‘₯ PRON cana-1902 82 23 , , PUNCT cana-1902 82 24 𝑑 𝑑 NOUN cana-1902 82 25 ) ) PUNCT cana-1902 82 26 = = PUNCT cana-1902 83 1 βˆ‘ βˆ‘ PUNCT cana-1902 83 2 𝑄𝑛(𝑑)π‘₯π‘›βˆž 𝑄𝑛(𝑑)π‘₯π‘›βˆž PROPN cana-1902 83 3 𝑛=0 𝑛=0 NOUN cana-1902 83 4 in in ADP cana-1902 83 5 most most ADJ cana-1902 83 6 cases case NOUN cana-1902 83 7 , , PUNCT cana-1902 83 8 when when SCONJ cana-1902 83 9 time time NOUN cana-1902 83 10 t t PROPN cana-1902 83 11 = = SYM cana-1902 83 12 0 0 NUM cana-1902 84 1 it it PRON cana-1902 84 2 is be AUX cana-1902 84 3 assumed assume VERB cana-1902 84 4 that that SCONJ cana-1902 84 5 there there PRON cana-1902 84 6 are be VERB cana-1902 84 7 no no DET cana-1902 84 8 customers customer NOUN cana-1902 84 9 in in ADP cana-1902 84 10 the the DET cana-1902 84 11 system system NOUN cana-1902 84 12 , , PUNCT cana-1902 84 13 denoted denote VERB cana-1902 84 14 as as ADP cana-1902 84 15 𝑄0(0 𝑄0(0 NOUN cana-1902 84 16 ) ) PUNCT cana-1902 84 17 = = PUNCT cana-1902 85 1 1 1 NUM cana-1902 85 2 the the DET cana-1902 85 3 probability probability NOUN cana-1902 85 4 of of ADP cana-1902 85 5 𝑄𝑛(𝑑 𝑄𝑛(𝑑 PROPN cana-1902 85 6 ) ) PUNCT cana-1902 85 7 as as ADP cana-1902 85 8 per per ADP cana-1902 85 9 the the DET cana-1902 85 10 system system NOUN cana-1902 85 11 of of ADP cana-1902 85 12 differential differential ADJ cana-1902 85 13 – – PUNCT cana-1902 85 14 difference difference NOUN cana-1902 85 15 equations equation NOUN cana-1902 85 16 . . PUNCT cana-1902 86 1 𝑄0 𝑄0 PROPN cana-1902 86 2 β€²(𝑑 β€²(𝑑 PROPN cana-1902 86 3 ) ) PUNCT cana-1902 86 4 = = PUNCT cana-1902 87 1 βˆ’πœ†π‘„0(𝑑 βˆ’πœ†π‘„0(𝑑 VERB cana-1902 87 2 ) ) PUNCT cana-1902 88 1 + + CCONJ cana-1902 88 2 { { PUNCT cana-1902 88 3 [ [ X cana-1902 88 4 π‘ πœ‡1 π‘ πœ‡1 ADJ cana-1902 88 5 + + CCONJ cana-1902 88 6 πœ‡2 πœ‡2 NOUN cana-1902 88 7 + + CCONJ cana-1902 88 8 ( ( PUNCT cana-1902 88 9 1 1 NUM cana-1902 88 10 βˆ’ βˆ’ PROPN cana-1902 88 11 𝑑 𝑑 PROPN cana-1902 88 12 βˆ’ βˆ’ PROPN cana-1902 88 13 𝑒)πœ‡3 𝑒)πœ‡3 PROPN cana-1902 88 14 ] ] PUNCT cana-1902 88 15 + + CCONJ cana-1902 89 1 [ [ X cana-1902 89 2 π‘ πœ‡1 π‘ πœ‡1 ADJ cana-1902 89 3 + + CCONJ cana-1902 89 4 πœ‡2 πœ‡2 PROPN cana-1902 89 5 + + CCONJ cana-1902 89 6 πœ‡3 πœ‡3 NOUN cana-1902 89 7 + + CCONJ cana-1902 89 8 π‘‘πœ‡2 π‘‘πœ‡2 ADV cana-1902 89 9 + + CCONJ cana-1902 89 10 ( ( PUNCT cana-1902 89 11 1 1 NUM cana-1902 89 12 βˆ’ βˆ’ PROPN cana-1902 89 13 𝑑 𝑑 PROPN cana-1902 89 14 βˆ’ βˆ’ PROPN cana-1902 89 15 𝑒)πœ‡3 𝑒)πœ‡3 PROPN cana-1902 89 16 ] ] PUNCT cana-1902 90 1 + + CCONJ cana-1902 90 2 [ [ X cana-1902 90 3 π‘ πœ‡1 π‘ πœ‡1 ADJ cana-1902 90 4 + + CCONJ cana-1902 90 5 πœ‡2 πœ‡2 PROPN cana-1902 90 6 + + CCONJ cana-1902 90 7 πœ‡3 πœ‡3 NOUN cana-1902 90 8 + + CCONJ cana-1902 90 9 π‘’πœ‡1 π‘’πœ‡1 VERB cana-1902 90 10 + + CCONJ cana-1902 90 11 πœ‡2 πœ‡2 NOUN cana-1902 90 12 + + CCONJ cana-1902 90 13 ( ( PUNCT cana-1902 90 14 1 1 NUM cana-1902 90 15 βˆ’ βˆ’ PROPN cana-1902 90 16 𝑑 𝑑 PROPN cana-1902 90 17 βˆ’ βˆ’ PROPN cana-1902 90 18 𝑒)πœ‡3 𝑒)πœ‡3 PROPN cana-1902 90 19 ] ] PUNCT cana-1902 91 1 + + CCONJ cana-1902 91 2 [ [ X cana-1902 91 3 ( ( PUNCT cana-1902 91 4 1 1 NUM cana-1902 91 5 βˆ’ βˆ’ NUM cana-1902 91 6 𝑠)πœ‡1 𝑠)πœ‡1 PROPN cana-1902 91 7 + + ADP cana-1902 91 8 πœ‡2 πœ‡2 PROPN cana-1902 91 9 + + CCONJ cana-1902 91 10 ( ( PUNCT cana-1902 91 11 1 1 NUM cana-1902 91 12 βˆ’ βˆ’ PROPN cana-1902 91 13 𝑑 𝑑 PROPN cana-1902 91 14 βˆ’ βˆ’ PROPN cana-1902 91 15 𝑒)πœ‡3 𝑒)πœ‡3 NOUN cana-1902 91 16 ) ) PUNCT cana-1902 91 17 ] ] PUNCT cana-1902 92 1 + + CCONJ cana-1902 92 2 [ [ X cana-1902 92 3 ( ( PUNCT cana-1902 92 4 1 1 NUM cana-1902 92 5 βˆ’ βˆ’ PROPN cana-1902 92 6 𝑠)𝑠1 𝑠)𝑠1 ADJ cana-1902 92 7 + + NUM cana-1902 92 8 𝑠2 𝑠2 NOUN cana-1902 92 9 + + CCONJ cana-1902 92 10 𝑠3 𝑠3 NOUN cana-1902 92 11 + + CCONJ cana-1902 92 12 𝑠𝑠2 𝑠𝑠2 NOUN cana-1902 92 13 + + CCONJ cana-1902 92 14 ( ( PUNCT cana-1902 92 15 1 1 NUM cana-1902 92 16 βˆ’ βˆ’ NOUN cana-1902 92 17 𝑠 𝑠 INTJ cana-1902 92 18 βˆ’ βˆ’ PROPN cana-1902 92 19 𝑠)𝑠3 𝑠)𝑠3 PROPN cana-1902 92 20 ] ] X cana-1902 93 1 + + CCONJ cana-1902 93 2 [ [ X cana-1902 93 3 ( ( PUNCT cana-1902 93 4 1 1 NUM cana-1902 93 5 βˆ’ βˆ’ NUM cana-1902 93 6 𝑠)πœ‡1 𝑠)πœ‡1 PROPN cana-1902 93 7 + + ADP cana-1902 93 8 πœ‡2 πœ‡2 PROPN cana-1902 93 9 + + CCONJ cana-1902 93 10 πœ‡3 πœ‡3 NOUN cana-1902 93 11 + + CCONJ cana-1902 93 12 π‘’πœ‡1 π‘’πœ‡1 VERB cana-1902 93 13 + + CCONJ cana-1902 93 14 πœ‡2 πœ‡2 NOUN cana-1902 93 15 + + CCONJ cana-1902 93 16 ( ( PUNCT cana-1902 93 17 1 1 NUM cana-1902 93 18 βˆ’ βˆ’ PROPN cana-1902 93 19 𝑑 𝑑 PROPN cana-1902 93 20 βˆ’ βˆ’ PROPN cana-1902 93 21 𝑒)πœ‡3]}𝑄1(𝑑 𝑒)πœ‡3]}𝑄1(𝑑 PROPN cana-1902 93 22 ) ) PUNCT cana-1902 93 23 + + NUM cana-1902 93 24 𝛾[1 𝛾[1 NOUN cana-1902 94 1 βˆ’ βˆ’ X cana-1902 94 2 𝑄0(𝑑 𝑄0(𝑑 NUM cana-1902 94 3 ) ) PUNCT cana-1902 94 4 ] ] PUNCT cana-1902 95 1 = = PUNCT cana-1902 95 2 βˆ’πœ†π‘„0(𝑑 βˆ’πœ†π‘„0(𝑑 ADJ cana-1902 95 3 ) ) PUNCT cana-1902 95 4 + + CCONJ cana-1902 96 1 [ [ X cana-1902 96 2 ( ( PUNCT cana-1902 96 3 3 3 NUM cana-1902 96 4 + + NUM cana-1902 96 5 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 96 6 + + CCONJ cana-1902 96 7 ( ( PUNCT cana-1902 96 8 9 9 NUM cana-1902 96 9 + + CCONJ cana-1902 96 10 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 96 11 + + CCONJ cana-1902 96 12 ( ( PUNCT cana-1902 96 13 10 10 NUM cana-1902 96 14 βˆ’ βˆ’ NOUN cana-1902 96 15 6𝑑 6𝑑 NOUN cana-1902 96 16 βˆ’ βˆ’ PROPN cana-1902 96 17 6𝑒)πœ‡3]𝑄1(𝑑 6𝑒)πœ‡3]𝑄1(𝑑 NOUN cana-1902 96 18 ) ) PUNCT cana-1902 97 1 + + NUM cana-1902 97 2 𝛾[1 𝛾[1 NOUN cana-1902 98 1 βˆ’ βˆ’ X cana-1902 98 2 𝑄0(𝑑 𝑄0(𝑑 NUM cana-1902 98 3 ) ) PUNCT cana-1902 98 4 ] ] PUNCT cana-1902 99 1 ( ( PUNCT cana-1902 99 2 1 1 X cana-1902 99 3 ) ) PUNCT cana-1902 99 4 n n NOUN cana-1902 99 5 = = NOUN cana-1902 99 6 1,2,3 1,2,3 NUM cana-1902 99 7 , , PUNCT cana-1902 99 8 . . PUNCT cana-1902 99 9 . . PUNCT cana-1902 100 1 . . PUNCT cana-1902 101 1 𝑄𝑛 𝑄𝑛 PROPN cana-1902 101 2 β€² β€² NOUN cana-1902 101 3 ( ( PUNCT cana-1902 101 4 𝑑 𝑑 NOUN cana-1902 101 5 ) ) PUNCT cana-1902 101 6 = = PUNCT cana-1902 101 7 πœ† πœ† DET cana-1902 101 8 π‘„π‘›βˆ’1 π‘„π‘›βˆ’1 PROPN cana-1902 101 9 ( ( PUNCT cana-1902 101 10 𝑑 𝑑 NOUN cana-1902 101 11 ) ) PUNCT cana-1902 101 12 βˆ’ βˆ’ PROPN cana-1902 101 13 [ [ PUNCT cana-1902 101 14 πœ† πœ† X cana-1902 101 15 + + X cana-1902 101 16 𝛾 𝛾 X cana-1902 101 17 + + X cana-1902 102 1 [ [ X cana-1902 102 2 ( ( PUNCT cana-1902 102 3 3 3 NUM cana-1902 102 4 + + NUM cana-1902 102 5 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 102 6 + + CCONJ cana-1902 102 7 ( ( PUNCT cana-1902 102 8 9 9 NUM cana-1902 102 9 + + CCONJ cana-1902 102 10 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 102 11 + + CCONJ cana-1902 102 12 ( ( PUNCT cana-1902 102 13 10 10 NUM cana-1902 102 14 βˆ’ βˆ’ NOUN cana-1902 102 15 6𝑑 6𝑑 NOUN cana-1902 102 16 βˆ’ βˆ’ NOUN cana-1902 102 17 6𝑒)πœ‡3]]𝑄𝑛(𝑑 6𝑒)πœ‡3]]𝑄𝑛(𝑑 NUM cana-1902 102 18 ) ) PUNCT cana-1902 102 19 + + CCONJ cana-1902 103 1 [ [ X cana-1902 103 2 3πœ‡1 3πœ‡1 NUM cana-1902 103 3 + + CCONJ cana-1902 103 4 6πœ‡2 6πœ‡2 NUM cana-1902 103 5 + + CCONJ cana-1902 103 6 2(3 2(3 NUM cana-1902 103 7 + + CCONJ cana-1902 103 8 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 103 9 + + CCONJ cana-1902 103 10 ( ( PUNCT cana-1902 103 11 9 9 NUM cana-1902 103 12 + + CCONJ cana-1902 103 13 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 103 14 + + CCONJ cana-1902 103 15 ( ( PUNCT cana-1902 103 16 10 10 NUM cana-1902 103 17 βˆ’ βˆ’ NOUN cana-1902 103 18 6𝑑 6𝑑 NOUN cana-1902 103 19 βˆ’ βˆ’ NOUN cana-1902 103 20 6𝑒)πœ‡3πœ‡3]𝑄𝑛+1(𝑑 6𝑒)πœ‡3πœ‡3]𝑄𝑛+1(𝑑 NUM cana-1902 103 21 ) ) PUNCT cana-1902 103 22 ( ( PUNCT cana-1902 103 23 2 2 X cana-1902 103 24 ) ) PUNCT cana-1902 103 25 in in ADP cana-1902 103 26 steady steady ADJ cana-1902 103 27 state state NOUN cana-1902 103 28 , , PUNCT cana-1902 103 29 π‘™π‘–π‘š π‘™π‘–π‘š VERB cana-1902 103 30 π‘›β†’βˆž π‘›β†’βˆž NUM cana-1902 103 31 𝑄𝑛(𝑑 𝑄𝑛(𝑑 PROPN cana-1902 103 32 ) ) PUNCT cana-1902 103 33 = = SYM cana-1902 103 34 𝑄𝑛 𝑄𝑛 PROPN cana-1902 103 35 and and CCONJ cana-1902 103 36 𝑄𝑛 𝑄𝑛 NOUN cana-1902 103 37 β€²(𝑑 β€²(𝑑 NOUN cana-1902 103 38 ) ) PUNCT cana-1902 103 39 = = SYM cana-1902 104 1 0 0 NUM cana-1902 104 2 π‘Žπ‘ π‘‘ π‘Žπ‘ π‘‘ ADJ cana-1902 104 3 β†’ β†’ SYM cana-1902 104 4 ∞ ∞ NUM cana-1902 104 5 communications communication NOUN cana-1902 104 6 on on ADP cana-1902 104 7 applied apply VERB cana-1902 104 8 nonlinear nonlinear ADJ cana-1902 104 9 analysis analysis NOUN cana-1902 104 10 issn issn NOUN cana-1902 104 11 : : PUNCT cana-1902 104 12 1074 1074 NUM cana-1902 104 13 - - PUNCT cana-1902 104 14 133x 133x NUM cana-1902 104 15 vol vol NOUN cana-1902 104 16 32 32 NUM cana-1902 104 17 no no NOUN cana-1902 104 18 . . NOUN cana-1902 104 19 3 3 NUM cana-1902 104 20 ( ( PUNCT cana-1902 104 21 2025 2025 NUM cana-1902 104 22 ) ) PUNCT cana-1902 104 23 4 4 NUM cana-1902 104 24 https://internationalpubls.com https://internationalpubls.com X cana-1902 104 25 these these PRON cana-1902 104 26 are be AUX cana-1902 104 27 the the DET cana-1902 104 28 steady steady ADJ cana-1902 104 29 - - PUNCT cana-1902 104 30 state state NOUN cana-1902 104 31 equations equation NOUN cana-1902 104 32 that that PRON cana-1902 104 33 correspond correspond VERB cana-1902 104 34 with with ADP cana-1902 104 35 equations equation NOUN cana-1902 104 36 ( ( PUNCT cana-1902 104 37 1 1 NUM cana-1902 104 38 ) ) PUNCT cana-1902 104 39 and and CCONJ cana-1902 104 40 ( ( PUNCT cana-1902 104 41 2 2 NUM cana-1902 104 42 ) ) PUNCT cana-1902 104 43 . . PUNCT cana-1902 104 44 0 0 PUNCT cana-1902 105 1 = = PUNCT cana-1902 105 2 βˆ’πœ†π‘„0 βˆ’πœ†π‘„0 X cana-1902 105 3 + + PUNCT cana-1902 106 1 [ [ X cana-1902 106 2 3πœ‡1 3πœ‡1 NUM cana-1902 106 3 + + CCONJ cana-1902 106 4 6πœ‡2 6πœ‡2 NUM cana-1902 106 5 + + CCONJ cana-1902 106 6 2πœ‡3]𝑄1 2πœ‡3]𝑄1 NUM cana-1902 106 7 + + CCONJ cana-1902 106 8 𝛾[1 𝛾[1 X cana-1902 106 9 βˆ’ βˆ’ PROPN cana-1902 106 10 𝑄0 𝑄0 X cana-1902 106 11 ] ] X cana-1902 106 12 ( ( PUNCT cana-1902 106 13 πœ† πœ† ADP cana-1902 106 14 + + PUNCT cana-1902 106 15 𝛾)𝑄0 𝛾)𝑄0 NOUN cana-1902 106 16 = = SYM cana-1902 106 17 𝛾 𝛾 X cana-1902 106 18 + + X cana-1902 107 1 [ [ X cana-1902 107 2 ( ( PUNCT cana-1902 107 3 3 3 NUM cana-1902 107 4 + + NUM cana-1902 107 5 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 107 6 + + CCONJ cana-1902 107 7 ( ( PUNCT cana-1902 107 8 9 9 NUM cana-1902 107 9 + + CCONJ cana-1902 107 10 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 107 11 + + CCONJ cana-1902 107 12 ( ( PUNCT cana-1902 107 13 10 10 NUM cana-1902 107 14 βˆ’ βˆ’ NOUN cana-1902 107 15 6𝑑 6𝑑 NOUN cana-1902 107 16 βˆ’ βˆ’ NOUN cana-1902 108 1 6𝑒)πœ‡3]𝑄1 6𝑒)πœ‡3]𝑄1 NUM cana-1902 108 2 ( ( PUNCT cana-1902 108 3 3 3 NUM cana-1902 108 4 ) ) PUNCT cana-1902 108 5 0 0 NUM cana-1902 109 1 = = PUNCT cana-1902 109 2 πœ†π‘„π‘›βˆ’1 πœ†π‘„π‘›βˆ’1 NOUN cana-1902 110 1 βˆ’ βˆ’ NOUN cana-1902 111 1 [ [ X cana-1902 111 2 πœ† πœ† X cana-1902 111 3 + + NOUN cana-1902 111 4 𝛾 𝛾 NOUN cana-1902 111 5 + + X cana-1902 111 6 [ [ X cana-1902 111 7 ( ( PUNCT cana-1902 111 8 3 3 NUM cana-1902 111 9 + + NUM cana-1902 111 10 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 111 11 + + CCONJ cana-1902 111 12 ( ( PUNCT cana-1902 111 13 9 9 NUM cana-1902 111 14 + + CCONJ cana-1902 111 15 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 111 16 + + CCONJ cana-1902 111 17 ( ( PUNCT cana-1902 111 18 10 10 NUM cana-1902 111 19 βˆ’ βˆ’ NOUN cana-1902 111 20 6𝑑 6𝑑 NOUN cana-1902 111 21 βˆ’ βˆ’ NOUN cana-1902 111 22 6𝑒)πœ‡3]]𝑄𝑛 6𝑒)πœ‡3]]𝑄𝑛 NOUN cana-1902 112 1 + + X cana-1902 112 2 [ [ X cana-1902 112 3 ( ( PUNCT cana-1902 112 4 3 3 NUM cana-1902 112 5 + + NUM cana-1902 112 6 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 112 7 + + CCONJ cana-1902 112 8 ( ( PUNCT cana-1902 112 9 9 9 NUM cana-1902 112 10 + + CCONJ cana-1902 112 11 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 112 12 + + CCONJ cana-1902 112 13 ( ( PUNCT cana-1902 112 14 10 10 NUM cana-1902 112 15 βˆ’ βˆ’ NOUN cana-1902 112 16 6𝑑 6𝑑 NOUN cana-1902 112 17 βˆ’ βˆ’ PROPN cana-1902 112 18 6𝑒)πœ‡3]𝑄𝑛+1 6𝑒)πœ‡3]𝑄𝑛+1 NUM cana-1902 113 1 [ [ X cana-1902 113 2 πœ† πœ† X cana-1902 113 3 + + NOUN cana-1902 113 4 𝛾 𝛾 X cana-1902 113 5 + + X cana-1902 113 6 [ [ X cana-1902 113 7 ( ( PUNCT cana-1902 113 8 3 3 NUM cana-1902 113 9 + + NUM cana-1902 113 10 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 113 11 + + CCONJ cana-1902 113 12 ( ( PUNCT cana-1902 113 13 9 9 NUM cana-1902 113 14 + + CCONJ cana-1902 113 15 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 113 16 + + CCONJ cana-1902 113 17 ( ( PUNCT cana-1902 113 18 10 10 NUM cana-1902 113 19 βˆ’ βˆ’ NOUN cana-1902 113 20 6𝑑 6𝑑 NOUN cana-1902 113 21 βˆ’ βˆ’ NOUN cana-1902 113 22 6𝑒)πœ‡3]]𝑄𝑛 6𝑒)πœ‡3]]𝑄𝑛 NOUN cana-1902 113 23 = = NOUN cana-1902 113 24 πœ†π‘„π‘›βˆ’1 πœ†π‘„π‘›βˆ’1 NOUN cana-1902 114 1 + + CCONJ cana-1902 114 2 [ [ X cana-1902 114 3 ( ( PUNCT cana-1902 114 4 3 3 NUM cana-1902 114 5 + + NUM cana-1902 114 6 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 114 7 + + CCONJ cana-1902 114 8 ( ( PUNCT cana-1902 114 9 9 9 NUM cana-1902 114 10 + + CCONJ cana-1902 114 11 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 114 12 + + CCONJ cana-1902 114 13 ( ( PUNCT cana-1902 114 14 10 10 NUM cana-1902 114 15 βˆ’ βˆ’ NOUN cana-1902 114 16 6𝑑 6𝑑 NOUN cana-1902 114 17 βˆ’ βˆ’ PROPN cana-1902 114 18 6𝑒)πœ‡3]𝑄𝑛+1 6𝑒)πœ‡3]𝑄𝑛+1 NUM cana-1902 114 19 ( ( PUNCT cana-1902 114 20 4 4 NUM cana-1902 114 21 ) ) PUNCT cana-1902 114 22 equation equation NOUN cana-1902 114 23 ( ( PUNCT cana-1902 114 24 3 3 NUM cana-1902 114 25 ) ) PUNCT cana-1902 114 26 ⟹ ⟹ NOUN cana-1902 114 27 𝛾 𝛾 NOUN cana-1902 114 28 = = SYM cana-1902 114 29 ( ( PUNCT cana-1902 114 30 πœ† πœ† NOUN cana-1902 114 31 + + PUNCT cana-1902 114 32 𝛾)𝑄0 𝛾)𝑄0 NOUN cana-1902 114 33 βˆ’ βˆ’ PROPN cana-1902 115 1 [ [ X cana-1902 115 2 ( ( PUNCT cana-1902 115 3 3 3 NUM cana-1902 115 4 + + NUM cana-1902 115 5 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 115 6 + + CCONJ cana-1902 115 7 ( ( PUNCT cana-1902 115 8 9 9 NUM cana-1902 115 9 + + CCONJ cana-1902 115 10 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 115 11 + + CCONJ cana-1902 115 12 ( ( PUNCT cana-1902 115 13 10 10 NUM cana-1902 115 14 βˆ’ βˆ’ NOUN cana-1902 115 15 6𝑑 6𝑑 NOUN cana-1902 115 16 βˆ’ βˆ’ NOUN cana-1902 115 17 6𝑒)πœ‡3]𝑄1 6𝑒)πœ‡3]𝑄1 NUM cana-1902 116 1 = = SYM cana-1902 117 1 [ [ X cana-1902 117 2 ( ( PUNCT cana-1902 117 3 πœ† πœ† NOUN cana-1902 117 4 + + PROPN cana-1902 117 5 𝛾 𝛾 NOUN cana-1902 117 6 ) ) PUNCT cana-1902 117 7 βˆ’ βˆ’ PUNCT cana-1902 118 1 [ [ X cana-1902 118 2 ( ( PUNCT cana-1902 118 3 3 3 NUM cana-1902 118 4 + + NUM cana-1902 118 5 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 118 6 + + CCONJ cana-1902 118 7 ( ( PUNCT cana-1902 118 8 9 9 NUM cana-1902 118 9 + + CCONJ cana-1902 118 10 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 118 11 + + CCONJ cana-1902 118 12 ( ( PUNCT cana-1902 118 13 10 10 NUM cana-1902 118 14 βˆ’ βˆ’ NOUN cana-1902 118 15 6𝑑 6𝑑 NOUN cana-1902 118 16 βˆ’ βˆ’ PROPN cana-1902 118 17 6𝑒)πœ‡3 6𝑒)πœ‡3 PROPN cana-1902 118 18 ] ] PUNCT cana-1902 118 19 𝑄1 𝑄1 PROPN cana-1902 118 20 𝑄0 𝑄0 PROPN cana-1902 118 21 ] ] PUNCT cana-1902 118 22 𝑄0 𝑄0 PROPN cana-1902 118 23 𝑄0 𝑄0 X cana-1902 119 1 = = PUNCT cana-1902 119 2 𝛾 𝛾 X cana-1902 119 3 ( ( PUNCT cana-1902 119 4 πœ†+𝛾)βˆ’[(3 πœ†+𝛾)βˆ’[(3 NOUN cana-1902 119 5 + + NOUN cana-1902 119 6 2𝑒)πœ‡1+(9+𝑑)πœ‡2+(10βˆ’6π‘‘βˆ’6𝑒)πœ‡3 2𝑒)πœ‡1+(9+𝑑)πœ‡2+(10βˆ’6π‘‘βˆ’6𝑒)πœ‡3 NOUN cana-1902 119 7 ] ] X cana-1902 119 8 𝑄1 𝑄1 NOUN cana-1902 119 9 𝑄0 𝑄0 PROPN cana-1902 120 1 ( ( PUNCT cana-1902 120 2 5 5 X cana-1902 120 3 ) ) PUNCT cana-1902 120 4 𝑄𝑛 𝑄𝑛 NOUN cana-1902 120 5 π‘„π‘›βˆ’1 π‘„π‘›βˆ’1 PROPN cana-1902 120 6 = = SYM cana-1902 121 1 πœ† πœ† PROPN cana-1902 121 2 ( ( PUNCT cana-1902 121 3 πœ†+𝛾+(3 πœ†+𝛾+(3 ADJ cana-1902 121 4 + + NOUN cana-1902 121 5 2𝑒)πœ‡1+(9+𝑑)πœ‡2+(10βˆ’6π‘‘βˆ’6𝑒)πœ‡3)βˆ’[(3 2𝑒)πœ‡1+(9+𝑑)πœ‡2+(10βˆ’6π‘‘βˆ’6𝑒)πœ‡3)βˆ’[(3 NUM cana-1902 121 6 + + NOUN cana-1902 121 7 2𝑒)πœ‡1+(9+𝑑)πœ‡2+(10βˆ’6π‘‘βˆ’6𝑒)πœ‡3 2𝑒)πœ‡1+(9+𝑑)πœ‡2+(10βˆ’6π‘‘βˆ’6𝑒)πœ‡3 NOUN cana-1902 121 8 ] ] X cana-1902 121 9 𝑄𝑛+1 𝑄𝑛+1 X cana-1902 122 1 𝑄𝑛 𝑄𝑛 NOUN cana-1902 122 2 ( ( PUNCT cana-1902 122 3 6 6 NUM cana-1902 122 4 ) ) PUNCT cana-1902 122 5 with with ADP cana-1902 122 6 the the DET cana-1902 122 7 continuing continue VERB cana-1902 122 8 fraction fraction NOUN cana-1902 122 9 and and CCONJ cana-1902 122 10 the the DET cana-1902 122 11 two two NUM cana-1902 122 12 equations equation NOUN cana-1902 122 13 mentioned mention VERB cana-1902 122 14 previously previously ADV cana-1902 122 15 , , PUNCT cana-1902 122 16 𝑄0 𝑄0 PROPN cana-1902 122 17 = = PUNCT cana-1902 122 18 𝛾 𝛾 X cana-1902 122 19 ( ( PUNCT cana-1902 122 20 πœ† πœ† NOUN cana-1902 122 21 + + CCONJ cana-1902 122 22 𝛾 𝛾 NOUN cana-1902 122 23 ) ) PUNCT cana-1902 122 24 βˆ’ βˆ’ NOUN cana-1902 122 25 πœ‚πœ† πœ‚πœ† X cana-1902 122 26 ( ( PUNCT cana-1902 122 27 πœ† πœ† PROPN cana-1902 122 28 + + ADP cana-1902 122 29 πœ‚ πœ‚ NOUN cana-1902 122 30 + + CCONJ cana-1902 122 31 𝛾 𝛾 NOUN cana-1902 122 32 ) ) PUNCT cana-1902 122 33 βˆ’ βˆ’ NOUN cana-1902 122 34 πœ‚ πœ‚ PROPN cana-1902 122 35 𝑄2 𝑄2 PROPN cana-1902 122 36 𝑄1 𝑄1 VERB cana-1902 122 37 where where SCONJ cana-1902 122 38 πœ‚ πœ‚ X cana-1902 122 39 = = SYM cana-1902 122 40 ( ( PUNCT cana-1902 122 41 3 3 NUM cana-1902 122 42 + + NUM cana-1902 122 43 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 122 44 + + CCONJ cana-1902 122 45 ( ( PUNCT cana-1902 122 46 9 9 NUM cana-1902 122 47 + + CCONJ cana-1902 122 48 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 122 49 + + CCONJ cana-1902 122 50 ( ( PUNCT cana-1902 122 51 10 10 NUM cana-1902 122 52 βˆ’ βˆ’ NOUN cana-1902 122 53 6𝑑 6𝑑 NOUN cana-1902 122 54 βˆ’ βˆ’ PROPN cana-1902 122 55 6𝑒)πœ‡3 6𝑒)πœ‡3 NOUN cana-1902 122 56 𝑄0 𝑄0 PUNCT cana-1902 122 57 = = PUNCT cana-1902 122 58 𝛾 𝛾 X cana-1902 122 59 ( ( PUNCT cana-1902 122 60 πœ† πœ† NOUN cana-1902 122 61 + + CCONJ cana-1902 122 62 𝛾 𝛾 NOUN cana-1902 122 63 ) ) PUNCT cana-1902 122 64 βˆ’ βˆ’ NOUN cana-1902 122 65 πœ‚ πœ‚ SYM cana-1902 122 66 πœ† πœ† NOUN cana-1902 122 67 ( ( PUNCT cana-1902 122 68 πœ† πœ† PROPN cana-1902 122 69 + + NOUN cana-1902 122 70 πœ‚ πœ‚ NOUN cana-1902 122 71 + + CCONJ cana-1902 122 72 𝛾 𝛾 NOUN cana-1902 122 73 ) ) PUNCT cana-1902 122 74 – – PUNCT cana-1902 122 75 πœ† πœ† X cana-1902 122 76 πœ‚ πœ‚ NOUN cana-1902 122 77 πœ† πœ† PROPN cana-1902 122 78 + + NUM cana-1902 122 79 πœ‚ πœ‚ NOUN cana-1902 122 80 + + CCONJ cana-1902 122 81 𝛾 𝛾 ADP cana-1902 122 82 βˆ’ βˆ’ NOUN cana-1902 122 83 β‹― β‹― PROPN cana-1902 122 84 . . PUNCT cana-1902 122 85 𝑄0 𝑄0 PROPN cana-1902 123 1 = = PUNCT cana-1902 123 2 𝛾 𝛾 PROPN cana-1902 123 3 ( ( PUNCT cana-1902 123 4 πœ†+ πœ†+ X cana-1902 123 5 𝛾 𝛾 NOUN cana-1902 123 6 ) ) PUNCT cana-1902 123 7 βˆ’π›Ό βˆ’π›Ό PROPN cana-1902 123 8 , , PUNCT cana-1902 123 9 𝛼 𝛼 X cana-1902 123 10 = = NOUN cana-1902 123 11 πœ‚ πœ‚ NOUN cana-1902 123 12 πœ† πœ† NOUN cana-1902 124 1 ( ( PUNCT cana-1902 124 2 πœ†+ πœ†+ NOUN cana-1902 124 3 πœ‚ πœ‚ X cana-1902 124 4 + + NOUN cana-1902 124 5 𝛾 𝛾 NOUN cana-1902 124 6 ) ) PUNCT cana-1902 124 7 βˆ’ βˆ’ PROPN cana-1902 124 8 πœ† πœ† ADP cana-1902 124 9 πœ‚ πœ‚ NOUN cana-1902 124 10 πœ†+ πœ†+ PUNCT cana-1902 124 11 πœ‚+ πœ‚+ X cana-1902 124 12 𝛾 𝛾 ADP cana-1902 124 13 βˆ’β‹―. βˆ’β‹―. NOUN cana-1902 124 14 ( ( PUNCT cana-1902 124 15 7 7 NUM cana-1902 124 16 ) ) PUNCT cana-1902 124 17 the the DET cana-1902 124 18 quadratic quadratic ADJ cana-1902 124 19 equation equation NOUN cana-1902 124 20 is be AUX cana-1902 124 21 satisfied satisfy VERB cana-1902 124 22 by by ADP cana-1902 124 23 equation equation NOUN cana-1902 124 24 ( ( PUNCT cana-1902 124 25 7 7 NUM cana-1902 124 26 ) ) PUNCT cana-1902 124 27 , , PUNCT cana-1902 124 28 𝛼2 𝛼2 PROPN cana-1902 124 29 βˆ’ βˆ’ PROPN cana-1902 124 30 ( ( PUNCT cana-1902 124 31 πœ† πœ† PROPN cana-1902 124 32 + + NUM cana-1902 124 33 πœ‚ πœ‚ NOUN cana-1902 124 34 + + NUM cana-1902 124 35 𝛾)𝛼 𝛾)𝛼 PUNCT cana-1902 124 36 + + CCONJ cana-1902 124 37 πœ†πœ‚ πœ†πœ‚ CCONJ cana-1902 124 38 = = SYM cana-1902 124 39 0 0 PUNCT cana-1902 125 1 therefore therefore ADV cana-1902 125 2 , , PUNCT cana-1902 125 3 the the DET cana-1902 125 4 roots root NOUN cana-1902 125 5 are be AUX cana-1902 125 6 π›½Β±βˆšπ›½2βˆ’4πœ†π›Ώ π›½Β±βˆšπ›½2βˆ’4πœ†π›Ώ PROPN cana-1902 125 7 2 2 NUM cana-1902 125 8 , , PUNCT cana-1902 125 9 where where SCONJ cana-1902 125 10 𝛽 𝛽 NOUN cana-1902 125 11 = = SYM cana-1902 125 12 πœ† πœ† PROPN cana-1902 125 13 + + PROPN cana-1902 125 14 Ξ· Ξ· AUX cana-1902 125 15 + + CCONJ cana-1902 125 16 Ξ³ Ξ³ X cana-1902 125 17 assuming assume VERB cana-1902 125 18 𝛼1 𝛼1 NOUN cana-1902 125 19 and and CCONJ cana-1902 125 20 𝛼2as 𝛼2a NOUN cana-1902 125 21 the the DET cana-1902 125 22 roots root NOUN cana-1902 125 23 , , PUNCT cana-1902 125 24 we we PRON cana-1902 125 25 extract extract VERB cana-1902 125 26 the the DET cana-1902 125 27 only only ADJ cana-1902 125 28 real real ADJ cana-1902 125 29 root root NOUN cana-1902 125 30 that that PRON cana-1902 125 31 falls fall VERB cana-1902 125 32 inside inside ADP cana-1902 125 33 [ [ X cana-1902 125 34 0 0 NUM cana-1902 125 35 , , PUNCT cana-1902 125 36 1 1 NUM cana-1902 125 37 ) ) PUNCT cana-1902 125 38 . . PUNCT cana-1902 126 1 substituting substitute VERB cana-1902 126 2 𝛼2 𝛼2 PROPN cana-1902 126 3 in in ADP cana-1902 126 4 equation equation NOUN cana-1902 126 5 ( ( PUNCT cana-1902 126 6 7 7 NUM cana-1902 126 7 ) ) PUNCT cana-1902 126 8 , , PUNCT cana-1902 126 9 we we PRON cana-1902 126 10 get get VERB cana-1902 126 11 𝑄0 𝑄0 X cana-1902 127 1 = = PUNCT cana-1902 127 2 𝛾 𝛾 PROPN cana-1902 127 3 ( ( PUNCT cana-1902 127 4 πœ†+𝛾)βˆ’ πœ†+𝛾)βˆ’ CCONJ cana-1902 127 5 π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ X cana-1902 127 6 2 2 NUM cana-1902 127 7 ( ( PUNCT cana-1902 127 8 8) 8) NUM cana-1902 127 9 𝑄0 𝑄0 NOUN cana-1902 127 10 = = SYM cana-1902 128 1 𝛾 𝛾 PROPN cana-1902 128 2 ( ( PUNCT cana-1902 128 3 𝛽 𝛽 NOUN cana-1902 128 4 βˆ’ βˆ’ PROPN cana-1902 128 5 πœ‚ πœ‚ PROPN cana-1902 128 6 ) ) PUNCT cana-1902 128 7 βˆ’ βˆ’ PROPN cana-1902 128 8 𝛽 𝛽 NOUN cana-1902 128 9 βˆ’ βˆ’ NOUN cana-1902 128 10 βˆšπ›½2 βˆšπ›½2 PROPN cana-1902 128 11 βˆ’ βˆ’ PROPN cana-1902 128 12 4πœ†πœ‚ 4πœ†πœ‚ NOUN cana-1902 128 13 2 2 NUM cana-1902 128 14 communications communication NOUN cana-1902 128 15 on on ADP cana-1902 128 16 applied apply VERB cana-1902 128 17 nonlinear nonlinear ADJ cana-1902 128 18 analysis analysis NOUN cana-1902 128 19 issn issn NOUN cana-1902 128 20 : : PUNCT cana-1902 128 21 1074 1074 NUM cana-1902 128 22 - - PUNCT cana-1902 128 23 133x 133x NUM cana-1902 128 24 vol vol NOUN cana-1902 128 25 32 32 NUM cana-1902 128 26 no no NOUN cana-1902 128 27 . . NOUN cana-1902 128 28 3 3 NUM cana-1902 128 29 ( ( PUNCT cana-1902 128 30 2025 2025 NUM cana-1902 128 31 ) ) PUNCT cana-1902 128 32 5 5 NUM cana-1902 128 33 https://internationalpubls.com https://internationalpubls.com X cana-1902 128 34 multiply multiply NOUN cana-1902 128 35 and and CCONJ cana-1902 128 36 divide divide VERB cana-1902 128 37 by by ADP cana-1902 128 38 π›½βˆ’βˆšπ›½2βˆ’4πœ†Ξ· π›½βˆ’βˆšπ›½2βˆ’4πœ†Ξ· NOUN cana-1902 128 39 2πœ†Ξ· 2πœ†Ξ· NOUN cana-1902 128 40 after after ADP cana-1902 128 41 some some DET cana-1902 128 42 algebraic algebraic ADJ cana-1902 128 43 calculation calculation NOUN cana-1902 128 44 , , PUNCT cana-1902 128 45 we we PRON cana-1902 128 46 get get VERB cana-1902 128 47 𝑄0 𝑄0 X cana-1902 129 1 = = SYM cana-1902 129 2 𝛾 𝛾 PROPN cana-1902 129 3 ( ( PUNCT cana-1902 129 4 π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ NOUN cana-1902 129 5 2πœ†πœ‚ 2πœ†πœ‚ NOUN cana-1902 129 6 ) ) PUNCT cana-1902 129 7 1βˆ’π›Ώ 1βˆ’π›Ώ NUM cana-1902 129 8 ( ( PUNCT cana-1902 129 9 π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ NOUN cana-1902 129 10 2πœ†πœ‚ 2πœ†πœ‚ NOUN cana-1902 129 11 ) ) PUNCT cana-1902 129 12 ( ( PUNCT cana-1902 129 13 9 9 X cana-1902 129 14 ) ) PUNCT cana-1902 129 15 after after ADP cana-1902 129 16 expanding expand VERB cana-1902 129 17 binomially binomially ADV cana-1902 129 18 , , PUNCT cana-1902 129 19 𝑄0 𝑄0 PUNCT cana-1902 129 20 = = PUNCT cana-1902 129 21 βˆ‘ βˆ‘ PUNCT cana-1902 129 22 πœ‚π‘› πœ‚π‘› NOUN cana-1902 129 23 ( ( PUNCT cana-1902 129 24 π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ NOUN cana-1902 129 25 2πœ†πœ‚ 2πœ†πœ‚ NOUN cana-1902 129 26 ) ) PUNCT cana-1902 130 1 𝑛+1 𝑛+1 ADP cana-1902 130 2 ∞ ∞ NUM cana-1902 130 3 𝑛=0 𝑛=0 PROPN cana-1902 130 4 + + CCONJ cana-1902 130 5 𝛾 𝛾 NOUN cana-1902 130 6 βˆ‘ βˆ‘ ADV cana-1902 130 7 πœ‚π‘› πœ‚π‘› NOUN cana-1902 130 8 ( ( PUNCT cana-1902 130 9 π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ NOUN cana-1902 130 10 2πœ†πœ‚ 2πœ†πœ‚ NOUN cana-1902 130 11 ) ) PUNCT cana-1902 131 1 𝑛+1 𝑛+1 ADP cana-1902 131 2 ∞ ∞ NUM cana-1902 131 3 𝑛=0 𝑛=0 PROPN cana-1902 131 4 ( ( PUNCT cana-1902 131 5 10 10 NUM cana-1902 131 6 ) ) PUNCT cana-1902 131 7 using use VERB cana-1902 131 8 equation equation NOUN cana-1902 131 9 ( ( PUNCT cana-1902 131 10 6 6 NUM cana-1902 131 11 ) ) PUNCT cana-1902 131 12 , , PUNCT cana-1902 131 13 we we PRON cana-1902 131 14 can can AUX cana-1902 131 15 now now ADV cana-1902 131 16 calculate calculate VERB cana-1902 131 17 the the DET cana-1902 131 18 remaining remain VERB cana-1902 131 19 steady steady ADJ cana-1902 131 20 state state NOUN cana-1902 131 21 probabilities probability NOUN cana-1902 131 22 in in ADP cana-1902 131 23 terms term NOUN cana-1902 131 24 of of ADP cana-1902 131 25 q q NOUN cana-1902 131 26 0 0 NUM cana-1902 131 27 , , PUNCT cana-1902 131 28 𝑄𝑛 𝑄𝑛 PROPN cana-1902 131 29 π‘„π‘›βˆ’1 π‘„π‘›βˆ’1 PROPN cana-1902 131 30 = = SYM cana-1902 131 31 𝛾 𝛾 PROPN cana-1902 131 32 ( ( PUNCT cana-1902 131 33 πœ†+𝛾+πœ‚ πœ†+𝛾+πœ‚ NOUN cana-1902 131 34 ) ) PUNCT cana-1902 131 35 βˆ’ βˆ’ PROPN cana-1902 132 1 πœ† πœ† PRON cana-1902 132 2 πœ‚ πœ‚ PROPN cana-1902 132 3 ( ( PUNCT cana-1902 132 4 πœ†+πœ‚+𝛾 πœ†+πœ‚+𝛾 NOUN cana-1902 132 5 ) ) PUNCT cana-1902 132 6 βˆ’ βˆ’ PROPN cana-1902 133 1 πœ† πœ† ADP cana-1902 133 2 πœ‚ πœ‚ NOUN cana-1902 133 3 πœ†+πœ‚+𝛾 πœ†+πœ‚+𝛾 NOUN cana-1902 133 4 βˆ’β‹―. βˆ’β‹―. NOUN cana-1902 133 5 using use VERB cana-1902 133 6 the the DET cana-1902 133 7 same same ADJ cana-1902 133 8 reasoning reasoning NOUN cana-1902 133 9 as as ADP cana-1902 133 10 before before ADV cana-1902 133 11 , , PUNCT cana-1902 133 12 the the DET cana-1902 133 13 equation equation NOUN cana-1902 133 14 above above ADV cana-1902 133 15 reduces reduce VERB cana-1902 133 16 to to ADP cana-1902 133 17 𝑄𝑛 𝑄𝑛 PROPN cana-1902 133 18 π‘„π‘›βˆ’1 π‘„π‘›βˆ’1 PROPN cana-1902 133 19 = = PUNCT cana-1902 133 20 πœ† πœ† X cana-1902 133 21 𝛽+βˆšπ›½2βˆ’4πœ†πœ‚ 𝛽+βˆšπ›½2βˆ’4πœ†πœ‚ X cana-1902 133 22 2 2 NUM cana-1902 133 23 , , PUNCT cana-1902 133 24 n n NOUN cana-1902 133 25 = = SYM cana-1902 133 26 1 1 NUM cana-1902 133 27 , , PUNCT cana-1902 133 28 2 2 NUM cana-1902 133 29 . . PUNCT cana-1902 133 30 . . PUNCT cana-1902 133 31 . . PUNCT cana-1902 133 32 . . PUNCT cana-1902 133 33 . . PUNCT cana-1902 134 1 ( ( PUNCT cana-1902 134 2 11 11 NUM cana-1902 134 3 ) ) PUNCT cana-1902 134 4 equations equation NOUN cana-1902 134 5 ( ( PUNCT cana-1902 134 6 11 11 NUM cana-1902 134 7 ) ) PUNCT cana-1902 134 8 can can AUX cana-1902 134 9 be be AUX cana-1902 134 10 multiplied multiply VERB cana-1902 134 11 and and CCONJ cana-1902 134 12 divided divide VERB cana-1902 134 13 by by ADP cana-1902 134 14 𝛽 𝛽 NOUN cana-1902 134 15 βˆ’ βˆ’ NOUN cana-1902 135 1 βˆšπ›½2 βˆšπ›½2 PROPN cana-1902 135 2 βˆ’ βˆ’ PROPN cana-1902 135 3 4πœ†Ξ· 4πœ†Ξ· ADJ cana-1902 135 4 𝑄𝑛 𝑄𝑛 PROPN cana-1902 135 5 = = SYM cana-1902 135 6 ( ( PUNCT cana-1902 135 7 π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ π›½βˆ’βˆšπ›½2βˆ’4πœ†πœ‚ NOUN cana-1902 135 8 2πœ‚ 2πœ‚ NOUN cana-1902 135 9 ) ) PUNCT cana-1902 135 10 𝑛 𝑛 DET cana-1902 135 11 𝑄0 𝑄0 PROPN cana-1902 135 12 , , PUNCT cana-1902 135 13 n n NOUN cana-1902 135 14 = = SYM cana-1902 135 15 1 1 NUM cana-1902 135 16 , , PUNCT cana-1902 135 17 2 2 NUM cana-1902 135 18 , , PUNCT cana-1902 135 19 . . PUNCT cana-1902 135 20 . . PUNCT cana-1902 136 1 . . PUNCT cana-1902 137 1 , , PUNCT cana-1902 137 2 ( ( PUNCT cana-1902 137 3 12 12 NUM cana-1902 137 4 ) ) PUNCT cana-1902 137 5 as as SCONJ cana-1902 137 6 we we PRON cana-1902 137 7 know know VERB cana-1902 137 8 𝛽 𝛽 NOUN cana-1902 137 9 = = SYM cana-1902 137 10 πœ† πœ† PROPN cana-1902 137 11 + + CCONJ cana-1902 137 12 Ξ³ Ξ³ PROPN cana-1902 137 13 + + CCONJ cana-1902 137 14 Ξ· Ξ· PROPN cana-1902 137 15 equations equation NOUN cana-1902 137 16 ( ( PUNCT cana-1902 137 17 10 10 NUM cana-1902 137 18 ) ) PUNCT cana-1902 137 19 and and CCONJ cana-1902 137 20 ( ( PUNCT cana-1902 137 21 11 11 NUM cana-1902 137 22 ) ) PUNCT cana-1902 137 23 gives give VERB cana-1902 137 24 the the DET cana-1902 137 25 probabilities probability NOUN cana-1902 137 26 for for ADP cana-1902 137 27 q q NOUN cana-1902 137 28 0 0 PUNCT cana-1902 137 29 and and CCONJ cana-1902 137 30 q q ADJ cana-1902 137 31 n n PROPN cana-1902 137 32 under under ADP cana-1902 137 33 steady steady ADJ cana-1902 137 34 state state NOUN cana-1902 137 35 condition condition NOUN cana-1902 137 36 for for ADP cana-1902 137 37 n n NOUN cana-1902 137 38 = = SYM cana-1902 137 39 1 1 NUM cana-1902 137 40 , , PUNCT cana-1902 137 41 2 2 NUM cana-1902 137 42 , , PUNCT cana-1902 137 43 . . PUNCT cana-1902 137 44 . . PUNCT cana-1902 138 1 . . PUNCT cana-1902 139 1 , , PUNCT cana-1902 139 2 2.1 2.1 NUM cana-1902 139 3 theorem theorem VERB cana-1902 139 4 the the DET cana-1902 139 5 average average ADJ cana-1902 139 6 queue queue NOUN cana-1902 139 7 length length NOUN cana-1902 139 8 asymptotic asymptotic ADJ cana-1902 139 9 behavior behavior NOUN cana-1902 139 10 in in ADP cana-1902 139 11 steady steady ADJ cana-1902 139 12 state state NOUN cana-1902 139 13 , , PUNCT cana-1902 139 14 if if SCONJ cana-1902 139 15 Ξ³ Ξ³ X cana-1902 139 16 > > X cana-1902 139 17 0 0 NUM cana-1902 139 18 , , PUNCT cana-1902 139 19 is be AUX cana-1902 139 20 πΏπ‘ž πΏπ‘ž PROPN cana-1902 139 21 = = PUNCT cana-1902 139 22 πœ†βˆ’πœ‚ πœ†βˆ’πœ‚ PROPN cana-1902 139 23 𝛾 𝛾 ADP cana-1902 139 24 + + ADV cana-1902 139 25 2 2 NUM cana-1902 139 26 πœ‚ πœ‚ SYM cana-1902 139 27 2 2 NUM cana-1902 139 28 ( ( PUNCT cana-1902 139 29 πœ†+ πœ†+ X cana-1902 139 30 𝛾 𝛾 NOUN cana-1902 139 31 ) ) PUNCT cana-1902 140 1 βˆ’ βˆ’ PROPN cana-1902 140 2 [ [ PUNCT cana-1902 140 3 ( ( PUNCT cana-1902 140 4 πœ†+πœ‚+𝛾 πœ†+πœ‚+𝛾 NOUN cana-1902 140 5 ) ) PUNCT cana-1902 140 6 βˆ’ βˆ’ NOUN cana-1902 141 1 √ √ NUM cana-1902 141 2 ( ( PUNCT cana-1902 141 3 πœ†+πœ‚+𝛾)2 πœ†+πœ‚+𝛾)2 PROPN cana-1902 141 4 – – PUNCT cana-1902 141 5 4 4 NUM cana-1902 141 6 πœ† πœ† SYM cana-1902 141 7 πœ‚ πœ‚ NOUN cana-1902 141 8 ] ] PUNCT cana-1902 141 9 , , PUNCT cana-1902 141 10 πœ‚ πœ‚ X cana-1902 141 11 = = SYM cana-1902 141 12 ( ( PUNCT cana-1902 141 13 3 3 NUM cana-1902 141 14 + + NUM cana-1902 141 15 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 141 16 + + CCONJ cana-1902 141 17 ( ( PUNCT cana-1902 141 18 9 9 NUM cana-1902 141 19 + + CCONJ cana-1902 141 20 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 141 21 + + CCONJ cana-1902 141 22 ( ( PUNCT cana-1902 141 23 10 10 NUM cana-1902 141 24 βˆ’ βˆ’ NOUN cana-1902 141 25 6𝑑 6𝑑 NOUN cana-1902 141 26 βˆ’ βˆ’ PROPN cana-1902 141 27 6𝑒)πœ‡3 6𝑒)πœ‡3 NOUN cana-1902 141 28 proof proof NOUN cana-1902 141 29 : : PUNCT cana-1902 141 30 examine examine NOUN cana-1902 141 31 equations equation NOUN cana-1902 141 32 ( ( PUNCT cana-1902 141 33 1 1 NUM cana-1902 141 34 ) ) PUNCT cana-1902 141 35 and and CCONJ cana-1902 141 36 ( ( PUNCT cana-1902 141 37 2 2 X cana-1902 141 38 ) ) PUNCT cana-1902 141 39 in in ADP cana-1902 141 40 relation relation NOUN cana-1902 141 41 to to ADP cana-1902 141 42 the the DET cana-1902 141 43 initial initial ADJ cana-1902 141 44 condition condition NOUN cana-1902 141 45 q q NOUN cana-1902 141 46 0 0 NUM cana-1902 141 47 ( ( PUNCT cana-1902 141 48 0 0 NUM cana-1902 141 49 ) ) PUNCT cana-1902 141 50 = = SYM cana-1902 142 1 1 1 X cana-1902 142 2 . . PUNCT cana-1902 142 3 πœ•π‘„(π‘₯,𝑑 πœ•π‘„(π‘₯,𝑑 NOUN cana-1902 142 4 ) ) PUNCT cana-1902 143 1 πœ•π‘‘ πœ•π‘‘ NOUN cana-1902 144 1 = = PUNCT cana-1902 145 1 [ [ X cana-1902 145 2 πœ†π‘₯ πœ†π‘₯ NOUN cana-1902 145 3 + + CCONJ cana-1902 145 4 πœ‚ πœ‚ NOUN cana-1902 145 5 π‘₯ π‘₯ X cana-1902 145 6 βˆ’ βˆ’ PROPN cana-1902 145 7 ( ( PUNCT cana-1902 145 8 πœ† πœ† PROPN cana-1902 145 9 + + CCONJ cana-1902 145 10 𝛾 𝛾 NOUN cana-1902 145 11 + + NUM cana-1902 145 12 πœ‚ πœ‚ NOUN cana-1902 145 13 ) ) PUNCT cana-1902 145 14 ] ] PUNCT cana-1902 146 1 𝑄(π‘₯ 𝑄(π‘₯ X cana-1902 146 2 , , PUNCT cana-1902 146 3 𝑑 𝑑 PROPN cana-1902 146 4 ) ) PUNCT cana-1902 146 5 + + NUM cana-1902 146 6 πœ‚ πœ‚ X cana-1902 146 7 ( ( PUNCT cana-1902 146 8 1 1 NUM cana-1902 146 9 βˆ’ βˆ’ PROPN cana-1902 146 10 1 1 NUM cana-1902 146 11 π‘₯ π‘₯ NOUN cana-1902 146 12 ) ) PUNCT cana-1902 146 13 𝑄0(π‘₯ 𝑄0(π‘₯ PUNCT cana-1902 146 14 ) ) PUNCT cana-1902 147 1 + + CCONJ cana-1902 147 2 Ξ³ Ξ³ X cana-1902 147 3 ( ( PUNCT cana-1902 147 4 13 13 NUM cana-1902 147 5 ) ) PUNCT cana-1902 147 6 the the DET cana-1902 147 7 mean mean ADJ cana-1902 147 8 size size NOUN cana-1902 147 9 is be AUX cana-1902 147 10 π‘š(𝑑 π‘š(𝑑 NOUN cana-1902 147 11 ) ) PUNCT cana-1902 147 12 = = PUNCT cana-1902 147 13 βˆ‘ βˆ‘ NOUN cana-1902 147 14 𝑛𝑄𝑛(𝑑 𝑛𝑄𝑛(𝑑 PROPN cana-1902 147 15 ) ) PUNCT cana-1902 148 1 = = SYM cana-1902 148 2 ∞ ∞ NUM cana-1902 148 3 𝑛=1 𝑛=1 NOUN cana-1902 148 4 πœ•π‘„(π‘₯,𝑑 πœ•π‘„(π‘₯,𝑑 NOUN cana-1902 148 5 ) ) PUNCT cana-1902 148 6 πœ•π‘‘ πœ•π‘‘ PROPN cana-1902 148 7 at at ADP cana-1902 148 8 x=1 x=1 PROPN cana-1902 148 9 by by ADP cana-1902 148 10 taking take VERB cana-1902 148 11 the the DET cana-1902 148 12 derivative derivative NOUN cana-1902 148 13 of of ADP cana-1902 148 14 equation equation NOUN cana-1902 148 15 ( ( PUNCT cana-1902 148 16 13 13 NUM cana-1902 148 17 ) ) PUNCT cana-1902 148 18 with with ADP cana-1902 148 19 respect respect NOUN cana-1902 148 20 to to ADP cana-1902 148 21 x x PUNCT cana-1902 148 22 and and CCONJ cana-1902 148 23 evaluating evaluate VERB cana-1902 148 24 it it PRON cana-1902 148 25 at at ADP cana-1902 148 26 x x X cana-1902 148 27 = = SYM cana-1902 148 28 1 1 NUM cana-1902 148 29 , , PUNCT cana-1902 148 30 we we PRON cana-1902 148 31 obtain obtain VERB cana-1902 148 32 π‘‘π‘š(𝑑 π‘‘π‘š(𝑑 NOUN cana-1902 148 33 ) ) PUNCT cana-1902 148 34 𝑑π‘₯ 𝑑π‘₯ VERB cana-1902 148 35 + + NOUN cana-1902 148 36 Ξ³π‘š(𝑑 Ξ³π‘š(𝑑 NOUN cana-1902 148 37 ) ) PUNCT cana-1902 148 38 = = SYM cana-1902 149 1 πœ† πœ† DET cana-1902 149 2 βˆ’ βˆ’ PROPN cana-1902 149 3 ( ( PUNCT cana-1902 149 4 1 1 NUM cana-1902 149 5 βˆ’ βˆ’ PROPN cana-1902 149 6 𝑄0)Ξ· 𝑄0)Ξ· ADP cana-1902 149 7 finding find VERB cana-1902 149 8 the the DET cana-1902 149 9 solution solution NOUN cana-1902 149 10 for for ADP cana-1902 149 11 m(t m(t NOUN cana-1902 149 12 ) ) PUNCT cana-1902 149 13 in in ADP cana-1902 149 14 the the DET cana-1902 149 15 differential differential ADJ cana-1902 149 16 equation equation NOUN cana-1902 149 17 above above ADP cana-1902 149 18 , , PUNCT cana-1902 149 19 where where SCONJ cana-1902 149 20 communications communication NOUN cana-1902 149 21 on on ADP cana-1902 149 22 applied apply VERB cana-1902 149 23 nonlinear nonlinear ADJ cana-1902 149 24 analysis analysis NOUN cana-1902 149 25 issn issn NOUN cana-1902 149 26 : : PUNCT cana-1902 149 27 1074 1074 NUM cana-1902 149 28 - - PUNCT cana-1902 149 29 133x 133x NUM cana-1902 149 30 vol vol NOUN cana-1902 149 31 32 32 NUM cana-1902 149 32 no no NOUN cana-1902 149 33 . . NOUN cana-1902 149 34 3 3 NUM cana-1902 149 35 ( ( PUNCT cana-1902 149 36 2025 2025 NUM cana-1902 149 37 ) ) PUNCT cana-1902 149 38 6 6 NUM cana-1902 149 39 https://internationalpubls.com https://internationalpubls.com X cana-1902 149 40 π‘š(0 π‘š(0 PROPN cana-1902 149 41 ) ) PUNCT cana-1902 149 42 = = SYM cana-1902 149 43 βˆ‘ βˆ‘ PUNCT cana-1902 149 44 𝑛𝑄𝑛(𝑑 𝑛𝑄𝑛(𝑑 PROPN cana-1902 149 45 ) ) PUNCT cana-1902 150 1 = = SYM cana-1902 150 2 ∞ ∞ NUM cana-1902 150 3 𝑛=1 𝑛=1 NOUN cana-1902 150 4 0 0 NUM cana-1902 150 5 π‘š(𝑑 π‘š(𝑑 NUM cana-1902 150 6 ) ) PUNCT cana-1902 150 7 = = PUNCT cana-1902 151 1 πœ† πœ† PRON cana-1902 151 2 Ξ³ Ξ³ X cana-1902 151 3 ( ( PUNCT cana-1902 151 4 1 1 NUM cana-1902 151 5 βˆ’ βˆ’ PROPN cana-1902 151 6 π‘’βˆ’Ξ³π‘‘ π‘’βˆ’Ξ³π‘‘ PROPN cana-1902 151 7 ) ) PUNCT cana-1902 151 8 βˆ’ βˆ’ PROPN cana-1902 151 9 Ξ· Ξ· PROPN cana-1902 151 10 Ξ³ Ξ³ X cana-1902 151 11 ( ( PUNCT cana-1902 151 12 1 1 NUM cana-1902 151 13 βˆ’ βˆ’ PROPN cana-1902 151 14 π‘’βˆ’Ξ³π‘‘ π‘’βˆ’Ξ³π‘‘ PROPN cana-1902 151 15 ) ) PUNCT cana-1902 151 16 + + NUM cana-1902 151 17 Ξ· Ξ· PROPN cana-1902 151 18 ∫ ∫ PROPN cana-1902 151 19 𝑄0(𝑒 𝑄0(𝑒 PROPN cana-1902 151 20 ) ) PUNCT cana-1902 151 21 𝑑 𝑑 PROPN cana-1902 151 22 0 0 PUNCT cana-1902 151 23 π‘’βˆ’Ξ³(π‘‘βˆ’π‘’)𝑑𝑒 π‘’βˆ’Ξ³(π‘‘βˆ’π‘’)𝑑𝑒 X cana-1902 151 24 ( ( PUNCT cana-1902 151 25 14 14 NUM cana-1902 151 26 ) ) PUNCT cana-1902 151 27 we we PRON cana-1902 151 28 get get VERB cana-1902 151 29 the the DET cana-1902 151 30 below below ADJ cana-1902 151 31 equation equation NOUN cana-1902 151 32 by by ADP cana-1902 151 33 applying apply VERB cana-1902 151 34 laplace laplace NOUN cana-1902 151 35 transform transform NOUN cana-1902 151 36 for for ADP cana-1902 151 37 equation equation NOUN cana-1902 151 38 ( ( PUNCT cana-1902 151 39 1 1 NUM cana-1902 151 40 ) ) PUNCT cana-1902 151 41 and and CCONJ cana-1902 151 42 ( ( PUNCT cana-1902 151 43 2 2 NUM cana-1902 151 44 ) ) PUNCT cana-1902 151 45 𝑄0 𝑄0 PROPN cana-1902 151 46 βˆ—(π‘₯ βˆ—(π‘₯ NOUN cana-1902 151 47 ) ) PUNCT cana-1902 152 1 = = SYM cana-1902 152 2 1 1 NUM cana-1902 152 3 + + CCONJ cana-1902 152 4 Ξ³ Ξ³ AUX cana-1902 152 5 π‘₯ π‘₯ X cana-1902 152 6 ( ( PUNCT cana-1902 152 7 π‘₯+πœ†+Ξ³)βˆ’ π‘₯+πœ†+Ξ³)βˆ’ X cana-1902 152 8 [ [ PUNCT cana-1902 152 9 π›½βˆ’βˆš π›½βˆ’βˆš PROPN cana-1902 152 10 𝛽2βˆ’ 𝛽2βˆ’ PROPN cana-1902 152 11 4 4 NUM cana-1902 152 12 πœ† πœ† SYM cana-1902 152 13 Ξ· Ξ· PROPN cana-1902 152 14 2 2 NUM cana-1902 152 15 ] ] PUNCT cana-1902 152 16 ( ( PUNCT cana-1902 152 17 15 15 X cana-1902 152 18 ) ) PUNCT cana-1902 152 19 taking take VERB cana-1902 152 20 laplace laplace NOUN cana-1902 152 21 transforms transform VERB cana-1902 152 22 for for ADP cana-1902 152 23 equation equation NOUN cana-1902 152 24 ( ( PUNCT cana-1902 152 25 14 14 NUM cana-1902 152 26 ) ) PUNCT cana-1902 152 27 , , PUNCT cana-1902 152 28 let let VERB cana-1902 152 29 π‘šβˆ—(π‘₯ π‘šβˆ—(π‘₯ PRON cana-1902 152 30 ) ) PUNCT cana-1902 152 31 be be VERB cana-1902 152 32 the the DET cana-1902 152 33 laplace laplace NOUN cana-1902 152 34 transform transform NOUN cana-1902 152 35 of of ADP cana-1902 152 36 π‘š(𝑑 π‘š(𝑑 NOUN cana-1902 152 37 ) ) PUNCT cana-1902 152 38 π‘šβˆ—(π‘₯ π‘šβˆ—(π‘₯ NOUN cana-1902 152 39 ) ) PUNCT cana-1902 152 40 = = SYM cana-1902 153 1 πœ†βˆ’Ξ· πœ†βˆ’Ξ· VERB cana-1902 153 2 π‘₯(π‘₯+Ξ³ π‘₯(π‘₯+Ξ³ PRON cana-1902 153 3 ) ) PUNCT cana-1902 154 1 + + CCONJ cana-1902 154 2 Ξ· Ξ· PROPN cana-1902 154 3 ( ( PUNCT cana-1902 154 4 π‘₯+Ξ³ π‘₯+Ξ³ PROPN cana-1902 154 5 ) ) PUNCT cana-1902 154 6 𝑄0 𝑄0 PROPN cana-1902 154 7 βˆ—(π‘₯ βˆ—(π‘₯ PROPN cana-1902 154 8 ) ) PUNCT cana-1902 154 9 ( ( PUNCT cana-1902 154 10 16 16 NUM cana-1902 154 11 ) ) PUNCT cana-1902 154 12 π‘™π‘–π‘š π‘™π‘–π‘š VERB cana-1902 154 13 π‘‘β†’βˆž π‘‘β†’βˆž NUM cana-1902 154 14 π‘š(𝑑 π‘š(𝑑 NOUN cana-1902 154 15 ) ) PUNCT cana-1902 154 16 = = VERB cana-1902 154 17 π‘™π‘–π‘š π‘™π‘–π‘š VERB cana-1902 154 18 π‘₯β†’0 π‘₯β†’0 X cana-1902 154 19 π‘₯ π‘₯ X cana-1902 154 20 π‘šβˆ—(π‘₯ π‘šβˆ—(π‘₯ PROPN cana-1902 154 21 ) ) PUNCT cana-1902 154 22 using use VERB cana-1902 154 23 the the DET cana-1902 154 24 laplace laplace NOUN cana-1902 154 25 transform transform NOUN cana-1902 154 26 to to PART cana-1902 154 27 solve solve VERB cana-1902 154 28 equations equation NOUN cana-1902 154 29 ( ( PUNCT cana-1902 154 30 1 1 NUM cana-1902 154 31 ) ) PUNCT cana-1902 154 32 and and CCONJ cana-1902 154 33 ( ( PUNCT cana-1902 154 34 2 2 NUM cana-1902 154 35 ) ) PUNCT cana-1902 154 36 , , PUNCT cana-1902 154 37 we we PRON cana-1902 154 38 obtain obtain VERB cana-1902 154 39 πΏπ‘ž πΏπ‘ž ADJ cana-1902 154 40 = = PUNCT cana-1902 154 41 π‘š(𝑑 π‘š(𝑑 X cana-1902 154 42 ) ) PUNCT cana-1902 154 43 = = SYM cana-1902 155 1 πœ† πœ† DET cana-1902 155 2 βˆ’ βˆ’ NOUN cana-1902 155 3 πœ‚ πœ‚ NOUN cana-1902 155 4 𝛾 𝛾 NOUN cana-1902 155 5 + + NUM cana-1902 155 6 2πœ‚ 2πœ‚ NOUN cana-1902 155 7 2(πœ† 2(πœ† NUM cana-1902 155 8 + + CCONJ cana-1902 155 9 𝛾 𝛾 NOUN cana-1902 155 10 ) ) PUNCT cana-1902 155 11 βˆ’ βˆ’ PUNCT cana-1902 156 1 [ [ X cana-1902 156 2 ( ( PUNCT cana-1902 156 3 πœ† πœ† PROPN cana-1902 156 4 + + PROPN cana-1902 156 5 πœ‚ πœ‚ NOUN cana-1902 156 6 + + CCONJ cana-1902 156 7 𝛾 𝛾 NOUN cana-1902 156 8 ) ) PUNCT cana-1902 156 9 βˆ’ βˆ’ NOUN cana-1902 156 10 √(πœ† √(πœ† NOUN cana-1902 156 11 + + CCONJ cana-1902 156 12 πœ‚ πœ‚ NOUN cana-1902 156 13 + + CCONJ cana-1902 156 14 𝛾)2 𝛾)2 NOUN cana-1902 156 15 βˆ’ βˆ’ PROPN cana-1902 156 16 4πœ†πœ‚ 4πœ†πœ‚ NOUN cana-1902 156 17 ] ] X cana-1902 156 18 3 3 X cana-1902 156 19 . . X cana-1902 156 20 balance balance NOUN cana-1902 156 21 equations equation NOUN cana-1902 156 22 using use VERB cana-1902 156 23 little little ADJ cana-1902 156 24 's 's PART cana-1902 156 25 formula formula NOUN cana-1902 156 26 , , PUNCT cana-1902 156 27 the the DET cana-1902 156 28 following follow VERB cana-1902 156 29 equations equation NOUN cana-1902 156 30 are be AUX cana-1902 156 31 obtained obtain VERB cana-1902 156 32 . . PUNCT cana-1902 157 1 average average ADJ cana-1902 157 2 queue queue NOUN cana-1902 157 3 length length NOUN cana-1902 157 4 of of ADP cana-1902 157 5 the the DET cana-1902 157 6 system system NOUN cana-1902 157 7 πΏπ‘ž πΏπ‘ž NOUN cana-1902 157 8 = = PUNCT cana-1902 157 9 πœ†βˆ’πœ‚ πœ†βˆ’πœ‚ PROPN cana-1902 157 10 𝛾 𝛾 ADP cana-1902 157 11 + + NUM cana-1902 157 12 2πœ‚ 2πœ‚ NOUN cana-1902 157 13 2(πœ†+𝛾)βˆ’[(πœ†+πœ‚+𝛾)βˆ’βˆš(πœ†+πœ‚+𝛾)2βˆ’4πœ†πœ‚ 2(πœ†+𝛾)βˆ’[(πœ†+πœ‚+𝛾)βˆ’βˆš(πœ†+πœ‚+𝛾)2βˆ’4πœ†πœ‚ NUM cana-1902 157 14 ] ] PUNCT cana-1902 157 15 , , PUNCT cana-1902 157 16 πœ‚ πœ‚ X cana-1902 157 17 = = SYM cana-1902 157 18 ( ( PUNCT cana-1902 157 19 3 3 NUM cana-1902 157 20 + + NUM cana-1902 157 21 2𝑒)πœ‡1 2𝑒)πœ‡1 NUM cana-1902 157 22 + + CCONJ cana-1902 157 23 ( ( PUNCT cana-1902 157 24 9 9 NUM cana-1902 157 25 + + CCONJ cana-1902 157 26 𝑑)πœ‡2 𝑑)πœ‡2 PROPN cana-1902 157 27 + + CCONJ cana-1902 157 28 ( ( PUNCT cana-1902 157 29 10 10 NUM cana-1902 157 30 βˆ’ βˆ’ NOUN cana-1902 157 31 6𝑑 6𝑑 NOUN cana-1902 157 32 βˆ’ βˆ’ NOUN cana-1902 157 33 6𝑒 6𝑒 NOUN cana-1902 157 34 ) ) PUNCT cana-1902 157 35 customer customer NOUN cana-1902 157 36 wait wait VERB cana-1902 157 37 time time NOUN cana-1902 157 38 in in ADP cana-1902 157 39 each each PRON cana-1902 157 40 of of ADP cana-1902 157 41 the the DET cana-1902 157 42 three three NUM cana-1902 157 43 lines line NOUN cana-1902 157 44 π‘Šπ‘ž π‘Šπ‘ž NOUN cana-1902 157 45 = = SYM cana-1902 158 1 πΏπ‘ž πΏπ‘ž PROPN cana-1902 158 2 πœ† πœ† NOUN cana-1902 159 1 = = PUNCT cana-1902 159 2 ( ( PUNCT cana-1902 159 3 πœ† πœ† PRON cana-1902 159 4 βˆ’ βˆ’ PROPN cana-1902 159 5 πœ‚ πœ‚ NOUN cana-1902 159 6 𝛾 𝛾 ADP cana-1902 159 7 + + NUM cana-1902 159 8 2πœ‚ 2πœ‚ NOUN cana-1902 159 9 2(πœ† 2(πœ† NUM cana-1902 159 10 + + CCONJ cana-1902 159 11 𝛾 𝛾 NOUN cana-1902 159 12 ) ) PUNCT cana-1902 159 13 βˆ’ βˆ’ PUNCT cana-1902 160 1 [ [ X cana-1902 160 2 ( ( PUNCT cana-1902 160 3 πœ† πœ† PROPN cana-1902 160 4 + + PROPN cana-1902 160 5 πœ‚ πœ‚ NOUN cana-1902 160 6 + + CCONJ cana-1902 160 7 𝛾 𝛾 NOUN cana-1902 160 8 ) ) PUNCT cana-1902 160 9 βˆ’ βˆ’ NOUN cana-1902 160 10 √(πœ† √(πœ† NOUN cana-1902 160 11 + + CCONJ cana-1902 160 12 πœ‚ πœ‚ NOUN cana-1902 160 13 + + CCONJ cana-1902 160 14 𝛾)2 𝛾)2 NOUN cana-1902 160 15 βˆ’ βˆ’ PROPN cana-1902 160 16 4πœ†πœ‚ 4πœ†πœ‚ NOUN cana-1902 160 17 ] ] PUNCT cana-1902 160 18 ) ) PUNCT cana-1902 160 19 1 1 NUM cana-1902 161 1 πœ† πœ† NOUN cana-1902 161 2 the the DET cana-1902 161 3 mean mean ADJ cana-1902 161 4 quantity quantity NOUN cana-1902 161 5 of of ADP cana-1902 161 6 customers customer NOUN cana-1902 161 7 within within ADP cana-1902 161 8 the the DET cana-1902 161 9 system system NOUN cana-1902 162 1 𝐿𝑠 𝐿𝑠 PROPN cana-1902 162 2 = = SYM cana-1902 162 3 πΏπ‘ž πΏπ‘ž PROPN cana-1902 162 4 + + CCONJ cana-1902 162 5 πœ† πœ† PRON cana-1902 162 6 πœ‡ πœ‡ ADP cana-1902 162 7 = = X cana-1902 162 8 ( ( PUNCT cana-1902 162 9 πœ† πœ† PRON cana-1902 162 10 βˆ’ βˆ’ PROPN cana-1902 162 11 πœ‚ πœ‚ NOUN cana-1902 162 12 𝛾 𝛾 ADP cana-1902 162 13 + + NUM cana-1902 162 14 2πœ‚ 2πœ‚ NOUN cana-1902 162 15 2(πœ† 2(πœ† NUM cana-1902 162 16 + + CCONJ cana-1902 162 17 𝛾 𝛾 NOUN cana-1902 162 18 ) ) PUNCT cana-1902 162 19 βˆ’ βˆ’ PUNCT cana-1902 163 1 [ [ X cana-1902 163 2 ( ( PUNCT cana-1902 163 3 πœ† πœ† PROPN cana-1902 163 4 + + PROPN cana-1902 163 5 πœ‚ πœ‚ NOUN cana-1902 163 6 + + CCONJ cana-1902 163 7 𝛾 𝛾 NOUN cana-1902 163 8 ) ) PUNCT cana-1902 163 9 βˆ’ βˆ’ NOUN cana-1902 163 10 √(πœ† √(πœ† NOUN cana-1902 163 11 + + CCONJ cana-1902 163 12 πœ‚ πœ‚ NOUN cana-1902 163 13 + + CCONJ cana-1902 163 14 𝛾)2 𝛾)2 NOUN cana-1902 163 15 βˆ’ βˆ’ PROPN cana-1902 163 16 4πœ†πœ‚ 4πœ†πœ‚ NOUN cana-1902 163 17 ] ] PUNCT cana-1902 163 18 ) ) PUNCT cana-1902 164 1 + + CCONJ cana-1902 164 2 πœ† πœ† ADP cana-1902 164 3 πœ‡ πœ‡ ADP cana-1902 164 4 customer customer NOUN cana-1902 164 5 's 's PART cana-1902 164 6 wait wait ADJ cana-1902 164 7 time time NOUN cana-1902 164 8 within within ADP cana-1902 164 9 the the DET cana-1902 164 10 system system NOUN cana-1902 164 11 π‘Šπ‘  π‘Šπ‘  PROPN cana-1902 164 12 = = SYM cana-1902 164 13 𝐿𝑠 𝐿𝑠 PROPN cana-1902 164 14 πœ† πœ† NOUN cana-1902 164 15 = = PUNCT cana-1902 164 16 [ [ PUNCT cana-1902 164 17 πœ† πœ† PRON cana-1902 164 18 βˆ’ βˆ’ PROPN cana-1902 164 19 πœ‚ πœ‚ NOUN cana-1902 164 20 𝛾 𝛾 NOUN cana-1902 164 21 + + NUM cana-1902 164 22 2πœ‚ 2πœ‚ NOUN cana-1902 164 23 2(πœ† 2(πœ† NUM cana-1902 164 24 + + CCONJ cana-1902 164 25 𝛾 𝛾 NOUN cana-1902 164 26 ) ) PUNCT cana-1902 164 27 βˆ’ βˆ’ PUNCT cana-1902 165 1 [ [ X cana-1902 165 2 ( ( PUNCT cana-1902 165 3 πœ† πœ† PROPN cana-1902 165 4 + + PROPN cana-1902 165 5 πœ‚ πœ‚ NOUN cana-1902 165 6 + + CCONJ cana-1902 165 7 𝛾 𝛾 NOUN cana-1902 165 8 ) ) PUNCT cana-1902 165 9 βˆ’ βˆ’ NOUN cana-1902 165 10 √(πœ† √(πœ† NOUN cana-1902 165 11 + + CCONJ cana-1902 165 12 πœ‚ πœ‚ NOUN cana-1902 165 13 + + CCONJ cana-1902 165 14 𝛾)2 𝛾)2 NOUN cana-1902 165 15 βˆ’ βˆ’ PROPN cana-1902 165 16 4πœ†πœ‚ 4πœ†πœ‚ NOUN cana-1902 165 17 ] ] PUNCT cana-1902 166 1 + + CCONJ cana-1902 166 2 πœ† πœ† ADP cana-1902 166 3 πœ‡ πœ‡ X cana-1902 166 4 ] ] X cana-1902 166 5 1 1 NUM cana-1902 166 6 πœ† πœ† NOUN cana-1902 166 7 for for ADP cana-1902 166 8 node node PROPN cana-1902 166 9 one one NUM cana-1902 166 10 , , PUNCT cana-1902 166 11 the the DET cana-1902 166 12 average average ADJ cana-1902 166 13 queue queue NOUN cana-1902 166 14 length length NOUN cana-1902 166 15 is be AUX cana-1902 166 16 communications communication NOUN cana-1902 166 17 on on ADP cana-1902 166 18 applied apply VERB cana-1902 166 19 nonlinear nonlinear ADJ cana-1902 166 20 analysis analysis NOUN cana-1902 166 21 issn issn NOUN cana-1902 166 22 : : PUNCT cana-1902 166 23 1074 1074 NUM cana-1902 166 24 - - PUNCT cana-1902 166 25 133x 133x NUM cana-1902 166 26 vol vol NOUN cana-1902 166 27 32 32 NUM cana-1902 166 28 no no NOUN cana-1902 166 29 . . NOUN cana-1902 166 30 3 3 NUM cana-1902 166 31 ( ( PUNCT cana-1902 166 32 2025 2025 NUM cana-1902 166 33 ) ) PUNCT cana-1902 166 34 7 7 NUM cana-1902 166 35 https://internationalpubls.com https://internationalpubls.com X cana-1902 166 36 πΏπ‘ž1 πΏπ‘ž1 NOUN cana-1902 167 1 = = PUNCT cana-1902 167 2 πœ†βˆ’πœ‚ πœ†βˆ’πœ‚ NUM cana-1902 167 3 𝛾 𝛾 ADP cana-1902 167 4 + + X cana-1902 167 5 2πœ‚ 2πœ‚ NOUN cana-1902 167 6 2(πœ†+𝛾)βˆ’[(πœ†+πœ‚+𝛾)βˆ’βˆš(πœ†+πœ‚+𝛾)2βˆ’4πœ†πœ‚ 2(πœ†+𝛾)βˆ’[(πœ†+πœ‚+𝛾)βˆ’βˆš(πœ†+πœ‚+𝛾)2βˆ’4πœ†πœ‚ NUM cana-1902 167 7 ] ] PUNCT cana-1902 167 8 , , PUNCT cana-1902 167 9 πœ‚ πœ‚ X cana-1902 167 10 = = SYM cana-1902 167 11 πœ‡1 πœ‡1 NOUN cana-1902 167 12 + + CCONJ cana-1902 167 13 2πœ‡2 2πœ‡2 NUM cana-1902 167 14 + + CCONJ cana-1902 167 15 2π‘’πœ‡3 2π‘’πœ‡3 NUM cana-1902 167 16 for for ADP cana-1902 167 17 node node NOUN cana-1902 167 18 two two NUM cana-1902 167 19 , , PUNCT cana-1902 167 20 the the DET cana-1902 167 21 average average ADJ cana-1902 167 22 queue queue NOUN cana-1902 167 23 length length NOUN cana-1902 167 24 is be AUX cana-1902 167 25 πΏπ‘ž2 πΏπ‘ž2 ADJ cana-1902 168 1 = = PUNCT cana-1902 168 2 πœ†βˆ’πœ‚ πœ†βˆ’πœ‚ PROPN cana-1902 168 3 𝛾 𝛾 ADP cana-1902 168 4 + + NUM cana-1902 168 5 2πœ‚ 2πœ‚ NOUN cana-1902 168 6 2(πœ†+𝛾)βˆ’[(πœ†+πœ‚+𝛾)βˆ’βˆš(πœ†+πœ‚+𝛾)2βˆ’4πœ†πœ‚ 2(πœ†+𝛾)βˆ’[(πœ†+πœ‚+𝛾)βˆ’βˆš(πœ†+πœ‚+𝛾)2βˆ’4πœ†πœ‚ NUM cana-1902 168 7 ] ] PUNCT cana-1902 168 8 , , PUNCT cana-1902 168 9 πœ‚ πœ‚ X cana-1902 168 10 = = SYM cana-1902 168 11 πœ‡1 πœ‡1 NOUN cana-1902 168 12 + + CCONJ cana-1902 168 13 2πœ‡2 2πœ‡2 NUM cana-1902 168 14 + + CCONJ cana-1902 168 15 2π‘‘πœ‡3 2π‘‘πœ‡3 NUM cana-1902 168 16 for for ADP cana-1902 168 17 node node NOUN cana-1902 168 18 three three NUM cana-1902 168 19 , , PUNCT cana-1902 168 20 the the DET cana-1902 168 21 average average ADJ cana-1902 168 22 queue queue NOUN cana-1902 168 23 length length NOUN cana-1902 168 24 is be AUX cana-1902 168 25 πΏπ‘ž3 πΏπ‘ž3 NOUN cana-1902 168 26 = = PUNCT cana-1902 168 27 πœ†βˆ’πœ‚ πœ†βˆ’πœ‚ PROPN cana-1902 169 1 𝛾 𝛾 AUX cana-1902 169 2 + + NUM cana-1902 169 3 2πœ‚ 2πœ‚ NOUN cana-1902 169 4 2(πœ†+𝛾)βˆ’[(πœ†+πœ‚+𝛾)βˆ’βˆš(πœ†+πœ‚+𝛾)2βˆ’4πœ†πœ‚ 2(πœ†+𝛾)βˆ’[(πœ†+πœ‚+𝛾)βˆ’βˆš(πœ†+πœ‚+𝛾)2βˆ’4πœ†πœ‚ NUM cana-1902 169 5 ] ] PUNCT cana-1902 169 6 , , PUNCT cana-1902 169 7 πœ‚ πœ‚ NOUN cana-1902 169 8 = = SYM cana-1902 169 9 2(1 2(1 NUM cana-1902 169 10 + + CCONJ cana-1902 169 11 𝑒)πœ‡1 𝑒)πœ‡1 PROPN cana-1902 169 12 + + CCONJ cana-1902 169 13 8πœ‡2 8πœ‡2 NUM cana-1902 169 14 + + NUM cana-1902 169 15 2π‘‘πœ‡3 2π‘‘πœ‡3 NUM cana-1902 169 16 using use VERB cana-1902 169 17 little little ADJ cana-1902 169 18 ’s ’s PART cana-1902 169 19 formula formula NOUN cana-1902 169 20 the the DET cana-1902 169 21 remaining remain VERB cana-1902 169 22 parameterswq1 parameterswq1 NOUN cana-1902 169 23 , , PUNCT cana-1902 169 24 wq2 wq2 PRON cana-1902 169 25 , , PUNCT cana-1902 169 26 wq3 wq3 NOUN cana-1902 169 27 , , PUNCT cana-1902 169 28 ls1 ls1 NOUN cana-1902 169 29 , , PUNCT cana-1902 169 30 ls2 ls2 PROPN cana-1902 169 31 , , PUNCT cana-1902 169 32 ls3 ls3 PROPN cana-1902 169 33 , , PUNCT cana-1902 169 34 ws1 ws1 INTJ cana-1902 169 35 , , PUNCT cana-1902 169 36 ws2 ws2 NOUN cana-1902 169 37 , , PUNCT cana-1902 169 38 ws3 ws3 VERB cana-1902 169 39 are be AUX cana-1902 169 40 calculated calculate VERB cana-1902 169 41 . . PUNCT cana-1902 170 1 4 4 X cana-1902 170 2 . . X cana-1902 170 3 particular particular ADJ cana-1902 170 4 case case NOUN cana-1902 170 5 : : PUNCT cana-1902 170 6 when when SCONJ cana-1902 170 7 ΞΌ ΞΌ PROPN cana-1902 170 8 1 1 X cana-1902 170 9 = = SYM cana-1902 170 10 ΞΌ ΞΌ PROPN cana-1902 170 11 and and CCONJ cana-1902 170 12 ΞΌ ΞΌ PROPN cana-1902 170 13 2 2 NUM cana-1902 170 14 = = SYM cana-1902 170 15 ΞΌ ΞΌ NOUN cana-1902 170 16 3 3 NUM cana-1902 170 17 = = SYM cana-1902 170 18 0 0 NUM cana-1902 170 19 , , PUNCT cana-1902 170 20 t t PROPN cana-1902 170 21 = = SYM cana-1902 170 22 s s PART cana-1902 170 23 = = SYM cana-1902 170 24 0 0 NUM cana-1902 170 25 , , PUNCT cana-1902 170 26 there there PRON cana-1902 170 27 will will AUX cana-1902 170 28 only only ADV cana-1902 170 29 be be AUX cana-1902 170 30 a a DET cana-1902 170 31 single single ADJ cana-1902 170 32 node node NOUN cana-1902 170 33 without without ADP cana-1902 170 34 feedback feedback NOUN cana-1902 170 35 . . PUNCT cana-1902 171 1 when when SCONJ cana-1902 171 2 s s VERB cana-1902 171 3 = = SYM cana-1902 171 4 0 0 NUM cana-1902 171 5 , , PUNCT cana-1902 171 6 there there PRON cana-1902 171 7 are be VERB cana-1902 171 8 no no DET cana-1902 171 9 retrials retrial NOUN cana-1902 171 10 leading lead VERB cana-1902 171 11 to to ADP cana-1902 171 12 Ξ· Ξ· PROPN cana-1902 171 13 = = PROPN cana-1902 171 14 ΞΌ ΞΌ PROPN cana-1902 171 15 . . PUNCT cana-1902 172 1 asymptotic asymptotic ADJ cana-1902 172 2 behavior behavior NOUN cana-1902 172 3 of of ADP cana-1902 172 4 the the DET cana-1902 172 5 system system NOUN cana-1902 172 6 lq lq VERB cana-1902 172 7 when when SCONJ cana-1902 172 8 Ξ³ Ξ³ X cana-1902 172 9 > > X cana-1902 172 10 0 0 NUM cana-1902 172 11 is be AUX cana-1902 172 12 πΏπ‘ž πΏπ‘ž PROPN cana-1902 172 13 = = PUNCT cana-1902 172 14 πœ†βˆ’πœ‡ πœ†βˆ’πœ‡ NOUN cana-1902 172 15 𝛾 𝛾 ADP cana-1902 172 16 + + X cana-1902 172 17 2πœ‡ 2πœ‡ NUM cana-1902 172 18 2(πœ†+𝛾)βˆ’[(πœ†+πœ‡+𝛾)βˆ’βˆš(πœ†+πœ‡+𝛾)2βˆ’4πœ†πœ‡ 2(πœ†+𝛾)βˆ’[(πœ†+πœ‡+𝛾)βˆ’βˆš(πœ†+πœ‡+𝛾)2βˆ’4πœ†πœ‡ NOUN cana-1902 172 19 ] ] X cana-1902 172 20 ( ( PUNCT cana-1902 172 21 17 17 NUM cana-1902 172 22 ) ) PUNCT cana-1902 172 23 case case NOUN cana-1902 172 24 1 1 NUM cana-1902 172 25 : : PUNCT cana-1902 172 26 when when SCONJ cana-1902 172 27 Ξ³ Ξ³ X cana-1902 172 28 > > X cana-1902 172 29 0 0 PROPN cana-1902 172 30 , , PUNCT cana-1902 172 31 the the DET cana-1902 172 32 average average ADJ cana-1902 172 33 queue queue NOUN cana-1902 172 34 length length NOUN cana-1902 172 35 of of ADP cana-1902 172 36 the the DET cana-1902 172 37 system system NOUN cana-1902 172 38 lq lq ADP cana-1902 172 39 behaves behave VERB cana-1902 172 40 asymptotically asymptotically ADV cana-1902 172 41 πΏπ‘ž πΏπ‘ž ADV cana-1902 172 42 = = PUNCT cana-1902 172 43 πœ†βˆ’πœ‡ πœ†βˆ’πœ‡ NOUN cana-1902 172 44 𝛾 𝛾 ADP cana-1902 172 45 + + X cana-1902 172 46 2πœ‡ 2πœ‡ NUM cana-1902 172 47 2(πœ†+𝛾)βˆ’[(πœ†+πœ‡+𝛾)βˆ’βˆš(πœ†+πœ‡+𝛾)2βˆ’π›Ό2 2(πœ†+𝛾)βˆ’[(πœ†+πœ‡+𝛾)βˆ’βˆš(πœ†+πœ‡+𝛾)2βˆ’π›Ό2 NUM cana-1902 172 48 ] ] PUNCT cana-1902 172 49 as as ADP cana-1902 172 50 t t PROPN cana-1902 172 51 β†’ β†’ SYM cana-1902 172 52 ∞ ∞ PROPN cana-1902 172 53 , , PUNCT cana-1902 172 54 𝛼 𝛼 X cana-1902 172 55 = = NOUN cana-1902 172 56 2√λμ 2√λμ NUM cana-1902 172 57 when when SCONJ cana-1902 172 58 Ξ³ Ξ³ X cana-1902 172 59 > > X cana-1902 172 60 0 0 PROPN cana-1902 172 61 , , PUNCT cana-1902 172 62 equation equation NOUN cana-1902 172 63 ( ( PUNCT cana-1902 172 64 17 17 NUM cana-1902 172 65 ) ) PUNCT cana-1902 172 66 agrees agree VERB cana-1902 172 67 with with ADP cana-1902 172 68 krishnakumar krishnakumar PROPN cana-1902 172 69 et et PROPN cana-1902 172 70 al al PROPN cana-1902 172 71 . . PUNCT cana-1902 173 1 [ [ X cana-1902 173 2 8 8 NUM cana-1902 173 3 ] ] PUNCT cana-1902 173 4 . . PUNCT cana-1902 174 1 case case NOUN cana-1902 174 2 2 2 NUM cana-1902 174 3 : : PUNCT cana-1902 174 4 the the DET cana-1902 174 5 mean mean ADJ cana-1902 174 6 queue queue NOUN cana-1902 174 7 length length NOUN cana-1902 174 8 m(t m(t NOUN cana-1902 174 9 ) ) PUNCT cana-1902 174 10 behaves behave VERB cana-1902 174 11 asymptotically asymptotically ADV cana-1902 174 12 changes change NOUN cana-1902 174 13 when when SCONJ cana-1902 174 14 Ξ³ Ξ³ X cana-1902 174 15 is be AUX cana-1902 174 16 greater great ADJ cana-1902 174 17 than than ADP cana-1902 174 18 0 0 NUM cana-1902 174 19 . . PUNCT cana-1902 175 1 πΏπ‘ž πΏπ‘ž ADJ cana-1902 175 2 = = PUNCT cana-1902 175 3 πœ†βˆ’πœ‡π‘ž πœ†βˆ’πœ‡π‘ž NOUN cana-1902 175 4 𝛾 𝛾 NOUN cana-1902 175 5 + + X cana-1902 175 6 2πœ‡π‘ž 2πœ‡π‘ž NOUN cana-1902 175 7 2(πœ†+𝛾)βˆ’[(πœ†+πœ‡π‘ž+𝛾)βˆ’βˆš(πœ†+πœ‡π‘ž+𝛾)2βˆ’4πœ†πœ‡π‘ž 2(πœ†+𝛾)βˆ’[(πœ†+πœ‡π‘ž+𝛾)βˆ’βˆš(πœ†+πœ‡π‘ž+𝛾)2βˆ’4πœ†πœ‡π‘ž NUM cana-1902 175 8 ] ] PUNCT cana-1902 175 9 as as ADP cana-1902 175 10 t t PROPN cana-1902 175 11 β†’ β†’ SYM cana-1902 175 12 ∞ ∞ NUM cana-1902 175 13 by by ADP cana-1902 175 14 assuming assume VERB cana-1902 175 15 q q X cana-1902 175 16 = = SYM cana-1902 175 17 1 1 NUM cana-1902 175 18 , , PUNCT cana-1902 175 19 the the DET cana-1902 175 20 equation equation NOUN cana-1902 175 21 ( ( PUNCT cana-1902 175 22 17 17 NUM cana-1902 175 23 ) ) PUNCT cana-1902 175 24 agrees agree VERB cana-1902 175 25 with with ADP cana-1902 175 26 thangaraj thangaraj PROPN cana-1902 175 27 et et PROPN cana-1902 175 28 al al PROPN cana-1902 175 29 . . PUNCT cana-1902 176 1 [ [ X cana-1902 176 2 13 13 NUM cana-1902 176 3 ] ] PUNCT cana-1902 176 4 . . PUNCT cana-1902 177 1 case case NOUN cana-1902 177 2 3 3 NUM cana-1902 177 3 : : PUNCT cana-1902 177 4 the the DET cana-1902 177 5 mean mean ADJ cana-1902 177 6 queue queue NOUN cana-1902 177 7 length length NOUN cana-1902 177 8 m(t m(t NOUN cana-1902 177 9 ) ) PUNCT cana-1902 177 10 exhibits exhibit VERB cana-1902 177 11 asymptotic asymptotic ADJ cana-1902 177 12 behavior behavior NOUN cana-1902 177 13 when when SCONJ cana-1902 177 14 Ξ³>0 Ξ³>0 VERB cana-1902 177 15 . . PUNCT cana-1902 178 1 πΏπ‘ž πΏπ‘ž NOUN cana-1902 178 2 = = PUNCT cana-1902 178 3 πœ†βˆ’π›½ πœ†βˆ’π›½ PROPN cana-1902 178 4 𝛾 𝛾 ADP cana-1902 178 5 + + X cana-1902 178 6 2𝛽 2𝛽 NOUN cana-1902 178 7 2(πœ†+𝛾)βˆ’[(πœ†+𝛽+𝛾)βˆ’βˆš(πœ†+𝛽+𝛾)2βˆ’4πœ†π›½ 2(πœ†+𝛾)βˆ’[(πœ†+𝛽+𝛾)βˆ’βˆš(πœ†+𝛽+𝛾)2βˆ’4πœ†π›½ NUM cana-1902 178 8 ] ] PUNCT cana-1902 178 9 as as ADP cana-1902 178 10 t t PROPN cana-1902 178 11 β†’ β†’ SYM cana-1902 178 12 ∞ ∞ PROPN cana-1902 178 13 where where SCONJ cana-1902 178 14 𝛽 𝛽 NOUN cana-1902 178 15 = = SYM cana-1902 178 16 ( ( PUNCT cana-1902 178 17 5 5 NUM cana-1902 178 18 + + NUM cana-1902 178 19 2𝑝)πœ‡1 2𝑝)πœ‡1 NUM cana-1902 178 20 + + CCONJ cana-1902 178 21 4πœ‡2 4πœ‡2 NUM cana-1902 178 22 + + SYM cana-1902 178 23 2πœ‡3 2πœ‡3 NUM cana-1902 178 24 equation equation NOUN cana-1902 178 25 ( ( PUNCT cana-1902 178 26 17 17 NUM cana-1902 178 27 ) ) PUNCT cana-1902 178 28 agrees agree VERB cana-1902 178 29 with with ADP cana-1902 178 30 shanmugasundaram shanmugasundaram PROPN cana-1902 178 31 et et PROPN cana-1902 178 32 al al PROPN cana-1902 178 33 . . PUNCT cana-1902 179 1 [ [ X cana-1902 179 2 11 11 NUM cana-1902 179 3 ] ] PUNCT cana-1902 179 4 when when SCONJ cana-1902 179 5 p p PROPN cana-1902 179 6 = = NOUN cana-1902 179 7 0 0 NUM cana-1902 179 8 , , PUNCT cana-1902 179 9 πœ‡1 πœ‡1 NOUN cana-1902 179 10 = = SYM cana-1902 179 11 0 0 NUM cana-1902 179 12 , , PUNCT cana-1902 179 13 πœ‡2 πœ‡2 NOUN cana-1902 179 14 = = SYM cana-1902 179 15 0 0 NUM cana-1902 179 16 , , PUNCT cana-1902 179 17 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ PROPN cana-1902 179 18 𝛽 𝛽 NOUN cana-1902 179 19 = = PUNCT cana-1902 179 20 πœ‡ πœ‡ ADP cana-1902 179 21 are be AUX cana-1902 179 22 taken take VERB cana-1902 179 23 . . PUNCT cana-1902 180 1 communications communication NOUN cana-1902 180 2 on on ADP cana-1902 180 3 applied apply VERB cana-1902 180 4 nonlinear nonlinear ADJ cana-1902 180 5 analysis analysis NOUN cana-1902 180 6 issn issn NOUN cana-1902 180 7 : : PUNCT cana-1902 180 8 1074 1074 NUM cana-1902 180 9 - - PUNCT cana-1902 180 10 133x 133x NUM cana-1902 180 11 vol vol NOUN cana-1902 180 12 32 32 NUM cana-1902 180 13 no no NOUN cana-1902 180 14 . . NOUN cana-1902 180 15 3 3 NUM cana-1902 180 16 ( ( PUNCT cana-1902 180 17 2025 2025 NUM cana-1902 180 18 ) ) PUNCT cana-1902 180 19 8 8 NUM cana-1902 180 20 https://internationalpubls.com https://internationalpubls.com X cana-1902 180 21 5 5 NUM cana-1902 180 22 . . NOUN cana-1902 180 23 numerical numerical ADJ cana-1902 180 24 examples example NOUN cana-1902 180 25 calculation calculation NOUN cana-1902 180 26 for for ADP cana-1902 180 27 the the DET cana-1902 180 28 system system NOUN cana-1902 180 29 for for ADP cana-1902 180 30 t=0.6 t=0.6 NOUN cana-1902 180 31 , , PUNCT cana-1902 180 32 u=0.4 u=0.4 NOUN cana-1902 180 33 , , PUNCT cana-1902 180 34 πœ‡1 πœ‡1 NOUN cana-1902 180 35 = = SYM cana-1902 180 36 7 7 NUM cana-1902 180 37 , , PUNCT cana-1902 180 38 πœ‡2 πœ‡2 NOUN cana-1902 180 39 = = SYM cana-1902 180 40 8 8 NUM cana-1902 180 41 , , PUNCT cana-1902 180 42 πœ‡3 πœ‡3 NOUN cana-1902 180 43 = = NOUN cana-1902 180 44 9 9 NUM cana-1902 180 45 , , PUNCT cana-1902 180 46 πœ† πœ† NOUN cana-1902 180 47 = = SYM cana-1902 180 48 1,2,3,4,5,6,7,8,9,10 1,2,3,4,5,6,7,8,9,10 NUM cana-1902 180 49 , , PUNCT cana-1902 180 50 𝛾 𝛾 PROPN cana-1902 180 51 = = SYM cana-1902 180 52 1,3,5,7,9 1,3,5,7,9 NUM cana-1902 180 53 total total ADJ cana-1902 180 54 number number NOUN cana-1902 180 55 of of ADP cana-1902 180 56 customers customer NOUN cana-1902 180 57 in in ADP cana-1902 180 58 all all DET cana-1902 180 59 the the DET cana-1902 180 60 three three NUM cana-1902 180 61 queues queue NOUN cana-1902 180 62 : : PUNCT cana-1902 180 63 table table NOUN cana-1902 180 64 i i PRON cana-1902 180 65 shows show VERB cana-1902 180 66 the the DET cana-1902 180 67 number number NOUN cana-1902 180 68 of of ADP cana-1902 180 69 customers customer NOUN cana-1902 180 70 in in ADP cana-1902 180 71 each each PRON cana-1902 180 72 of of ADP cana-1902 180 73 the the DET cana-1902 180 74 three three NUM cana-1902 180 75 nodes node NOUN cana-1902 180 76 for for ADP cana-1902 180 77 arrival arrival NOUN cana-1902 180 78 rates rate NOUN cana-1902 180 79 Ξ» Ξ» PROPN cana-1902 180 80 , , PUNCT cana-1902 180 81 which which PRON cana-1902 180 82 ranges range VERB cana-1902 180 83 from from ADP cana-1902 180 84 1 1 NUM cana-1902 180 85 to to ADP cana-1902 180 86 10 10 NUM cana-1902 180 87 and and CCONJ cana-1902 180 88 for for ADP cana-1902 180 89 the the DET cana-1902 180 90 disaster disaster NOUN cana-1902 180 91 impact impact NOUN cana-1902 180 92 Ξ³ Ξ³ NOUN cana-1902 180 93 , , PUNCT cana-1902 180 94 varying vary VERB cana-1902 180 95 from from ADP cana-1902 180 96 1 1 NUM cana-1902 180 97 to to ADP cana-1902 180 98 9 9 NUM cana-1902 180 99 . . PUNCT cana-1902 180 100 table table NOUN cana-1902 181 1 i i NOUN cana-1902 181 2 1 1 NUM cana-1902 181 3 3 3 NUM cana-1902 181 4 5 5 NUM cana-1902 181 5 7 7 NUM cana-1902 181 6 9 9 NUM cana-1902 181 7 1 1 NUM cana-1902 181 8 0.007173 0.007173 NUM cana-1902 181 9 0.007071 0.007071 NUM cana-1902 181 10 0.006972 0.006972 NUM cana-1902 181 11 0.006875 0.006875 NUM cana-1902 181 12 0.006781 0.006781 NUM cana-1902 181 13 2 2 NUM cana-1902 181 14 0.014449 0.014449 NUM cana-1902 181 15 0.014241 0.014241 NUM cana-1902 181 16 0.014038 0.014038 NUM cana-1902 181 17 0.013841 0.013841 NUM cana-1902 181 18 0.01365 0.01365 NUM cana-1902 181 19 3 3 NUM cana-1902 181 20 0.021831 0.021831 NUM cana-1902 181 21 0.021511 0.021511 NUM cana-1902 181 22 0.021201 0.021201 NUM cana-1902 181 23 0.020899 0.020899 NUM cana-1902 181 24 0.020606 0.020606 NUM cana-1902 181 25 4 4 NUM cana-1902 181 26 0.029319 0.029319 NUM cana-1902 181 27 0.028884 0.028884 NUM cana-1902 181 28 0.028461 0.028461 NUM cana-1902 181 29 0.028051 0.028051 NUM cana-1902 181 30 0.027653 0.027653 NUM cana-1902 181 31 5 5 NUM cana-1902 181 32 0.036918 0.036918 NUM cana-1902 181 33 0.036361 0.036361 NUM cana-1902 181 34 0.035822 0.035822 NUM cana-1902 181 35 0.035299 0.035299 NUM cana-1902 181 36 0.034792 0.034792 NUM cana-1902 181 37 6 6 NUM cana-1902 181 38 0.044628 0.044628 NUM cana-1902 181 39 0.043946 0.043946 NUM cana-1902 181 40 0.043285 0.043285 NUM cana-1902 181 41 0.042644 0.042644 NUM cana-1902 181 42 0.042023 0.042023 NUM cana-1902 181 43 7 7 NUM cana-1902 181 44 0.052453 0.052453 NUM cana-1902 181 45 0.05164 0.05164 NUM cana-1902 181 46 0.050852 0.050852 NUM cana-1902 181 47 0.050089 0.050089 NUM cana-1902 181 48 0.04935 0.04935 NUM cana-1902 181 49 8 8 NUM cana-1902 181 50 0.060395 0.060395 NUM cana-1902 181 51 0.059445 0.059445 NUM cana-1902 181 52 0.058525 0.058525 NUM cana-1902 181 53 0.057635 0.057635 NUM cana-1902 181 54 0.056773 0.056773 NUM cana-1902 181 55 9 9 NUM cana-1902 181 56 0.068457 0.068457 NUM cana-1902 181 57 0.067364 0.067364 NUM cana-1902 181 58 0.066307 0.066307 NUM cana-1902 181 59 0.065285 0.065285 NUM cana-1902 181 60 0.064296 0.064296 NUM cana-1902 181 61 10 10 NUM cana-1902 181 62 0.076642 0.076642 NUM cana-1902 181 63 0.0754 0.0754 NUM cana-1902 181 64 0.0742 0.0742 NUM cana-1902 181 65 0.07304 0.07304 NUM cana-1902 181 66 0.071918 0.071918 NUM cana-1902 181 67 fig fig NOUN cana-1902 181 68 . . PUNCT cana-1902 181 69 2 2 NUM cana-1902 182 1 the the DET cana-1902 182 2 number number NOUN cana-1902 182 3 of of ADP cana-1902 182 4 customers customer NOUN cana-1902 182 5 in in ADP cana-1902 182 6 the the DET cana-1902 182 7 three three NUM cana-1902 182 8 queues queue NOUN cana-1902 182 9 varies vary VERB cana-1902 182 10 depending depend VERB cana-1902 182 11 on on ADP cana-1902 182 12 the the DET cana-1902 182 13 arrival arrival NOUN cana-1902 182 14 rate rate NOUN cana-1902 182 15 under under ADP cana-1902 182 16 calamity calamity NOUN cana-1902 182 17 impact impact NOUN cana-1902 182 18 it it PRON cana-1902 182 19 is be AUX cana-1902 182 20 evident evident ADJ cana-1902 182 21 from from ADP cana-1902 182 22 fig fig NOUN cana-1902 182 23 . . PUNCT cana-1902 183 1 2 2 NUM cana-1902 184 1 that that SCONJ cana-1902 184 2 when when SCONJ cana-1902 184 3 the the DET cana-1902 184 4 arrival arrival NOUN cana-1902 184 5 rate rate NOUN cana-1902 184 6 rises rise NOUN cana-1902 184 7 , , PUNCT cana-1902 184 8 there there PRON cana-1902 184 9 are be VERB cana-1902 184 10 more more ADJ cana-1902 184 11 customers customer NOUN cana-1902 184 12 in in ADP cana-1902 184 13 the the DET cana-1902 184 14 three three NUM cana-1902 184 15 queues queue NOUN cana-1902 184 16 , , PUNCT cana-1902 184 17 and and CCONJ cana-1902 184 18 when when SCONJ cana-1902 184 19 Ξ³ Ξ³ X cana-1902 184 20 value value NOUN cana-1902 184 21 rises rise VERB cana-1902 184 22 , , PUNCT cana-1902 184 23 there there PRON cana-1902 184 24 are be VERB cana-1902 184 25 less less ADJ cana-1902 184 26 customers customer NOUN cana-1902 184 27 in in ADP cana-1902 184 28 three three NUM cana-1902 184 29 queues queue NOUN cana-1902 184 30 . . PUNCT cana-1902 185 1 customer customer NOUN cana-1902 185 2 's 's PART cana-1902 185 3 waiting waiting NOUN cana-1902 185 4 time time NOUN cana-1902 185 5 in in ADP cana-1902 185 6 the the DET cana-1902 185 7 three three NUM cana-1902 185 8 queues queue NOUN cana-1902 185 9 : : PUNCT cana-1902 185 10 in in ADP cana-1902 185 11 table table PROPN cana-1902 185 12 ii ii PROPN cana-1902 185 13 , , PUNCT cana-1902 185 14 the the DET cana-1902 185 15 customer customer NOUN cana-1902 185 16 's 's PART cana-1902 185 17 waiting waiting NOUN cana-1902 185 18 time time NOUN cana-1902 185 19 in in ADP cana-1902 185 20 the the DET cana-1902 185 21 three three NUM cana-1902 185 22 queues queue NOUN cana-1902 185 23 is be AUX cana-1902 185 24 determined determine VERB cana-1902 185 25 for for ADP cana-1902 185 26 arrival arrival NOUN cana-1902 185 27 rates rate NOUN cana-1902 185 28 Ξ» Ξ» VERB cana-1902 185 29 ranging range VERB cana-1902 185 30 from from ADP cana-1902 185 31 1 1 NUM cana-1902 185 32 to to ADP cana-1902 185 33 10 10 NUM cana-1902 185 34 , , PUNCT cana-1902 185 35 and and CCONJ cana-1902 185 36 for for ADP cana-1902 185 37 Ξ³ Ξ³ X cana-1902 185 38 ( ( PUNCT cana-1902 185 39 catastrophe catastrophe NOUN cana-1902 185 40 effect effect NOUN cana-1902 185 41 ) ) PUNCT cana-1902 185 42 ranging range VERB cana-1902 185 43 from from ADP cana-1902 185 44 1 1 NUM cana-1902 185 45 to to ADP cana-1902 185 46 9 9 NUM cana-1902 185 47 . . PUNCT cana-1902 185 48 table table NOUN cana-1902 185 49 ii ii PROPN cana-1902 185 50 1 1 NUM cana-1902 185 51 3 3 NUM cana-1902 185 52 5 5 NUM cana-1902 185 53 7 7 NUM cana-1902 185 54 9 9 NUM cana-1902 185 55 1 1 NUM cana-1902 185 56 0.007173 0.007173 NUM cana-1902 185 57 0.007071 0.007071 NUM cana-1902 185 58 0.006972 0.006972 NUM cana-1902 186 1 0.006875 0.006875 NUM cana-1902 186 2 0.006781 0.006781 NUM cana-1902 186 3 2 2 NUM cana-1902 186 4 0.007225 0.007225 NUM cana-1902 186 5 0.00712 0.00712 NUM cana-1902 186 6 0.007019 0.007019 NUM cana-1902 186 7 0.006921 0.006921 NUM cana-1902 186 8 0.006825 0.006825 NUM cana-1902 186 9 3 3 NUM cana-1902 186 10 0.007277 0.007277 NUM cana-1902 186 11 0.00717 0.00717 NUM cana-1902 186 12 0.007067 0.007067 NUM cana-1902 186 13 0.006966 0.006966 NUM cana-1902 186 14 0.006869 0.006869 NUM cana-1902 186 15 4 4 NUM cana-1902 186 16 0.00733 0.00733 NUM cana-1902 186 17 0.007221 0.007221 NUM cana-1902 186 18 0.007115 0.007115 NUM cana-1902 187 1 0.007013 0.007013 NUM cana-1902 187 2 0.006913 0.006913 NUM cana-1902 187 3 communications communication NOUN cana-1902 187 4 on on ADP cana-1902 187 5 applied apply VERB cana-1902 187 6 nonlinear nonlinear ADJ cana-1902 187 7 analysis analysis NOUN cana-1902 187 8 issn issn NOUN cana-1902 187 9 : : PUNCT cana-1902 187 10 1074 1074 NUM cana-1902 187 11 - - PUNCT cana-1902 187 12 133x 133x NUM cana-1902 187 13 vol vol NOUN cana-1902 187 14 32 32 NUM cana-1902 187 15 no no NOUN cana-1902 187 16 . . NOUN cana-1902 187 17 3 3 NUM cana-1902 187 18 ( ( PUNCT cana-1902 187 19 2025 2025 NUM cana-1902 187 20 ) ) PUNCT cana-1902 188 1 9 9 NUM cana-1902 188 2 https://internationalpubls.com https://internationalpubls.com X cana-1902 188 3 5 5 NUM cana-1902 188 4 0.007384 0.007384 NUM cana-1902 188 5 0.007272 0.007272 NUM cana-1902 188 6 0.007164 0.007164 NUM cana-1902 188 7 0.00706 0.00706 NUM cana-1902 188 8 0.006958 0.006958 NUM cana-1902 188 9 6 6 NUM cana-1902 188 10 0.007438 0.007438 NUM cana-1902 188 11 0.007324 0.007324 NUM cana-1902 188 12 0.007214 0.007214 NUM cana-1902 188 13 0.007107 0.007107 NUM cana-1902 188 14 0.007004 0.007004 NUM cana-1902 188 15 7 7 NUM cana-1902 188 16 0.007493 0.007493 NUM cana-1902 188 17 0.007377 0.007377 NUM cana-1902 188 18 0.007265 0.007265 NUM cana-1902 188 19 0.007156 0.007156 NUM cana-1902 188 20 0.00705 0.00705 NUM cana-1902 188 21 8 8 NUM cana-1902 188 22 0.007549 0.007549 NUM cana-1902 188 23 0.007431 0.007431 NUM cana-1902 188 24 0.007316 0.007316 NUM cana-1902 188 25 0.007204 0.007204 NUM cana-1902 188 26 0.007097 0.007097 NUM cana-1902 188 27 9 9 NUM cana-1902 188 28 0.007606 0.007606 NUM cana-1902 188 29 0.007485 0.007485 NUM cana-1902 188 30 0.007367 0.007367 NUM cana-1902 188 31 0.007254 0.007254 NUM cana-1902 188 32 0.007144 0.007144 NUM cana-1902 188 33 10 10 NUM cana-1902 188 34 0.007664 0.007664 NUM cana-1902 188 35 0.00754 0.00754 NUM cana-1902 188 36 0.00742 0.00742 NUM cana-1902 188 37 0.007304 0.007304 NUM cana-1902 188 38 0.007192 0.007192 NUM cana-1902 188 39 fig fig NOUN cana-1902 188 40 3 3 NUM cana-1902 188 41 . . PUNCT cana-1902 189 1 for for ADP cana-1902 189 2 different different ADJ cana-1902 189 3 arrival arrival NOUN cana-1902 189 4 rate rate NOUN cana-1902 189 5 the the DET cana-1902 189 6 waiting waiting NOUN cana-1902 189 7 time time NOUN cana-1902 189 8 of of ADP cana-1902 189 9 a a DET cana-1902 189 10 customer customer NOUN cana-1902 189 11 in in ADP cana-1902 189 12 all all DET cana-1902 189 13 the the DET cana-1902 189 14 three three NUM cana-1902 189 15 queues queue NOUN cana-1902 189 16 under under ADP cana-1902 189 17 catastrophe catastrophe NOUN cana-1902 189 18 effect effect NOUN cana-1902 189 19 it it PRON cana-1902 189 20 is be AUX cana-1902 189 21 evident evident ADJ cana-1902 189 22 from from ADP cana-1902 189 23 fig fig NOUN cana-1902 189 24 . . PUNCT cana-1902 190 1 3 3 NUM cana-1902 190 2 that that SCONJ cana-1902 190 3 when when SCONJ cana-1902 190 4 the the DET cana-1902 190 5 arrival arrival NOUN cana-1902 190 6 rate rate NOUN cana-1902 190 7 rises rise NOUN cana-1902 190 8 , , PUNCT cana-1902 190 9 customer customer NOUN cana-1902 190 10 waiting wait VERB cana-1902 190 11 times time NOUN cana-1902 190 12 in in ADP cana-1902 190 13 all all DET cana-1902 190 14 three three NUM cana-1902 190 15 queues queue NOUN cana-1902 190 16 increase increase NOUN cana-1902 190 17 , , PUNCT cana-1902 190 18 and and CCONJ cana-1902 190 19 when when SCONJ cana-1902 190 20 Ξ³ Ξ³ X cana-1902 190 21 value value NOUN cana-1902 190 22 rises rise VERB cana-1902 190 23 , , PUNCT cana-1902 190 24 customers customer NOUN cana-1902 190 25 are be AUX cana-1902 190 26 waiting wait VERB cana-1902 190 27 time time NOUN cana-1902 190 28 in in ADP cana-1902 190 29 all all DET cana-1902 190 30 three three NUM cana-1902 190 31 queues queue NOUN cana-1902 190 32 decrease decrease NOUN cana-1902 190 33 . . PUNCT cana-1902 191 1 for for ADP cana-1902 191 2 t t NOUN cana-1902 191 3 = = SYM cana-1902 191 4 0.6 0.6 NUM cana-1902 191 5 , , PUNCT cana-1902 191 6 u u NOUN cana-1902 191 7 = = NOUN cana-1902 191 8 0.4 0.4 NUM cana-1902 191 9 , , PUNCT cana-1902 191 10 πœ‡1 πœ‡1 NOUN cana-1902 191 11 = = SYM cana-1902 191 12 5,5.2,5.4,5.6,5.8,6.0,6.2,6.4,6.6,6.8 5,5.2,5.4,5.6,5.8,6.0,6.2,6.4,6.6,6.8 PROPN cana-1902 191 13 , , PUNCT cana-1902 191 14 πœ‡2 πœ‡2 NOUN cana-1902 191 15 = = NOUN cana-1902 191 16 7 7 NUM cana-1902 191 17 , , PUNCT cana-1902 191 18 πœ‡3 πœ‡3 NOUN cana-1902 191 19 = = NOUN cana-1902 191 20 8 8 NUM cana-1902 191 21 , , PUNCT cana-1902 191 22 πœ† πœ† NOUN cana-1902 191 23 = = SYM cana-1902 191 24 6 6 NUM cana-1902 191 25 , , PUNCT cana-1902 191 26 𝛾 𝛾 NOUN cana-1902 191 27 = = SYM cana-1902 191 28 1,3,5,7,9 1,3,5,7,9 NUM cana-1902 191 29 number number NOUN cana-1902 191 30 of of ADP cana-1902 191 31 customers customer NOUN cana-1902 191 32 in in ADP cana-1902 191 33 the the DET cana-1902 191 34 system system NOUN cana-1902 191 35 : : PUNCT cana-1902 191 36 table table NOUN cana-1902 191 37 iii iii NOUN cana-1902 191 38 shows show VERB cana-1902 191 39 the the DET cana-1902 191 40 total total ADJ cana-1902 191 41 customers customer NOUN cana-1902 191 42 in in ADP cana-1902 191 43 the the DET cana-1902 191 44 system system NOUN cana-1902 191 45 with with ADP cana-1902 191 46 service service NOUN cana-1902 191 47 rate rate NOUN cana-1902 191 48 πœ‡1 πœ‡1 PROPN cana-1902 191 49 varying vary VERB cana-1902 191 50 from from ADP cana-1902 191 51 5 5 NUM cana-1902 191 52 to to ADP cana-1902 191 53 6.8 6.8 NUM cana-1902 191 54 and and CCONJ cana-1902 191 55 catastrophe catastrophe NOUN cana-1902 191 56 effect effect NOUN cana-1902 191 57 Ξ³ Ξ³ NOUN cana-1902 191 58 ranging range VERB cana-1902 191 59 from from ADP cana-1902 191 60 1 1 NUM cana-1902 191 61 to to ADP cana-1902 191 62 9 9 NUM cana-1902 191 63 . . PUNCT cana-1902 192 1 table table NOUN cana-1902 192 2 iii iii NOUN cana-1902 192 3 1 1 NUM cana-1902 192 4 3 3 NUM cana-1902 192 5 5 5 NUM cana-1902 192 6 7 7 NUM cana-1902 192 7 9 9 NUM cana-1902 192 8 5 5 NUM cana-1902 192 9 0.952979 0.952979 NUM cana-1902 192 10 0.952013 0.952013 NUM cana-1902 192 11 0.951083 0.951083 NUM cana-1902 192 12 0.950188 0.950188 NUM cana-1902 192 13 0.949324 0.949324 NUM cana-1902 192 14 5.2 5.2 NUM cana-1902 192 15 0.943715 0.943715 NUM cana-1902 192 16 0.942762 0.942762 NUM cana-1902 192 17 0.941845 0.941845 NUM cana-1902 192 18 0.940961 0.940961 NUM cana-1902 192 19 0.940108 0.940108 NUM cana-1902 192 20 5.4 5.4 NUM cana-1902 192 21 0.93463 0.93463 NUM cana-1902 192 22 0.93369 0.93369 NUM cana-1902 192 23 0.932785 0.932785 NUM cana-1902 192 24 0.931912 0.931912 NUM cana-1902 192 25 0.931071 0.931071 NUM cana-1902 192 26 5.6 5.6 NUM cana-1902 192 27 0.92572 0.92572 NUM cana-1902 192 28 0.924792 0.924792 NUM cana-1902 192 29 0.923899 0.923899 NUM cana-1902 192 30 0.923037 0.923037 NUM cana-1902 192 31 0.922206 0.922206 NUM cana-1902 192 32 5.8 5.8 NUM cana-1902 192 33 0.916979 0.916979 NUM cana-1902 192 34 0.916064 0.916064 NUM cana-1902 192 35 0.915182 0.915182 NUM cana-1902 192 36 0.914331 0.914331 NUM cana-1902 192 37 0.91351 0.91351 NUM cana-1902 192 38 6 6 NUM cana-1902 192 39 0.908402 0.908402 NUM cana-1902 192 40 0.907499 0.907499 NUM cana-1902 192 41 0.906628 0.906628 NUM cana-1902 192 42 0.905789 0.905789 NUM cana-1902 192 43 0.904978 0.904978 NUM cana-1902 192 44 6.2 6.2 NUM cana-1902 192 45 0.899986 0.899986 NUM cana-1902 193 1 0.899094 0.899094 NUM cana-1902 193 2 0.898235 0.898235 NUM cana-1902 193 3 0.897405 0.897405 NUM cana-1902 193 4 0.896605 0.896605 NUM cana-1902 193 5 6.4 6.4 NUM cana-1902 193 6 0.891724 0.891724 NUM cana-1902 193 7 0.890844 0.890844 NUM cana-1902 193 8 0.889996 0.889996 NUM cana-1902 193 9 0.889177 0.889177 NUM cana-1902 193 10 0.888386 0.888386 NUM cana-1902 193 11 6.6 6.6 NUM cana-1902 193 12 0.883614 0.883614 NUM cana-1902 193 13 0.882745 0.882745 NUM cana-1902 193 14 0.881907 0.881907 NUM cana-1902 193 15 0.881099 0.881099 NUM cana-1902 193 16 0.880317 0.880317 NUM cana-1902 193 17 6.8 6.8 NUM cana-1902 193 18 0.875651 0.875651 NUM cana-1902 193 19 0.874793 0.874793 NUM cana-1902 193 20 0.873966 0.873966 NUM cana-1902 193 21 0.873167 0.873167 NUM cana-1902 193 22 0.872395 0.872395 NUM cana-1902 193 23 communications communication NOUN cana-1902 193 24 on on ADP cana-1902 193 25 applied apply VERB cana-1902 193 26 nonlinear nonlinear ADJ cana-1902 193 27 analysis analysis NOUN cana-1902 193 28 issn issn NOUN cana-1902 193 29 : : PUNCT cana-1902 193 30 1074 1074 NUM cana-1902 193 31 - - PUNCT cana-1902 193 32 133x 133x NUM cana-1902 193 33 vol vol NOUN cana-1902 193 34 32 32 NUM cana-1902 193 35 no no NOUN cana-1902 193 36 . . NOUN cana-1902 193 37 3 3 NUM cana-1902 193 38 ( ( PUNCT cana-1902 193 39 2025 2025 NUM cana-1902 193 40 ) ) PUNCT cana-1902 193 41 10 10 NUM cana-1902 193 42 https://internationalpubls.com https://internationalpubls.com X cana-1902 193 43 fig fig NOUN cana-1902 193 44 4 4 NUM cana-1902 193 45 . . PUNCT cana-1902 194 1 for for ADP cana-1902 194 2 different different ADJ cana-1902 194 3 service service NOUN cana-1902 194 4 rate rate NOUN cana-1902 194 5 number number NOUN cana-1902 194 6 of of ADP cana-1902 194 7 customers customer NOUN cana-1902 194 8 in in ADP cana-1902 194 9 the the DET cana-1902 194 10 system system NOUN cana-1902 194 11 under under ADP cana-1902 194 12 catastrophe catastrophe NOUN cana-1902 194 13 effect effect NOUN cana-1902 194 14 it it PRON cana-1902 194 15 is be AUX cana-1902 194 16 evident evident ADJ cana-1902 194 17 from from ADP cana-1902 194 18 figure figure NOUN cana-1902 194 19 4 4 NUM cana-1902 194 20 that that SCONJ cana-1902 194 21 when when SCONJ cana-1902 194 22 the the DET cana-1902 194 23 service service NOUN cana-1902 194 24 rate rate NOUN cana-1902 194 25 rises rise NOUN cana-1902 194 26 , , PUNCT cana-1902 194 27 the the DET cana-1902 194 28 number number NOUN cana-1902 194 29 of of ADP cana-1902 194 30 customers customer NOUN cana-1902 194 31 in in ADP cana-1902 194 32 the the DET cana-1902 194 33 system system NOUN cana-1902 194 34 falls fall VERB cana-1902 194 35 for for ADP cana-1902 194 36 different different ADJ cana-1902 194 37 values value NOUN cana-1902 194 38 of of ADP cana-1902 194 39 Ξ³ Ξ³ PROPN cana-1902 194 40 . . PUNCT cana-1902 194 41 customer customer PROPN cana-1902 194 42 's 's PART cana-1902 194 43 waiting waiting NOUN cana-1902 194 44 time time NOUN cana-1902 194 45 within within ADP cana-1902 194 46 the the DET cana-1902 194 47 system system NOUN cana-1902 194 48 : : PUNCT cana-1902 194 49 table table NOUN cana-1902 194 50 iv iv NUM cana-1902 194 51 determines determine VERB cana-1902 194 52 the the DET cana-1902 194 53 customer customer NOUN cana-1902 194 54 's 's PART cana-1902 194 55 waiting waiting NOUN cana-1902 194 56 time time NOUN cana-1902 194 57 based base VERB cana-1902 194 58 on on ADP cana-1902 194 59 two two NUM cana-1902 194 60 factors factor NOUN cana-1902 194 61 : : PUNCT cana-1902 194 62 the the DET cana-1902 194 63 service service NOUN cana-1902 194 64 rate rate NOUN cana-1902 194 65 ( ( PUNCT cana-1902 194 66 πœ‡1 πœ‡1 NOUN cana-1902 194 67 ) ) PUNCT cana-1902 194 68 which which PRON cana-1902 194 69 ranges range VERB cana-1902 194 70 from from ADP cana-1902 194 71 5 5 NUM cana-1902 194 72 to to ADP cana-1902 194 73 6.8 6.8 NUM cana-1902 194 74 and and CCONJ cana-1902 194 75 the the DET cana-1902 194 76 catastrophe catastrophe NOUN cana-1902 194 77 effect effect NOUN cana-1902 194 78 ( ( PUNCT cana-1902 194 79 Ξ³ Ξ³ X cana-1902 194 80 ) ) PUNCT cana-1902 194 81 which which PRON cana-1902 194 82 ranges range VERB cana-1902 194 83 from from ADP cana-1902 194 84 1 1 NUM cana-1902 194 85 to to ADP cana-1902 194 86 9 9 NUM cana-1902 194 87 . . PUNCT cana-1902 194 88 table table NOUN cana-1902 194 89 iv iv NUM cana-1902 194 90 1 1 NUM cana-1902 194 91 3 3 NUM cana-1902 194 92 5 5 NUM cana-1902 194 93 7 7 NUM cana-1902 194 94 9 9 NUM cana-1902 194 95 5 5 NUM cana-1902 194 96 0.15883 0.15883 NUM cana-1902 194 97 0.158669 0.158669 NUM cana-1902 194 98 0.158514 0.158514 NUM cana-1902 194 99 0.158365 0.158365 NUM cana-1902 194 100 0.158221 0.158221 NUM cana-1902 194 101 5.2 5.2 NUM cana-1902 194 102 0.157286 0.157286 NUM cana-1902 194 103 0.157127 0.157127 NUM cana-1902 194 104 0.156974 0.156974 NUM cana-1902 194 105 0.156827 0.156827 NUM cana-1902 194 106 0.156685 0.156685 NUM cana-1902 194 107 5.4 5.4 NUM cana-1902 194 108 0.155772 0.155772 NUM cana-1902 194 109 0.155615 0.155615 NUM cana-1902 194 110 0.155464 0.155464 NUM cana-1902 194 111 0.155319 0.155319 NUM cana-1902 194 112 0.155178 0.155178 NUM cana-1902 194 113 5.6 5.6 NUM cana-1902 194 114 0.154287 0.154287 NUM cana-1902 194 115 0.154132 0.154132 NUM cana-1902 194 116 0.153983 0.153983 NUM cana-1902 194 117 0.15384 0.15384 NUM cana-1902 194 118 0.153701 0.153701 NUM cana-1902 194 119 5.8 5.8 NUM cana-1902 194 120 0.15283 0.15283 NUM cana-1902 194 121 0.152677 0.152677 NUM cana-1902 195 1 0.15253 0.15253 NUM cana-1902 195 2 0.152389 0.152389 NUM cana-1902 195 3 0.152252 0.152252 NUM cana-1902 195 4 6 6 NUM cana-1902 195 5 0.1514 0.1514 NUM cana-1902 195 6 0.15125 0.15125 NUM cana-1902 195 7 0.151105 0.151105 NUM cana-1902 195 8 0.150965 0.150965 NUM cana-1902 195 9 0.15083 0.15083 NUM cana-1902 195 10 6.2 6.2 NUM cana-1902 195 11 0.149998 0.149998 NUM cana-1902 195 12 0.149849 0.149849 NUM cana-1902 195 13 0.149706 0.149706 NUM cana-1902 195 14 0.149568 0.149568 NUM cana-1902 195 15 0.149434 0.149434 NUM cana-1902 195 16 6.4 6.4 NUM cana-1902 195 17 0.148621 0.148621 NUM cana-1902 195 18 0.148474 0.148474 NUM cana-1902 195 19 0.148333 0.148333 NUM cana-1902 195 20 0.148196 0.148196 NUM cana-1902 195 21 0.148064 0.148064 NUM cana-1902 195 22 6.6 6.6 NUM cana-1902 195 23 0.147269 0.147269 NUM cana-1902 195 24 0.147124 0.147124 NUM cana-1902 195 25 0.146985 0.146985 NUM cana-1902 195 26 0.14685 0.14685 NUM cana-1902 195 27 0.14672 0.14672 NUM cana-1902 195 28 6.8 6.8 NUM cana-1902 195 29 0.145942 0.145942 NUM cana-1902 195 30 0.145799 0.145799 NUM cana-1902 195 31 0.145661 0.145661 NUM cana-1902 195 32 0.145528 0.145528 NUM cana-1902 195 33 0.145399 0.145399 NUM cana-1902 195 34 fig fig NOUN cana-1902 195 35 5 5 NUM cana-1902 195 36 . . PUNCT cana-1902 195 37 for for ADP cana-1902 195 38 different different ADJ cana-1902 195 39 service service NOUN cana-1902 195 40 rate rate NOUN cana-1902 195 41 the the DET cana-1902 195 42 waiting waiting NOUN cana-1902 195 43 time time NOUN cana-1902 195 44 of of ADP cana-1902 195 45 the the DET cana-1902 195 46 customer customer NOUN cana-1902 195 47 in in ADP cana-1902 195 48 the the DET cana-1902 195 49 system system NOUN cana-1902 195 50 under under ADP cana-1902 195 51 catastrophe catastrophe NOUN cana-1902 195 52 effect effect NOUN cana-1902 195 53 it it PRON cana-1902 195 54 is be AUX cana-1902 195 55 evident evident ADJ cana-1902 195 56 from from ADP cana-1902 195 57 fig fig NOUN cana-1902 195 58 . . PUNCT cana-1902 196 1 5 5 NUM cana-1902 196 2 that that SCONJ cana-1902 196 3 when when SCONJ cana-1902 196 4 the the DET cana-1902 196 5 service service NOUN cana-1902 196 6 rate rate NOUN cana-1902 196 7 rises rise NOUN cana-1902 196 8 , , PUNCT cana-1902 196 9 customer customer NOUN cana-1902 196 10 waiting wait VERB cana-1902 196 11 times time NOUN cana-1902 196 12 in in ADP cana-1902 196 13 the the DET cana-1902 196 14 system system NOUN cana-1902 196 15 get get VERB cana-1902 196 16 shorter short ADJ cana-1902 196 17 for for ADP cana-1902 196 18 different different ADJ cana-1902 196 19 values value NOUN cana-1902 196 20 of of ADP cana-1902 196 21 Ξ³ Ξ³ PROPN cana-1902 196 22 . . PROPN cana-1902 196 23 communications communication NOUN cana-1902 196 24 on on ADP cana-1902 196 25 applied apply VERB cana-1902 196 26 nonlinear nonlinear ADJ cana-1902 196 27 analysis analysis NOUN cana-1902 196 28 issn issn NOUN cana-1902 196 29 : : PUNCT cana-1902 196 30 1074 1074 NUM cana-1902 196 31 - - PUNCT cana-1902 196 32 133x 133x NUM cana-1902 196 33 vol vol NOUN cana-1902 196 34 32 32 NUM cana-1902 196 35 no no NOUN cana-1902 196 36 . . NOUN cana-1902 196 37 3 3 NUM cana-1902 196 38 ( ( PUNCT cana-1902 196 39 2025 2025 NUM cana-1902 196 40 ) ) PUNCT cana-1902 196 41 11 11 NUM cana-1902 196 42 https://internationalpubls.com https://internationalpubls.com X cana-1902 196 43 6 6 NUM cana-1902 196 44 . . PUNCT cana-1902 196 45 conclusion conclusion NOUN cana-1902 196 46 here here ADV cana-1902 196 47 , , PUNCT cana-1902 196 48 we we PRON cana-1902 196 49 examine examine VERB cana-1902 196 50 the the DET cana-1902 196 51 feedback feedback NOUN cana-1902 196 52 retrial retrial NOUN cana-1902 196 53 queueing queue VERB cana-1902 196 54 network network NOUN cana-1902 196 55 's 's PART cana-1902 196 56 steady steady ADJ cana-1902 196 57 state state NOUN cana-1902 196 58 probability probability NOUN cana-1902 196 59 in in ADP cana-1902 196 60 the the DET cana-1902 196 61 event event NOUN cana-1902 196 62 of of ADP cana-1902 196 63 a a DET cana-1902 196 64 catastrophe catastrophe NOUN cana-1902 196 65 and and CCONJ cana-1902 196 66 calculate𝑄0(𝑑 calculate𝑄0(𝑑 NOUN cana-1902 196 67 ) ) PUNCT cana-1902 196 68 or or CCONJ cana-1902 196 69 the the DET cana-1902 196 70 number number NOUN cana-1902 196 71 of of ADP cana-1902 196 72 customers customer NOUN cana-1902 196 73 in in ADP cana-1902 196 74 the the DET cana-1902 196 75 system system NOUN cana-1902 196 76 at at ADP cana-1902 196 77 time time NOUN cana-1902 196 78 t t PROPN cana-1902 196 79 , , PUNCT cana-1902 196 80 and and CCONJ cana-1902 196 81 𝑄𝑛(𝑑 𝑄𝑛(𝑑 NOUN cana-1902 196 82 ) ) PUNCT cana-1902 196 83 . . PUNCT cana-1902 197 1 we we PRON cana-1902 197 2 also also ADV cana-1902 197 3 determineπΏπ‘ž determineπΏπ‘ž PROPN cana-1902 197 4 , , PUNCT cana-1902 197 5 π‘Šπ‘ž π‘Šπ‘ž PROPN cana-1902 197 6 , , PUNCT cana-1902 197 7 𝐿𝑠 𝐿𝑠 PROPN cana-1902 197 8 , , PUNCT cana-1902 197 9 and and CCONJ cana-1902 197 10 π‘Šπ‘ for π‘Šπ‘ for ADP cana-1902 197 11 each each PRON cana-1902 197 12 of of ADP cana-1902 197 13 the the DET cana-1902 197 14 three three NUM cana-1902 197 15 nodes node NOUN cana-1902 197 16 . . PUNCT cana-1902 198 1 the the DET cana-1902 198 2 numerical numerical ADJ cana-1902 198 3 example example NOUN cana-1902 198 4 displays display VERB cana-1902 198 5 the the DET cana-1902 198 6 number number NOUN cana-1902 198 7 of of ADP cana-1902 198 8 customers customer NOUN cana-1902 198 9 in in ADP cana-1902 198 10 each each PRON cana-1902 198 11 of of ADP cana-1902 198 12 the the DET cana-1902 198 13 three three NUM cana-1902 198 14 system system NOUN cana-1902 198 15 nodes node NOUN cana-1902 198 16 , , PUNCT cana-1902 198 17 the the DET cana-1902 198 18 number number NOUN cana-1902 198 19 of of ADP cana-1902 198 20 customers customer NOUN cana-1902 198 21 in in ADP cana-1902 198 22 the the DET cana-1902 198 23 system system NOUN cana-1902 198 24 , , PUNCT cana-1902 198 25 and and CCONJ cana-1902 198 26 the the DET cana-1902 198 27 amount amount NOUN cana-1902 198 28 of of ADP cana-1902 198 29 time time NOUN cana-1902 198 30 a a DET cana-1902 198 31 client client NOUN cana-1902 198 32 has have VERB cana-1902 198 33 to to PART cana-1902 198 34 wait wait VERB cana-1902 198 35 in in ADP cana-1902 198 36 each each PRON cana-1902 198 37 of of ADP cana-1902 198 38 the the DET cana-1902 198 39 three three NUM cana-1902 198 40 system system NOUN cana-1902 198 41 queues queue NOUN cana-1902 198 42 . . PUNCT cana-1902 199 1 it it PRON cana-1902 199 2 shows show VERB cana-1902 199 3 the the DET cana-1902 199 4 correctness correctness NOUN cana-1902 199 5 of of ADP cana-1902 199 6 the the DET cana-1902 199 7 results result NOUN cana-1902 199 8 . . PUNCT cana-1902 200 1 references reference NOUN cana-1902 200 2 [ [ X cana-1902 200 3 1 1 NUM cana-1902 200 4 ] ] PUNCT cana-1902 200 5 ankita ankita PROPN cana-1902 200 6 roy roy PROPN cana-1902 200 7 chowdhury chowdhury PROPN cana-1902 200 8 , , PUNCT cana-1902 200 9 indra indra PROPN cana-1902 200 10 rani rani PROPN cana-1902 200 11 , , PUNCT cana-1902 200 12 steady steady ADJ cana-1902 200 13 - - PUNCT cana-1902 200 14 state state NOUN cana-1902 200 15 solution solution NOUN cana-1902 200 16 of of ADP cana-1902 200 17 catastrophic catastrophic ADJ cana-1902 200 18 feedback feedback NOUN cana-1902 200 19 queue queue NOUN cana-1902 200 20 subject subject NOUN cana-1902 200 21 to to ADP cana-1902 200 22 balking balk VERB cana-1902 200 23 using use VERB cana-1902 200 24 matrix matrix NOUN cana-1902 200 25 - - PUNCT cana-1902 200 26 geometric geometric ADJ cana-1902 200 27 approach approach NOUN cana-1902 200 28 , , PUNCT cana-1902 200 29 journal journal NOUN cana-1902 200 30 of of ADP cana-1902 200 31 scientific scientific ADJ cana-1902 200 32 research research NOUN cana-1902 200 33 , , PUNCT cana-1902 200 34 6 6 NUM cana-1902 200 35 ( ( PUNCT cana-1902 200 36 65 65 NUM cana-1902 200 37 ) ) PUNCT cana-1902 200 38 ( ( PUNCT cana-1902 200 39 2021 2021 NUM cana-1902 200 40 ) ) PUNCT cana-1902 200 41 , , PUNCT cana-1902 200 42 100 100 NUM cana-1902 200 43 – – SYM cana-1902 200 44 105 105 NUM cana-1902 200 45 . . PUNCT cana-1902 201 1 [ [ X cana-1902 201 2 2 2 NUM cana-1902 201 3 ] ] X cana-1902 201 4 chao chao PROPN cana-1902 201 5 x x PROPN cana-1902 201 6 , , PUNCT cana-1902 201 7 a a DET cana-1902 201 8 queuing queue VERB cana-1902 201 9 network network NOUN cana-1902 201 10 model model NOUN cana-1902 201 11 with with ADP cana-1902 201 12 catastrophes catastrophe NOUN cana-1902 201 13 and and CCONJ cana-1902 201 14 product product NOUN cana-1902 201 15 form form NOUN cana-1902 201 16 solution solution NOUN cana-1902 201 17 , , PUNCT cana-1902 201 18 operation operation NOUN cana-1902 201 19 research research NOUN cana-1902 201 20 letters letter NOUN cana-1902 201 21 , , PUNCT cana-1902 201 22 18 18 NUM cana-1902 201 23 ( ( PUNCT cana-1902 201 24 1995 1995 NUM cana-1902 201 25 ) ) PUNCT cana-1902 201 26 , , PUNCT cana-1902 201 27 75 75 NUM cana-1902 201 28 - - SYM cana-1902 201 29 79 79 NUM cana-1902 201 30 . . PUNCT cana-1902 202 1 [ [ X cana-1902 202 2 3 3 X cana-1902 202 3 ] ] PUNCT cana-1902 202 4 chandrasekaran chandrasekaran ADJ cana-1902 202 5 v.m v.m PROPN cana-1902 202 6 , , PUNCT cana-1902 202 7 saravanarajan saravanarajan PROPN cana-1902 202 8 m.c m.c PROPN cana-1902 202 9 , , PUNCT cana-1902 202 10 transient transient NOUN cana-1902 202 11 and and CCONJ cana-1902 202 12 reliability reliability NOUN cana-1902 202 13 analysis analysis NOUN cana-1902 202 14 of of ADP cana-1902 202 15 m m PROPN cana-1902 202 16 / / SYM cana-1902 202 17 m/1 m/1 NOUN cana-1902 202 18 feedback feedback NOUN cana-1902 202 19 queue queue NOUN cana-1902 202 20 subject subject NOUN cana-1902 202 21 to to ADP cana-1902 202 22 catastrophes catastrophe NOUN cana-1902 202 23 , , PUNCT cana-1902 202 24 server server NOUN cana-1902 202 25 failures failure NOUN cana-1902 202 26 and and CCONJ cana-1902 202 27 repairs repair NOUN cana-1902 202 28 , , PUNCT cana-1902 202 29 international international ADJ cana-1902 202 30 journal journal NOUN cana-1902 202 31 of of ADP cana-1902 202 32 pure pure ADJ cana-1902 202 33 and and CCONJ cana-1902 202 34 applied applied ADJ cana-1902 202 35 mathematics mathematic NOUN cana-1902 202 36 , , PUNCT cana-1902 202 37 77 77 NUM cana-1902 202 38 ( ( PUNCT cana-1902 202 39 5 5 NUM cana-1902 202 40 ) ) PUNCT cana-1902 202 41 ( ( PUNCT cana-1902 202 42 2012 2012 NUM cana-1902 202 43 ) ) PUNCT cana-1902 202 44 , , PUNCT cana-1902 202 45 605 605 NUM cana-1902 202 46 - - SYM cana-1902 202 47 625 625 NUM cana-1902 202 48 . . PUNCT cana-1902 203 1 [ [ X cana-1902 203 2 4 4 X cana-1902 203 3 ] ] PUNCT cana-1902 203 4 erlang erlang PROPN cana-1902 203 5 a.k a.k PROPN cana-1902 203 6 , , PUNCT cana-1902 203 7 the the DET cana-1902 203 8 theory theory NOUN cana-1902 203 9 of of ADP cana-1902 203 10 probabilities probability NOUN cana-1902 203 11 and and CCONJ cana-1902 203 12 telephone telephone NOUN cana-1902 203 13 conversations conversation NOUN cana-1902 203 14 , , PUNCT cana-1902 203 15 nyt nyt PROPN cana-1902 203 16 j j PROPN cana-1902 203 17 inds inds PROPN cana-1902 203 18 skriff skriff PROPN cana-1902 203 19 math.b20 math.b20 PROPN cana-1902 203 20 , , PUNCT cana-1902 203 21 ( ( PUNCT cana-1902 203 22 1909 1909 NUM cana-1902 203 23 ) ) PUNCT cana-1902 203 24 , , PUNCT cana-1902 203 25 33 33 NUM cana-1902 203 26 - - SYM cana-1902 203 27 39 39 NUM cana-1902 203 28 . . PUNCT cana-1902 204 1 [ [ X cana-1902 204 2 5 5 NUM cana-1902 204 3 ] ] X cana-1902 204 4 falin falin PROPN cana-1902 204 5 g.i g.i PROPN cana-1902 204 6 , , PUNCT cana-1902 204 7 a a DET cana-1902 204 8 survey survey NOUN cana-1902 204 9 of of ADP cana-1902 204 10 retrial retrial ADJ cana-1902 204 11 queues queue NOUN cana-1902 204 12 , , PUNCT cana-1902 204 13 queueing queue VERB cana-1902 204 14 system system NOUN cana-1902 204 15 , , PUNCT cana-1902 204 16 7(1990 7(1990 NUM cana-1902 204 17 ) ) PUNCT cana-1902 204 18 , , PUNCT cana-1902 204 19 127 127 NUM cana-1902 204 20 - - SYM cana-1902 204 21 167 167 NUM cana-1902 204 22 . . PUNCT cana-1902 205 1 [ [ X cana-1902 205 2 6 6 NUM cana-1902 205 3 ] ] X cana-1902 205 4 gelenbe gelenbe NOUN cana-1902 205 5 e e NOUN cana-1902 205 6 , , PUNCT cana-1902 205 7 product product NOUN cana-1902 205 8 form form NOUN cana-1902 205 9 queueing queue VERB cana-1902 205 10 networks network NOUN cana-1902 205 11 with with ADP cana-1902 205 12 positive positive ADJ cana-1902 205 13 and and CCONJ cana-1902 205 14 negative negative ADJ cana-1902 205 15 customers customer NOUN cana-1902 205 16 , , PUNCT cana-1902 205 17 journal journal NOUN cana-1902 205 18 of of ADP cana-1902 205 19 applied apply VERB cana-1902 205 20 probability probability NOUN cana-1902 205 21 , , PUNCT cana-1902 205 22 28(3 28(3 NUM cana-1902 205 23 ) ) PUNCT cana-1902 205 24 ( ( PUNCT cana-1902 205 25 1991 1991 NUM cana-1902 205 26 ) ) PUNCT cana-1902 205 27 , , PUNCT cana-1902 205 28 656 656 NUM cana-1902 205 29 - - SYM cana-1902 205 30 663 663 NUM cana-1902 205 31 . . PUNCT cana-1902 206 1 [ [ X cana-1902 206 2 7 7 NUM cana-1902 206 3 ] ] X cana-1902 206 4 jackson jackson PROPN cana-1902 206 5 j.r j.r PROPN cana-1902 206 6 , , PUNCT cana-1902 206 7 networks network NOUN cana-1902 206 8 of of ADP cana-1902 206 9 waiting wait VERB cana-1902 206 10 lines line NOUN cana-1902 206 11 , , PUNCT cana-1902 206 12 operation operation NOUN cana-1902 206 13 research research NOUN cana-1902 206 14 , , PUNCT cana-1902 206 15 5(40 5(40 NUM cana-1902 206 16 ) ) PUNCT cana-1902 206 17 ( ( PUNCT cana-1902 206 18 1957 1957 NUM cana-1902 206 19 ) ) PUNCT cana-1902 206 20 , , PUNCT cana-1902 206 21 518 518 NUM cana-1902 206 22 - - SYM cana-1902 206 23 521 521 NUM cana-1902 206 24 . . PUNCT cana-1902 207 1 [ [ X cana-1902 207 2 8 8 NUM cana-1902 207 3 ] ] X cana-1902 207 4 jackson jackson PROPN cana-1902 207 5 j.r j.r PROPN cana-1902 207 6 , , PUNCT cana-1902 207 7 jobshop jobshop ADJ cana-1902 207 8 - - PUNCT cana-1902 207 9 like like ADJ cana-1902 207 10 queueing queue VERB cana-1902 207 11 systems system NOUN cana-1902 207 12 , , PUNCT cana-1902 207 13 management management NOUN cana-1902 207 14 science science NOUN cana-1902 207 15 , , PUNCT cana-1902 207 16 10 10 NUM cana-1902 207 17 ( ( PUNCT cana-1902 207 18 1963 1963 NUM cana-1902 207 19 ) ) PUNCT cana-1902 207 20 , , PUNCT cana-1902 207 21 131 131 NUM cana-1902 207 22 - - SYM cana-1902 207 23 142 142 NUM cana-1902 207 24 . . PUNCT cana-1902 208 1 [ [ X cana-1902 208 2 9 9 NUM cana-1902 208 3 ] ] PUNCT cana-1902 208 4 kosten kosten PROPN cana-1902 208 5 l l PROPN cana-1902 208 6 , , PUNCT cana-1902 208 7 on on ADP cana-1902 208 8 the the DET cana-1902 208 9 influence influence NOUN cana-1902 208 10 of of ADP cana-1902 208 11 repeated repeat VERB cana-1902 208 12 calls call NOUN cana-1902 208 13 in in ADP cana-1902 208 14 the the DET cana-1902 208 15 theory theory NOUN cana-1902 208 16 of of ADP cana-1902 208 17 probabilities probability NOUN cana-1902 208 18 of of ADP cana-1902 208 19 blocking block VERB cana-1902 208 20 , , PUNCT cana-1902 208 21 deingenieur deingenieur PROPN cana-1902 208 22 , , PUNCT cana-1902 208 23 ( ( PUNCT cana-1902 208 24 1947 1947 NUM cana-1902 208 25 ) ) PUNCT cana-1902 208 26 , , PUNCT cana-1902 208 27 591625 591625 NUM cana-1902 208 28 . . PUNCT cana-1902 209 1 [ [ X cana-1902 209 2 10 10 NUM cana-1902 209 3 ] ] X cana-1902 209 4 krishna krishna PROPN cana-1902 209 5 kumar kumar PROPN cana-1902 209 6 b b PROPN cana-1902 209 7 , , PUNCT cana-1902 209 8 arivudainambi arivudainambi PROPN cana-1902 209 9 d d NOUN cana-1902 209 10 , , PUNCT cana-1902 209 11 transient transient ADJ cana-1902 209 12 solution solution NOUN cana-1902 209 13 of of ADP cana-1902 209 14 an an DET cana-1902 209 15 m m NOUN cana-1902 209 16 / / SYM cana-1902 209 17 m/1queue m/1queue NOUN cana-1902 209 18 with with ADP cana-1902 209 19 catastrophes catastrophe NOUN cana-1902 209 20 , , PUNCT cana-1902 209 21 computers computer NOUN cana-1902 209 22 and and CCONJ cana-1902 209 23 mathematics mathematic NOUN cana-1902 209 24 with with ADP cana-1902 209 25 applications application NOUN cana-1902 209 26 , , PUNCT cana-1902 209 27 40 40 NUM cana-1902 209 28 ( ( PUNCT cana-1902 209 29 2000 2000 NUM cana-1902 209 30 ) ) PUNCT cana-1902 209 31 , , PUNCT cana-1902 209 32 1233 1233 NUM cana-1902 209 33 - - SYM cana-1902 209 34 1240 1240 NUM cana-1902 209 35 . . PUNCT cana-1902 210 1 [ [ X cana-1902 210 2 11 11 NUM cana-1902 210 3 ] ] X cana-1902 210 4 kumar kumar PROPN cana-1902 210 5 b.k b.k PROPN cana-1902 210 6 , , PUNCT cana-1902 210 7 anantha anantha PROPN cana-1902 210 8 lakshmi lakshmi PROPN cana-1902 210 9 s. s. PROPN cana-1902 210 10 r r PROPN cana-1902 210 11 , , PUNCT cana-1902 210 12 anbarasu anbarasu PROPN cana-1902 210 13 s s PROPN cana-1902 210 14 , , PUNCT cana-1902 210 15 pavai pavai VERB cana-1902 210 16 madheswari madheswari PROPN cana-1902 210 17 s s SYM cana-1902 210 18 , , PUNCT cana-1902 210 19 transient transient ADJ cana-1902 210 20 and and CCONJ cana-1902 210 21 steady steady ADJ cana-1902 210 22 - - PUNCT cana-1902 210 23 state state NOUN cana-1902 210 24 analysis analysis NOUN cana-1902 210 25 of of ADP cana-1902 210 26 queueing queue VERB cana-1902 210 27 systems system NOUN cana-1902 210 28 with with ADP cana-1902 210 29 catastrophes catastrophe NOUN cana-1902 210 30 and and CCONJ cana-1902 210 31 impatient impatient ADJ cana-1902 210 32 customers customer NOUN cana-1902 210 33 , , PUNCT cana-1902 210 34 international international ADJ cana-1902 210 35 journal journal NOUN cana-1902 210 36 of of ADP cana-1902 210 37 mathematics mathematic NOUN cana-1902 210 38 in in ADP cana-1902 210 39 operational operational ADJ cana-1902 210 40 research research NOUN cana-1902 210 41 , , PUNCT cana-1902 210 42 6(5 6(5 NUM cana-1902 210 43 ) ) PUNCT cana-1902 210 44 ( ( PUNCT cana-1902 210 45 2014 2014 NUM cana-1902 210 46 ) ) PUNCT cana-1902 210 47 , , PUNCT cana-1902 210 48 523 523 NUM cana-1902 210 49 - - SYM cana-1902 210 50 549 549 NUM cana-1902 210 51 . . PUNCT cana-1902 211 1 [ [ X cana-1902 211 2 12 12 NUM cana-1902 211 3 ] ] X cana-1902 211 4 shanmugasundaram shanmugasundaram PROPN cana-1902 211 5 s s PROPN cana-1902 211 6 , , PUNCT cana-1902 211 7 baby baby NOUN cana-1902 211 8 c c NOUN cana-1902 211 9 , , PUNCT cana-1902 211 10 study study NOUN cana-1902 211 11 of of ADP cana-1902 211 12 m m PROPN cana-1902 211 13 / / SYM cana-1902 211 14 m/1 m/1 NOUN cana-1902 211 15 feedback feedback NOUN cana-1902 211 16 retrial retrial NOUN cana-1902 211 17 queueing queue VERB cana-1902 211 18 network network NOUN cana-1902 211 19 with with ADP cana-1902 211 20 three three NUM cana-1902 211 21 nodes node NOUN cana-1902 211 22 when when SCONJ cana-1902 211 23 catastrophe catastrophe NOUN cana-1902 211 24 occurs occur VERB cana-1902 211 25 , , PUNCT cana-1902 211 26 mathematicial mathematicial ADJ cana-1902 211 27 statistician statistician NOUN cana-1902 211 28 and and CCONJ cana-1902 211 29 engineering engineering NOUN cana-1902 211 30 applications application NOUN cana-1902 211 31 , , PUNCT cana-1902 211 32 71(4 71(4 NUM cana-1902 211 33 ) ) PUNCT cana-1902 211 34 ( ( PUNCT cana-1902 211 35 2022 2022 NUM cana-1902 211 36 ) ) PUNCT cana-1902 211 37 , , PUNCT cana-1902 211 38 3482 3482 NUM cana-1902 211 39 – – PUNCT cana-1902 211 40 3494 3494 NUM cana-1902 211 41 . . PUNCT cana-1902 212 1 [ [ X cana-1902 212 2 13 13 NUM cana-1902 212 3 ] ] X cana-1902 212 4 shanmugasundaram shanmugasundaram PROPN cana-1902 212 5 s s PROPN cana-1902 212 6 , , PUNCT cana-1902 212 7 chitra chitra PROPN cana-1902 212 8 s s PROPN cana-1902 212 9 , , PUNCT cana-1902 212 10 time time NOUN cana-1902 212 11 dependentsolution dependentsolution NOUN cana-1902 212 12 of of ADP cana-1902 212 13 m m PROPN cana-1902 212 14 / / SYM cana-1902 212 15 m/1retrialqueue m/1retrialqueue NOUN cana-1902 212 16 and and CCONJ cana-1902 212 17 feedback feedback NOUN cana-1902 212 18 on on ADP cana-1902 212 19 non non ADJ cana-1902 212 20 - - ADJ cana-1902 212 21 retrial retrial ADJ cana-1902 212 22 customers customer NOUN cana-1902 212 23 with with ADP cana-1902 212 24 catastrophes catastrophe NOUN cana-1902 212 25 , , PUNCT cana-1902 212 26 global global ADJ cana-1902 212 27 journal journal NOUN cana-1902 212 28 of of ADP cana-1902 212 29 pure pure ADJ cana-1902 212 30 and and CCONJ cana-1902 212 31 applied applied ADJ cana-1902 212 32 mathematics mathematic NOUN cana-1902 212 33 , , PUNCT cana-1902 212 34 11(1 11(1 NUM cana-1902 212 35 ) ) PUNCT cana-1902 212 36 ( ( PUNCT cana-1902 212 37 2015 2015 NUM cana-1902 212 38 ) ) PUNCT cana-1902 212 39 , , PUNCT cana-1902 212 40 512 512 NUM cana-1902 212 41 - - SYM cana-1902 212 42 521 521 NUM cana-1902 212 43 . . PUNCT cana-1902 213 1 [ [ X cana-1902 213 2 14 14 NUM cana-1902 213 3 ] ] PUNCT cana-1902 213 4 shanmgasundaram shanmgasundaram PROPN cana-1902 213 5 s s PART cana-1902 213 6 , , PUNCT cana-1902 213 7 vanitha vanitha PROPN cana-1902 213 8 s s ADJ cana-1902 213 9 , , PUNCT cana-1902 213 10 steady steady ADJ cana-1902 213 11 state state NOUN cana-1902 213 12 analysis analysis NOUN cana-1902 213 13 of of ADP cana-1902 213 14 m m PROPN cana-1902 213 15 / / SYM cana-1902 213 16 m/1 m/1 NOUN cana-1902 213 17 retrial retrial NOUN cana-1902 213 18 queueing queue VERB cana-1902 213 19 network network NOUN cana-1902 213 20 with with ADP cana-1902 213 21 catastrophes catastrophe NOUN cana-1902 213 22 , , PUNCT cana-1902 213 23 international international ADJ cana-1902 213 24 journal journal NOUN cana-1902 213 25 of of ADP cana-1902 213 26 mathematics mathematics NOUN cana-1902 213 27 trends trend NOUN cana-1902 213 28 and and CCONJ cana-1902 213 29 technology technology NOUN cana-1902 213 30 , , PUNCT cana-1902 213 31 26(12 26(12 NUM cana-1902 213 32 ) ) PUNCT cana-1902 213 33 ( ( PUNCT cana-1902 213 34 2020 2020 NUM cana-1902 213 35 ) ) PUNCT cana-1902 213 36 , , PUNCT cana-1902 213 37 170 170 NUM cana-1902 213 38 – – SYM cana-1902 213 39 181 181 NUM cana-1902 213 40 . . PUNCT cana-1902 214 1 [ [ X cana-1902 214 2 15 15 NUM cana-1902 214 3 ] ] X cana-1902 214 4 takacs takacs PROPN cana-1902 214 5 l l NOUN cana-1902 214 6 , , PUNCT cana-1902 214 7 a a DET cana-1902 214 8 single single ADJ cana-1902 214 9 server server NOUN cana-1902 214 10 queue queue NOUN cana-1902 214 11 with with ADP cana-1902 214 12 feedback feedback NOUN cana-1902 214 13 , , PUNCT cana-1902 214 14 the the DET cana-1902 214 15 bell bell NOUN cana-1902 214 16 system system NOUN cana-1902 214 17 technical technical ADJ cana-1902 214 18 journal journal NOUN cana-1902 214 19 , , PUNCT cana-1902 214 20 42 42 NUM cana-1902 214 21 ( ( PUNCT cana-1902 214 22 1963 1963 NUM cana-1902 214 23 ) ) PUNCT cana-1902 214 24 , , PUNCT cana-1902 214 25 505 505 NUM cana-1902 214 26 - - SYM cana-1902 214 27 519 519 NUM cana-1902 214 28 . . PUNCT cana-1902 215 1 [ [ X cana-1902 215 2 16 16 NUM cana-1902 215 3 ] ] X cana-1902 215 4 thangaraj thangaraj PROPN cana-1902 215 5 v v PROPN cana-1902 215 6 , , PUNCT cana-1902 215 7 vanitha vanitha PROPN cana-1902 215 8 s s ADJ cana-1902 215 9 , , PUNCT cana-1902 215 10 on on ADP cana-1902 215 11 the the DET cana-1902 215 12 analysis analysis NOUN cana-1902 215 13 of of ADP cana-1902 215 14 m m PROPN cana-1902 215 15 / / SYM cana-1902 215 16 m/1 m/1 NOUN cana-1902 215 17 feedback feedback NOUN cana-1902 215 18 queue queue NOUN cana-1902 215 19 with with ADP cana-1902 215 20 catastrophes catastrophe NOUN cana-1902 215 21 using use VERB cana-1902 215 22 continued continued ADJ cana-1902 215 23 fractions fraction NOUN cana-1902 215 24 , , PUNCT cana-1902 215 25 international international ADJ cana-1902 215 26 journal journal NOUN cana-1902 215 27 of of ADP cana-1902 215 28 pure pure ADJ cana-1902 215 29 and and CCONJ cana-1902 215 30 applied applied ADJ cana-1902 215 31 mathematics mathematic NOUN cana-1902 215 32 , , PUNCT cana-1902 215 33 53(1 53(1 NOUN cana-1902 215 34 ) ) PUNCT cana-1902 215 35 ( ( PUNCT cana-1902 215 36 2009 2009 NUM cana-1902 215 37 ) ) PUNCT cana-1902 215 38 , , PUNCT cana-1902 215 39 133 133 NUM cana-1902 215 40 - - SYM cana-1902 215 41 151 151 NUM cana-1902 215 42 . . PUNCT cana-1902 216 1 [ [ X cana-1902 216 2 17 17 NUM cana-1902 216 3 ] ] PUNCT cana-1902 216 4 varalakshmi varalakshmi NOUN cana-1902 216 5 , , PUNCT cana-1902 216 6 m m PRON cana-1902 216 7 , , PUNCT cana-1902 216 8 chandrasekaran chandrasekaran ADJ cana-1902 216 9 , , PUNCT cana-1902 216 10 v. v. PROPN cana-1902 216 11 m m PROPN cana-1902 216 12 , , PUNCT cana-1902 216 13 saravanarajan saravanarajan NOUN cana-1902 216 14 , , PUNCT cana-1902 216 15 m. m. NOUN cana-1902 216 16 c c PROPN cana-1902 216 17 , , PUNCT cana-1902 216 18 a a DET cana-1902 216 19 single single ADJ cana-1902 216 20 server server NOUN cana-1902 216 21 queue queue NOUN cana-1902 216 22 with with ADP cana-1902 216 23 immediate immediate ADJ cana-1902 216 24 feedback feedback NOUN cana-1902 216 25 , , PUNCT cana-1902 216 26 working work VERB cana-1902 216 27 vacation vacation NOUN cana-1902 216 28 and and CCONJ cana-1902 216 29 server server NOUN cana-1902 216 30 breakdown breakdown NOUN cana-1902 216 31 , , PUNCT cana-1902 216 32 international international ADJ cana-1902 216 33 journal journal NOUN cana-1902 216 34 of of ADP cana-1902 216 35 engineering engineering PROPN cana-1902 216 36 & & CCONJ cana-1902 216 37 technology technology PROPN cana-1902 216 38 , , PUNCT cana-1902 216 39 7 7 NUM cana-1902 216 40 ( ( PUNCT cana-1902 216 41 4 4 NUM cana-1902 216 42 ) ) PUNCT cana-1902 216 43 ( ( PUNCT cana-1902 216 44 2018 2018 NUM cana-1902 216 45 ) ) PUNCT cana-1902 216 46 , , PUNCT cana-1902 216 47 476479 476479 NUM cana-1902 216 48 . . PUNCT