id sid tid token lemma pos cana-3613 1 1 communications communication NOUN cana-3613 1 2 on on ADP cana-3613 1 3 applied apply VERB cana-3613 1 4 nonlinear nonlinear ADJ cana-3613 1 5 analysis analysis NOUN cana-3613 1 6 issn issn NOUN cana-3613 1 7 : : PUNCT cana-3613 1 8 1074 1074 NUM cana-3613 1 9 - - PUNCT cana-3613 1 10 133x 133x NUM cana-3613 1 11 vol vol NOUN cana-3613 1 12 32 32 NUM cana-3613 1 13 no no NOUN cana-3613 1 14 . . PUNCT cana-3613 2 1 8s 8s PROPN cana-3613 2 2 ( ( PUNCT cana-3613 2 3 2025 2025 NUM cana-3613 2 4 ) ) PUNCT cana-3613 2 5 123 123 NUM cana-3613 2 6 https://internationalpubls.com https://internationalpubls.com NUM cana-3613 2 7 impatient impatient ADJ cana-3613 2 8 customer customer NOUN cana-3613 2 9 queue queue NOUN cana-3613 2 10 with with ADP cana-3613 2 11 single single ADJ cana-3613 2 12 working work VERB cana-3613 2 13 vacation vacation NOUN cana-3613 2 14 a.saila a.saila ADP cana-3613 2 15 kumari1 kumari1 NOUN cana-3613 3 1 * * PUNCT cana-3613 3 2 k. k. PROPN cana-3613 3 3 v. v. PROPN cana-3613 3 4 s. s. PROPN cana-3613 3 5 nagalakshmi nagalakshmi PROPN cana-3613 3 6 2 2 NUM cana-3613 3 7 1 1 NUM cana-3613 3 8 . . PUNCT cana-3613 3 9 .a.saila .a.saila PUNCT cana-3613 4 1 kumari kumari PROPN cana-3613 4 2 , , PUNCT cana-3613 4 3 associate associate NOUN cana-3613 4 4 professor professor NOUN cana-3613 4 5 , , PUNCT cana-3613 4 6 department department NOUN cana-3613 4 7 of of ADP cana-3613 4 8 mathematics mathematics PROPN cana-3613 4 9 , , PUNCT cana-3613 4 10 jntua jntua VERB cana-3613 4 11 college college NOUN cana-3613 4 12 of of ADP cana-3613 4 13 engineering engineering NOUN cana-3613 4 14 , , PUNCT cana-3613 4 15 anantapur-515002 anantapur-515002 NOUN cana-3613 4 16 2 2 NUM cana-3613 4 17 . . PUNCT cana-3613 4 18 research research NOUN cana-3613 4 19 scholar scholar NOUN cana-3613 4 20 and and CCONJ cana-3613 4 21 lecturer lecturer NOUN cana-3613 4 22 in in ADP cana-3613 4 23 mathematics mathematic NOUN cana-3613 4 24 , , PUNCT cana-3613 4 25 govt govt NOUN cana-3613 4 26 . . PUNCT cana-3613 4 27 degree degree NOUN cana-3613 4 28 college college NOUN cana-3613 4 29 , , PUNCT cana-3613 4 30 visakha visakha ADJ cana-3613 4 31 women woman NOUN cana-3613 4 32 ’s ’s PART cana-3613 4 33 , , PUNCT cana-3613 4 34 visakhapatnam visakhapatnam PROPN cana-3613 4 35 article article NOUN cana-3613 4 36 history history NOUN cana-3613 4 37 : : PUNCT cana-3613 4 38 received receive VERB cana-3613 4 39 : : PUNCT cana-3613 4 40 28 28 NUM cana-3613 4 41 - - SYM cana-3613 4 42 10 10 NUM cana-3613 4 43 - - PUNCT cana-3613 4 44 2024 2024 NUM cana-3613 4 45 revised revise VERB cana-3613 4 46 : : PUNCT cana-3613 4 47 18 18 NUM cana-3613 4 48 - - SYM cana-3613 4 49 11 11 NUM cana-3613 4 50 - - PUNCT cana-3613 4 51 2024 2024 NUM cana-3613 4 52 accepted accept VERB cana-3613 4 53 : : PUNCT cana-3613 4 54 19 19 NUM cana-3613 4 55 - - SYM cana-3613 4 56 12 12 NUM cana-3613 4 57 - - PUNCT cana-3613 4 58 2024 2024 NUM cana-3613 4 59 abstract abstract NOUN cana-3613 4 60 : : PUNCT cana-3613 4 61 this this DET cana-3613 4 62 paper paper NOUN cana-3613 4 63 analyzes analyze VERB cana-3613 4 64 an an DET cana-3613 4 65 infinite infinite ADJ cana-3613 4 66 buffer buffer NOUN cana-3613 4 67 m m PROPN cana-3613 4 68 / / SYM cana-3613 4 69 m/1 m/1 NOUN cana-3613 4 70 queue queue NOUN cana-3613 4 71 with with ADP cana-3613 4 72 single single ADJ cana-3613 4 73 working work VERB cana-3613 4 74 vacation vacation NOUN cana-3613 4 75 in in ADP cana-3613 4 76 which which PRON cana-3613 4 77 customers customer NOUN cana-3613 4 78 arrive arrive VERB cana-3613 4 79 according accord VERB cana-3613 4 80 to to ADP cana-3613 4 81 a a DET cana-3613 4 82 poisson poisson NOUN cana-3613 4 83 process process NOUN cana-3613 4 84 . . PUNCT cana-3613 5 1 as as ADV cana-3613 5 2 soon soon ADV cana-3613 5 3 as as SCONJ cana-3613 5 4 the the DET cana-3613 5 5 system system NOUN cana-3613 5 6 becomes become VERB cana-3613 5 7 empty empty ADJ cana-3613 5 8 , , PUNCT cana-3613 5 9 the the DET cana-3613 5 10 server server NOUN cana-3613 5 11 takes take VERB cana-3613 5 12 working work VERB cana-3613 5 13 vacation vacation NOUN cana-3613 5 14 . . PUNCT cana-3613 6 1 the the DET cana-3613 6 2 service service NOUN cana-3613 6 3 rate rate NOUN cana-3613 6 4 during during ADP cana-3613 6 5 regular regular ADJ cana-3613 6 6 busy busy ADJ cana-3613 6 7 period period NOUN cana-3613 6 8 , , PUNCT cana-3613 6 9 working work VERB cana-3613 6 10 vacation vacation NOUN cana-3613 6 11 period period NOUN cana-3613 6 12 and and CCONJ cana-3613 6 13 vacation vacation NOUN cana-3613 6 14 times time NOUN cana-3613 6 15 are be AUX cana-3613 6 16 assumed assume VERB cana-3613 6 17 to to PART cana-3613 6 18 be be AUX cana-3613 6 19 exponentially exponentially ADV cana-3613 6 20 distributed distribute VERB cana-3613 6 21 . . PUNCT cana-3613 7 1 during during ADP cana-3613 7 2 working work VERB cana-3613 7 3 vacation vacation NOUN cana-3613 7 4 customers customer NOUN cana-3613 7 5 may may AUX cana-3613 7 6 renege renege VERB cana-3613 7 7 due due ADJ cana-3613 7 8 to to ADP cana-3613 7 9 impatience impatience NOUN cana-3613 7 10 and and CCONJ cana-3613 7 11 the the DET cana-3613 7 12 impatient impatient ADJ cana-3613 7 13 timer timer NOUN cana-3613 7 14 follows follow VERB cana-3613 7 15 exponential exponential ADJ cana-3613 7 16 distribution distribution NOUN cana-3613 7 17 . . PUNCT cana-3613 8 1 the the DET cana-3613 8 2 steady steady ADJ cana-3613 8 3 - - PUNCT cana-3613 8 4 state state NOUN cana-3613 8 5 probabilities probability NOUN cana-3613 8 6 and and CCONJ cana-3613 8 7 performance performance NOUN cana-3613 8 8 measures measure NOUN cana-3613 8 9 are be AUX cana-3613 8 10 obtained obtain VERB cana-3613 8 11 by by ADP cana-3613 8 12 using use VERB cana-3613 8 13 probability probability NOUN cana-3613 8 14 generating generating NOUN cana-3613 8 15 function function NOUN cana-3613 8 16 . . PUNCT cana-3613 9 1 various various ADJ cana-3613 9 2 numerical numerical ADJ cana-3613 9 3 results result NOUN cana-3613 9 4 are be AUX cana-3613 9 5 presented present VERB cana-3613 9 6 to to PART cana-3613 9 7 show show VERB cana-3613 9 8 the the DET cana-3613 9 9 effect effect NOUN cana-3613 9 10 of of ADP cana-3613 9 11 the the DET cana-3613 9 12 some some DET cana-3613 9 13 parameters parameter NOUN cana-3613 9 14 on on ADP cana-3613 9 15 the the DET cana-3613 9 16 system system NOUN cana-3613 9 17 performance performance NOUN cana-3613 9 18 measures measure NOUN cana-3613 9 19 . . PUNCT cana-3613 10 1 keywords keyword NOUN cana-3613 10 2 : : PUNCT cana-3613 10 3 queue queue NOUN cana-3613 10 4 , , PUNCT cana-3613 10 5 single single ADJ cana-3613 10 6 working working NOUN cana-3613 10 7 vacation vacation NOUN cana-3613 10 8 , , PUNCT cana-3613 10 9 reneging renege VERB cana-3613 10 10 , , PUNCT cana-3613 10 11 probability probability NOUN cana-3613 10 12 generating generating NOUN cana-3613 10 13 function function NOUN cana-3613 10 14 . . PUNCT cana-3613 11 1 1 1 NUM cana-3613 11 2 introduction introduction NOUN cana-3613 11 3 the the DET cana-3613 11 4 queueing queue VERB cana-3613 11 5 model model NOUN cana-3613 11 6 with with ADP cana-3613 11 7 server server NOUN cana-3613 11 8 vacations vacation NOUN cana-3613 11 9 has have AUX cana-3613 11 10 been be AUX cana-3613 11 11 well well ADV cana-3613 11 12 studied study VERB cana-3613 11 13 in in ADP cana-3613 11 14 the the DET cana-3613 11 15 past past ADJ cana-3613 11 16 three three NUM cana-3613 11 17 decades decade NOUN cana-3613 11 18 and and CCONJ cana-3613 11 19 successfully successfully ADV cana-3613 11 20 applied apply VERB cana-3613 11 21 in in ADP cana-3613 11 22 many many ADJ cana-3613 11 23 areas area NOUN cana-3613 11 24 such such ADJ cana-3613 11 25 as as ADP cana-3613 11 26 manufacturing manufacturing NOUN cana-3613 11 27 and and CCONJ cana-3613 11 28 production production NOUN cana-3613 11 29 systems system NOUN cana-3613 11 30 , , PUNCT cana-3613 11 31 computer computer NOUN cana-3613 11 32 and and CCONJ cana-3613 11 33 communication communication NOUN cana-3613 11 34 systems system NOUN cana-3613 11 35 , , PUNCT cana-3613 11 36 etc etc X cana-3613 11 37 . . X cana-3613 11 38 excellent excellent ADJ cana-3613 11 39 surveys survey NOUN cana-3613 11 40 on on ADP cana-3613 11 41 the the DET cana-3613 11 42 earlier early ADJ cana-3613 11 43 works work NOUN cana-3613 11 44 of of ADP cana-3613 11 45 vacation vacation NOUN cana-3613 11 46 models model NOUN cana-3613 11 47 have have AUX cana-3613 11 48 been be AUX cana-3613 11 49 reported report VERB cana-3613 11 50 by by ADP cana-3613 11 51 doshi doshi PROPN cana-3613 11 52 [ [ X cana-3613 11 53 2 2 NUM cana-3613 11 54 ] ] PUNCT cana-3613 11 55 , , PUNCT cana-3613 11 56 tian tian PROPN cana-3613 11 57 and and CCONJ cana-3613 11 58 zhang zhang PROPN cana-3613 12 1 [ [ X cana-3613 12 2 9 9 NUM cana-3613 12 3 ] ] PUNCT cana-3613 12 4 , , PUNCT cana-3613 12 5 ke ke PROPN cana-3613 12 6 et et PROPN cana-3613 12 7 al al PROPN cana-3613 12 8 . . PUNCT cana-3613 13 1 [ [ X cana-3613 13 2 4 4 X cana-3613 13 3 ] ] PUNCT cana-3613 13 4 and and CCONJ cana-3613 13 5 so so ADV cana-3613 13 6 on on ADV cana-3613 13 7 . . PUNCT cana-3613 14 1 working work VERB cana-3613 14 2 vacation vacation NOUN cana-3613 14 3 ( ( PUNCT cana-3613 14 4 π‘Šπ‘‰ π‘Šπ‘‰ PROPN cana-3613 14 5 ) ) PUNCT cana-3613 14 6 is be AUX cana-3613 14 7 one one NUM cana-3613 14 8 kind kind NOUN cana-3613 14 9 of of ADP cana-3613 14 10 vacation vacation NOUN cana-3613 14 11 policy policy NOUN cana-3613 14 12 under under ADP cana-3613 14 13 which which PRON cana-3613 14 14 the the DET cana-3613 14 15 server server NOUN cana-3613 14 16 provides provide VERB cana-3613 14 17 service service NOUN cana-3613 14 18 at at ADP cana-3613 14 19 a a DET cana-3613 14 20 lower low ADJ cana-3613 14 21 speed speed NOUN cana-3613 14 22 during during ADP cana-3613 14 23 the the DET cana-3613 14 24 vacation vacation NOUN cana-3613 14 25 period period NOUN cana-3613 14 26 rather rather ADV cana-3613 14 27 than than ADP cana-3613 14 28 stopping stop VERB cana-3613 14 29 service service NOUN cana-3613 14 30 completely completely ADV cana-3613 14 31 . . PUNCT cana-3613 15 1 it it PRON cana-3613 15 2 was be AUX cana-3613 15 3 introduced introduce VERB cana-3613 15 4 by by ADP cana-3613 15 5 servi servi PROPN cana-3613 15 6 and and CCONJ cana-3613 15 7 finn finn PROPN cana-3613 16 1 [ [ X cana-3613 16 2 7 7 X cana-3613 16 3 ] ] PUNCT cana-3613 16 4 in in ADP cana-3613 16 5 an an DET cana-3613 16 6 𝑀/𝑀/1 𝑀/𝑀/1 NOUN cana-3613 16 7 queueing queue VERB cana-3613 16 8 system system NOUN cana-3613 16 9 . . PUNCT cana-3613 17 1 the the DET cana-3613 17 2 π‘Šπ‘‰ π‘Šπ‘‰ PROPN cana-3613 17 3 policies policy NOUN cana-3613 17 4 are be AUX cana-3613 17 5 classified classify VERB cana-3613 17 6 as as ADP cana-3613 17 7 single single ADJ cana-3613 17 8 working work VERB cana-3613 17 9 vacation vacation NOUN cana-3613 17 10 ( ( PUNCT cana-3613 17 11 π‘†π‘Šπ‘‰ π‘†π‘Šπ‘‰ PROPN cana-3613 17 12 ) ) PUNCT cana-3613 17 13 and and CCONJ cana-3613 17 14 multiple multiple ADJ cana-3613 17 15 working work VERB cana-3613 17 16 vacation vacation NOUN cana-3613 17 17 ( ( PUNCT cana-3613 17 18 π‘€π‘Šπ‘‰ π‘€π‘Šπ‘‰ PROPN cana-3613 17 19 ) ) PUNCT cana-3613 17 20 . . PUNCT cana-3613 18 1 under under ADP cana-3613 18 2 the the DET cana-3613 18 3 π‘†π‘Šπ‘‰ π‘†π‘Šπ‘‰ NOUN cana-3613 18 4 policy policy NOUN cana-3613 18 5 the the DET cana-3613 18 6 server server NOUN cana-3613 18 7 enters enter VERB cana-3613 18 8 into into ADP cana-3613 18 9 vacation vacation NOUN cana-3613 18 10 , , PUNCT cana-3613 18 11 when when SCONJ cana-3613 18 12 there there PRON cana-3613 18 13 are be VERB cana-3613 18 14 no no DET cana-3613 18 15 customers customer NOUN cana-3613 18 16 in in ADP cana-3613 18 17 the the DET cana-3613 18 18 queue queue NOUN cana-3613 18 19 and and CCONJ cana-3613 18 20 serves serve VERB cana-3613 18 21 at at ADP cana-3613 18 22 a a DET cana-3613 18 23 lower low ADJ cana-3613 18 24 rate rate NOUN cana-3613 18 25 to to ADP cana-3613 18 26 the the PRON cana-3613 18 27 . . PUNCT cana-3613 19 1 meanwhile meanwhile ADV cana-3613 19 2 , , PUNCT cana-3613 19 3 he he PRON cana-3613 19 4 only only ADV cana-3613 19 5 takes take VERB cana-3613 19 6 one one NUM cana-3613 19 7 each each DET cana-3613 19 8 time time NOUN cana-3613 19 9 , , PUNCT cana-3613 19 10 and and CCONJ cana-3613 19 11 must must AUX cana-3613 19 12 come come VERB cana-3613 19 13 back back ADV cana-3613 19 14 to to ADP cana-3613 19 15 the the DET cana-3613 19 16 normal normal ADJ cana-3613 19 17 working working NOUN cana-3613 19 18 level level NOUN cana-3613 19 19 no no ADV cana-3613 19 20 matter matter ADV cana-3613 19 21 whether whether SCONJ cana-3613 19 22 there there PRON cana-3613 19 23 are be VERB cana-3613 19 24 customers customer NOUN cana-3613 19 25 at at ADP cana-3613 19 26 the the DET cana-3613 19 27 vacation vacation NOUN cana-3613 19 28 ending end VERB cana-3613 19 29 instant instant NOUN cana-3613 19 30 . . PUNCT cana-3613 20 1 if if SCONJ cana-3613 20 2 there there PRON cana-3613 20 3 are be VERB cana-3613 20 4 customers customer NOUN cana-3613 20 5 at at ADP cana-3613 20 6 the the DET cana-3613 20 7 vacation vacation NOUN cana-3613 20 8 ends end VERB cana-3613 20 9 , , PUNCT cana-3613 20 10 the the DET cana-3613 20 11 server server NOUN cana-3613 20 12 begins begin VERB cana-3613 20 13 to to PART cana-3613 20 14 serve serve VERB cana-3613 20 15 one one NUM cana-3613 20 16 customer customer NOUN cana-3613 20 17 at at ADP cana-3613 20 18 the the DET cana-3613 20 19 normal normal ADJ cana-3613 20 20 rate rate NOUN cana-3613 20 21 immediately immediately ADV cana-3613 20 22 ; ; PUNCT cana-3613 20 23 otherwise otherwise ADV cana-3613 20 24 , , PUNCT cana-3613 20 25 he he PRON cana-3613 20 26 will will AUX cana-3613 20 27 stay stay VERB cana-3613 20 28 in in ADP cana-3613 20 29 an an DET cana-3613 20 30 idle idle ADJ cana-3613 20 31 period period NOUN cana-3613 20 32 . . PUNCT cana-3613 21 1 wu wu PROPN cana-3613 21 2 and and CCONJ cana-3613 21 3 takagi takagi PROPN cana-3613 21 4 [ [ X cana-3613 21 5 12 12 NUM cana-3613 21 6 ] ] X cana-3613 21 7 generalized generalize VERB cana-3613 21 8 servi servi PROPN cana-3613 21 9 and and CCONJ cana-3613 21 10 finn finn PROPN cana-3613 22 1 [ [ X cana-3613 22 2 7 7 NUM cana-3613 22 3 ] ] X cana-3613 22 4 𝑀/𝑀/1/π‘Šπ‘‰ 𝑀/𝑀/1/π‘Šπ‘‰ ADJ cana-3613 22 5 queue queue NOUN cana-3613 22 6 to to ADP cana-3613 22 7 an an DET cana-3613 22 8 𝑀/𝐺/1/π‘Šπ‘‰ 𝑀/𝐺/1/π‘Šπ‘‰ ADJ cana-3613 22 9 queue queue NOUN cana-3613 22 10 . . PUNCT cana-3613 23 1 baba baba PROPN cana-3613 24 1 [ [ X cana-3613 24 2 1 1 X cana-3613 24 3 ] ] PUNCT cana-3613 24 4 analyzed analyze VERB cana-3613 24 5 a a DET cana-3613 24 6 𝐺/𝑀/1 𝐺/𝑀/1 NOUN cana-3613 24 7 queue queue NOUN cana-3613 24 8 with with ADP cana-3613 24 9 π‘€π‘Šπ‘‰. π‘€π‘Šπ‘‰. PROPN cana-3613 24 10 tian tian PROPN cana-3613 24 11 et et PROPN cana-3613 24 12 al al PROPN cana-3613 24 13 . . PUNCT cana-3613 25 1 [ [ X cana-3613 25 2 10 10 NUM cana-3613 25 3 ] ] PUNCT cana-3613 25 4 studied study VERB cana-3613 25 5 and and CCONJ cana-3613 25 6 𝑀/𝑀/1 𝑀/𝑀/1 NOUN cana-3613 25 7 queue queue NOUN cana-3613 25 8 with with ADP cana-3613 25 9 π‘†π‘Šπ‘‰ π‘†π‘Šπ‘‰ NOUN cana-3613 25 10 using use VERB cana-3613 25 11 matrix matrix NOUN cana-3613 25 12 geometric geometric ADJ cana-3613 25 13 method method NOUN cana-3613 25 14 . . PUNCT cana-3613 26 1 li li PROPN cana-3613 26 2 and and CCONJ cana-3613 26 3 tian tian ADJ cana-3613 27 1 [ [ X cana-3613 27 2 5 5 NUM cana-3613 27 3 ] ] PUNCT cana-3613 27 4 generalized generalize VERB cana-3613 27 5 this this DET cana-3613 27 6 study study NOUN cana-3613 27 7 to to ADP cana-3613 27 8 𝐺𝐼/𝑀/1 𝐺𝐼/𝑀/1 NOUN cana-3613 27 9 queue queue NOUN cana-3613 27 10 with with ADP cana-3613 27 11 π‘†π‘Šπ‘‰ π‘†π‘Šπ‘‰ NOUN cana-3613 27 12 and and CCONJ cana-3613 27 13 obtained obtain VERB cana-3613 27 14 the the DET cana-3613 27 15 queue queue NOUN cana-3613 27 16 length length NOUN cana-3613 27 17 distributions distribution NOUN cana-3613 27 18 at at ADP cana-3613 27 19 pre pre ADJ cana-3613 27 20 - - NOUN cana-3613 27 21 arrival arrival NOUN cana-3613 27 22 and and CCONJ cana-3613 27 23 arbitrary arbitrary ADJ cana-3613 27 24 epochs epoch NOUN cana-3613 27 25 using use VERB cana-3613 27 26 matrix matrix NOUN cana-3613 27 27 geometric geometric ADJ cana-3613 27 28 approach approach NOUN cana-3613 27 29 . . PUNCT cana-3613 28 1 impatient impatient PROPN cana-3613 28 2 is be AUX cana-3613 28 3 the the DET cana-3613 28 4 most most ADV cana-3613 28 5 prominent prominent ADJ cana-3613 28 6 characteristic characteristic NOUN cana-3613 28 7 as as SCONJ cana-3613 28 8 individuals individual NOUN cana-3613 28 9 always always ADV cana-3613 28 10 feel feel VERB cana-3613 28 11 anxious anxious ADJ cana-3613 28 12 and and CCONJ cana-3613 28 13 impatient impatient ADJ cana-3613 28 14 during during ADP cana-3613 28 15 waiting wait VERB cana-3613 28 16 for for ADP cana-3613 28 17 service service NOUN cana-3613 28 18 in in ADP cana-3613 28 19 real real ADJ cana-3613 28 20 life life NOUN cana-3613 28 21 . . PUNCT cana-3613 29 1 the the DET cana-3613 29 2 customers customer NOUN cana-3613 29 3 ’ ' PUNCT cana-3613 29 4 impatient impatient ADJ cana-3613 29 5 acts act NOUN cana-3613 29 6 should should AUX cana-3613 29 7 be be AUX cana-3613 29 8 involved involve VERB cana-3613 29 9 in in ADP cana-3613 29 10 the the DET cana-3613 29 11 study study NOUN cana-3613 29 12 of of ADP cana-3613 29 13 queueing queue VERB cana-3613 29 14 system system NOUN cana-3613 29 15 to to PART cana-3613 29 16 model model VERB cana-3613 29 17 real real ADJ cana-3613 29 18 situations situation NOUN cana-3613 29 19 exactly exactly ADV cana-3613 29 20 . . PUNCT cana-3613 30 1 intermittent intermittent ADJ cana-3613 30 2 operation operation NOUN cana-3613 30 3 of of ADP cana-3613 30 4 a a DET cana-3613 30 5 service service NOUN cana-3613 30 6 can can AUX cana-3613 30 7 be be AUX cana-3613 30 8 economically economically ADV cana-3613 30 9 appealing appealing ADJ cana-3613 30 10 whenever whenever SCONJ cana-3613 30 11 full full ADJ cana-3613 30 12 time time NOUN cana-3613 30 13 service service NOUN cana-3613 30 14 would would AUX cana-3613 30 15 result result VERB cana-3613 30 16 in in ADP cana-3613 30 17 significant significant ADJ cana-3613 30 18 server server NOUN cana-3613 30 19 idle idle ADJ cana-3613 30 20 time time NOUN cana-3613 30 21 or or CCONJ cana-3613 30 22 would would AUX cana-3613 30 23 preclude preclude VERB cana-3613 30 24 the the DET cana-3613 30 25 use use NOUN cana-3613 30 26 of of ADP cana-3613 30 27 the the DET cana-3613 30 28 server server NOUN cana-3613 30 29 in in ADP cana-3613 30 30 some some DET cana-3613 30 31 other other ADJ cana-3613 30 32 productive productive ADJ cana-3613 30 33 capacity capacity NOUN cana-3613 30 34 . . PUNCT cana-3613 31 1 on on ADP cana-3613 31 2 the the DET cana-3613 31 3 other other ADJ cana-3613 31 4 hand hand NOUN cana-3613 31 5 , , PUNCT cana-3613 31 6 having have VERB cana-3613 31 7 the the DET cana-3613 31 8 communications communication NOUN cana-3613 31 9 on on ADP cana-3613 31 10 applied apply VERB cana-3613 31 11 nonlinear nonlinear ADJ cana-3613 31 12 analysis analysis NOUN cana-3613 31 13 issn issn NOUN cana-3613 31 14 : : PUNCT cana-3613 31 15 1074 1074 NUM cana-3613 31 16 - - PUNCT cana-3613 31 17 133x 133x NUM cana-3613 31 18 vol vol NOUN cana-3613 31 19 32 32 NUM cana-3613 31 20 no no NOUN cana-3613 31 21 . . PUNCT cana-3613 32 1 8s 8s PROPN cana-3613 32 2 ( ( PUNCT cana-3613 32 3 2025 2025 NUM cana-3613 32 4 ) ) PUNCT cana-3613 32 5 124 124 NUM cana-3613 32 6 https://internationalpubls.com https://internationalpubls.com X cana-3613 32 7 server server NOUN cana-3613 32 8 in in ADP cana-3613 32 9 operative operative NOUN cana-3613 32 10 for for ADP cana-3613 32 11 periods period NOUN cana-3613 32 12 of of ADP cana-3613 32 13 time time NOUN cana-3613 32 14 may may AUX cana-3613 32 15 increase increase VERB cana-3613 32 16 the the DET cana-3613 32 17 probability probability NOUN cana-3613 32 18 of of ADP cana-3613 32 19 customer customer NOUN cana-3613 32 20 loss loss NOUN cana-3613 32 21 due due ADJ cana-3613 32 22 to to ADP cana-3613 32 23 reneging renege VERB cana-3613 32 24 . . PUNCT cana-3613 33 1 an an DET cana-3613 33 2 𝑀/𝑀/1 𝑀/𝑀/1 NOUN cana-3613 33 3 queue queue NOUN cana-3613 33 4 with with ADP cana-3613 33 5 customers customer NOUN cana-3613 33 6 reneging renege VERB cana-3613 33 7 has have AUX cana-3613 33 8 been be AUX cana-3613 33 9 discussed discuss VERB cana-3613 33 10 in in ADP cana-3613 33 11 haight haight NOUN cana-3613 34 1 [ [ X cana-3613 34 2 3 3 NUM cana-3613 34 3 ] ] PUNCT cana-3613 34 4 . . PUNCT cana-3613 35 1 laxmi laxmi PROPN cana-3613 35 2 et et PROPN cana-3613 35 3 al.[6 al.[6 PROPN cana-3613 35 4 ] ] PUNCT cana-3613 35 5 presented present VERB cana-3613 35 6 the the DET cana-3613 35 7 analysis analysis NOUN cana-3613 35 8 of of ADP cana-3613 35 9 finite finite ADJ cana-3613 35 10 buffer buffer NOUN cana-3613 35 11 markovian markovian PROPN cana-3613 35 12 queue queue NOUN cana-3613 35 13 with with ADP cana-3613 35 14 balking balk VERB cana-3613 35 15 , , PUNCT cana-3613 35 16 reneging renege VERB cana-3613 35 17 , , PUNCT cana-3613 35 18 and and CCONJ cana-3613 35 19 working working NOUN cana-3613 35 20 vacations vacation NOUN cana-3613 35 21 . . PUNCT cana-3613 36 1 selvaraju selvaraju NOUN cana-3613 36 2 and and CCONJ cana-3613 36 3 goswami goswami PROPN cana-3613 36 4 [ [ X cana-3613 36 5 8 8 NUM cana-3613 36 6 ] ] PUNCT cana-3613 36 7 studied study VERB cana-3613 36 8 impatient impatient ADJ cana-3613 36 9 customers customer NOUN cana-3613 36 10 in in ADP cana-3613 36 11 an an DET cana-3613 36 12 𝑀/𝑀/1 𝑀/𝑀/1 NOUN cana-3613 36 13 queue queue NOUN cana-3613 36 14 with with ADP cana-3613 36 15 single single ADJ cana-3613 36 16 and and CCONJ cana-3613 36 17 multiple multiple ADJ cana-3613 36 18 working work VERB cana-3613 36 19 vacations vacation NOUN cana-3613 36 20 . . PUNCT cana-3613 37 1 vijaya vijaya PROPN cana-3613 37 2 laxmi laxmi PROPN cana-3613 37 3 and and CCONJ cana-3613 37 4 jyotsna jyotsna NOUN cana-3613 38 1 [ [ X cana-3613 38 2 11 11 NUM cana-3613 38 3 ] ] PUNCT cana-3613 38 4 , , PUNCT cana-3613 38 5 analyzed analyze VERB cana-3613 38 6 the the DET cana-3613 38 7 impatient impatient ADJ cana-3613 38 8 customer customer NOUN cana-3613 38 9 queue queue NOUN cana-3613 38 10 with with ADP cana-3613 38 11 bernoulli bernoulli PROPN cana-3613 38 12 schedule schedule NOUN cana-3613 38 13 vacation vacation NOUN cana-3613 38 14 interruption interruption NOUN cana-3613 38 15 . . PUNCT cana-3613 39 1 this this DET cana-3613 39 2 paper paper NOUN cana-3613 39 3 is be AUX cana-3613 39 4 an an DET cana-3613 39 5 extension extension NOUN cana-3613 39 6 of of ADP cana-3613 39 7 the the DET cana-3613 39 8 earlier early ADJ cana-3613 39 9 of of ADP cana-3613 39 10 the the DET cana-3613 39 11 earlier early ADJ cana-3613 39 12 works work NOUN cana-3613 39 13 tian tian PROPN cana-3613 39 14 et et PROPN cana-3613 39 15 al al PROPN cana-3613 39 16 . . PUNCT cana-3613 40 1 [ [ X cana-3613 40 2 10 10 NUM cana-3613 40 3 ] ] PUNCT cana-3613 40 4 by by ADP cana-3613 40 5 including include VERB cana-3613 40 6 reneging renege VERB cana-3613 40 7 . . PUNCT cana-3613 41 1 using use VERB cana-3613 41 2 probability probability NOUN cana-3613 41 3 generating generating NOUN cana-3613 41 4 functions function NOUN cana-3613 41 5 , , PUNCT cana-3613 41 6 explicit explicit ADJ cana-3613 41 7 expressions expression NOUN cana-3613 41 8 of of ADP cana-3613 41 9 the the DET cana-3613 41 10 steady steady ADJ cana-3613 41 11 - - PUNCT cana-3613 41 12 state state NOUN cana-3613 41 13 probabilities probability NOUN cana-3613 41 14 are be AUX cana-3613 41 15 obtained obtain VERB cana-3613 41 16 . . PUNCT cana-3613 42 1 various various ADJ cana-3613 42 2 performance performance NOUN cana-3613 42 3 measures measure NOUN cana-3613 42 4 such such ADJ cana-3613 42 5 as as ADP cana-3613 42 6 the the DET cana-3613 42 7 average average ADJ cana-3613 42 8 system system NOUN cana-3613 42 9 length length NOUN cana-3613 42 10 , , PUNCT cana-3613 42 11 average average ADJ cana-3613 42 12 reneging renege VERB cana-3613 42 13 rate rate NOUN cana-3613 42 14 are be AUX cana-3613 42 15 discussed discuss VERB cana-3613 42 16 with with ADP cana-3613 42 17 these these DET cana-3613 42 18 performance performance NOUN cana-3613 42 19 measures measure NOUN cana-3613 42 20 , , PUNCT cana-3613 42 21 we we PRON cana-3613 42 22 demonstrate demonstrate VERB cana-3613 42 23 the the DET cana-3613 42 24 parameter parameter NOUN cana-3613 42 25 effect effect NOUN cana-3613 42 26 on on ADP cana-3613 42 27 the the DET cana-3613 42 28 performance performance NOUN cana-3613 42 29 indices index NOUN cana-3613 42 30 of of ADP cana-3613 42 31 the the DET cana-3613 42 32 system system NOUN cana-3613 42 33 . . PUNCT cana-3613 43 1 the the DET cana-3613 43 2 rest rest NOUN cana-3613 43 3 of of ADP cana-3613 43 4 the the DET cana-3613 43 5 paper paper NOUN cana-3613 43 6 is be AUX cana-3613 43 7 organized organize VERB cana-3613 43 8 as as SCONJ cana-3613 43 9 follows follow VERB cana-3613 43 10 . . PUNCT cana-3613 44 1 section section NOUN cana-3613 44 2 2 2 NUM cana-3613 44 3 presents present VERB cana-3613 44 4 description description NOUN cana-3613 44 5 of of ADP cana-3613 44 6 the the DET cana-3613 44 7 model model NOUN cana-3613 44 8 . . PUNCT cana-3613 45 1 the the DET cana-3613 45 2 explicit explicit ADJ cana-3613 45 3 expressions expression NOUN cana-3613 45 4 of of ADP cana-3613 45 5 the the DET cana-3613 45 6 steady steady ADJ cana-3613 45 7 - - PUNCT cana-3613 45 8 state state NOUN cana-3613 45 9 probabilities probability NOUN cana-3613 45 10 are be AUX cana-3613 45 11 obtained obtain VERB cana-3613 45 12 in in ADP cana-3613 45 13 section section NOUN cana-3613 45 14 3 3 NUM cana-3613 45 15 . . PUNCT cana-3613 46 1 a a DET cana-3613 46 2 variety variety NOUN cana-3613 46 3 of of ADP cana-3613 46 4 numerical numerical ADJ cana-3613 46 5 results result NOUN cana-3613 46 6 are be AUX cana-3613 46 7 presented present VERB cana-3613 46 8 in in ADP cana-3613 46 9 section section NOUN cana-3613 46 10 4 4 NUM cana-3613 46 11 followed follow VERB cana-3613 46 12 by by ADP cana-3613 46 13 conclusion conclusion NOUN cana-3613 46 14 in in ADP cana-3613 46 15 section section NOUN cana-3613 46 16 5 5 NUM cana-3613 46 17 . . SYM cana-3613 46 18 2 2 NUM cana-3613 46 19 model model NOUN cana-3613 46 20 description description NOUN cana-3613 46 21 let let VERB cana-3613 46 22 us we PRON cana-3613 46 23 consider consider VERB cana-3613 46 24 an an DET cana-3613 46 25 infinite infinite ADJ cana-3613 46 26 buffer buffer NOUN cana-3613 46 27 single single ADJ cana-3613 46 28 server server NOUN cana-3613 46 29 queueing queue VERB cana-3613 46 30 system system NOUN cana-3613 46 31 in in ADP cana-3613 46 32 which which PRON cana-3613 46 33 customers customer NOUN cana-3613 46 34 arrive arrive VERB cana-3613 46 35 according accord VERB cana-3613 46 36 to to ADP cana-3613 46 37 a a DET cana-3613 46 38 poisson poisson NOUN cana-3613 46 39 process process NOUN cana-3613 46 40 with with ADP cana-3613 46 41 rate rate NOUN cana-3613 46 42 πœ† πœ† NOUN cana-3613 46 43 and and CCONJ cana-3613 46 44 server server NOUN cana-3613 46 45 can can AUX cana-3613 46 46 serve serve VERB cana-3613 46 47 only only ADV cana-3613 46 48 one one NUM cana-3613 46 49 customer customer NOUN cana-3613 46 50 at at ADP cana-3613 46 51 a a DET cana-3613 46 52 time time NOUN cana-3613 46 53 with with ADP cana-3613 46 54 an an DET cana-3613 46 55 exponential exponential ADJ cana-3613 46 56 rate rate NOUN cana-3613 46 57 πœ‡. πœ‡. NOUN cana-3613 47 1 the the DET cana-3613 47 2 server server NOUN cana-3613 47 3 begins begin VERB cana-3613 47 4 a a DET cana-3613 47 5 working work VERB cana-3613 47 6 vacation vacation NOUN cana-3613 47 7 of of ADP cana-3613 47 8 random random ADJ cana-3613 47 9 length length NOUN cana-3613 47 10 𝑉 𝑉 PROPN cana-3613 47 11 at at ADP cana-3613 47 12 the the DET cana-3613 47 13 instant instant NOUN cana-3613 47 14 when when SCONJ cana-3613 47 15 the the DET cana-3613 47 16 queue queue NOUN cana-3613 47 17 becomes become VERB cana-3613 47 18 empty empty ADJ cana-3613 47 19 , , PUNCT cana-3613 47 20 and and CCONJ cana-3613 47 21 vacation vacation NOUN cana-3613 47 22 duration duration NOUN cana-3613 47 23 𝑉 𝑉 PROPN cana-3613 47 24 follows follow VERB cana-3613 47 25 an an DET cana-3613 47 26 exponential exponential ADJ cana-3613 47 27 distribution distribution NOUN cana-3613 47 28 with with ADP cana-3613 47 29 parameter parameter NOUN cana-3613 47 30 πœ™ πœ™ PROPN cana-3613 47 31 . . PUNCT cana-3613 48 1 during during ADP cana-3613 48 2 a a DET cana-3613 48 3 working work VERB cana-3613 48 4 vacation vacation NOUN cana-3613 48 5 an an DET cana-3613 48 6 arriving arrive VERB cana-3613 48 7 customer customer NOUN cana-3613 48 8 is be AUX cana-3613 48 9 served serve VERB cana-3613 48 10 at at ADP cana-3613 48 11 a a DET cana-3613 48 12 rate rate NOUN cana-3613 48 13 πœ‚. πœ‚. NOUN cana-3613 48 14 when when SCONJ cana-3613 48 15 a a DET cana-3613 48 16 vacation vacation NOUN cana-3613 48 17 ends end VERB cana-3613 48 18 , , PUNCT cana-3613 48 19 if if SCONJ cana-3613 48 20 there there PRON cana-3613 48 21 are be VERB cana-3613 48 22 customers customer NOUN cana-3613 48 23 in in ADP cana-3613 48 24 the the DET cana-3613 48 25 queue queue NOUN cana-3613 48 26 , , PUNCT cana-3613 48 27 the the DET cana-3613 48 28 server server NOUN cana-3613 48 29 changes change NOUN cana-3613 48 30 service service NOUN cana-3613 48 31 rate rate NOUN cana-3613 48 32 from from ADP cana-3613 48 33 πœ‚ πœ‚ NOUN cana-3613 48 34 to to ADP cana-3613 48 35 πœ‡ πœ‡ ADP cana-3613 48 36 and and CCONJ cana-3613 48 37 a a DET cana-3613 48 38 regular regular ADJ cana-3613 48 39 busy busy ADJ cana-3613 48 40 period period NOUN cana-3613 48 41 starts start VERB cana-3613 48 42 . . PUNCT cana-3613 49 1 otherwise otherwise ADV cana-3613 49 2 the the DET cana-3613 49 3 server server NOUN cana-3613 49 4 enters enter VERB cana-3613 49 5 idle idle ADJ cana-3613 49 6 period period NOUN cana-3613 49 7 , , PUNCT cana-3613 49 8 and and CCONJ cana-3613 49 9 a a DET cana-3613 49 10 new new ADJ cana-3613 49 11 regular regular ADJ cana-3613 49 12 busy busy ADJ cana-3613 49 13 period period NOUN cana-3613 49 14 starts start VERB cana-3613 49 15 when when SCONJ cana-3613 49 16 a a DET cana-3613 49 17 customer customer NOUN cana-3613 49 18 arrival arrival NOUN cana-3613 49 19 occurs occur VERB cana-3613 49 20 . . PUNCT cana-3613 50 1 an an DET cana-3613 50 2 arriving arrive VERB cana-3613 50 3 customer customer NOUN cana-3613 50 4 who who PRON cana-3613 50 5 joins join VERB cana-3613 50 6 the the DET cana-3613 50 7 system system NOUN cana-3613 50 8 and and CCONJ cana-3613 50 9 finds find VERB cana-3613 50 10 the the DET cana-3613 50 11 server server NOUN cana-3613 50 12 in in ADP cana-3613 50 13 π‘Šπ‘‰ π‘Šπ‘‰ PROPN cana-3613 50 14 , , PUNCT cana-3613 50 15 activates activate VERB cana-3613 50 16 an an DET cana-3613 50 17 impatient impatient ADJ cana-3613 50 18 timer timer NOUN cana-3613 50 19 𝑇 𝑇 PROPN cana-3613 50 20 , , PUNCT cana-3613 50 21 which which PRON cana-3613 50 22 is be AUX cana-3613 50 23 exponential exponential ADJ cana-3613 50 24 with with ADP cana-3613 50 25 rate rate NOUN cana-3613 50 26 𝛼. 𝛼. NOUN cana-3613 50 27 if if SCONJ cana-3613 50 28 the the DET cana-3613 50 29 server server NOUN cana-3613 50 30 is be AUX cana-3613 50 31 available available ADJ cana-3613 50 32 during during ADP cana-3613 50 33 π‘Šπ‘‰ π‘Šπ‘‰ PROPN cana-3613 50 34 before before ADP cana-3613 50 35 the the DET cana-3613 50 36 time time NOUN cana-3613 50 37 𝑇 𝑇 PROPN cana-3613 50 38 expires expire VERB cana-3613 50 39 , , PUNCT cana-3613 50 40 the the DET cana-3613 50 41 customer customer NOUN cana-3613 50 42 is be AUX cana-3613 50 43 served serve VERB cana-3613 50 44 with with ADP cana-3613 50 45 πœ‚. πœ‚. NOUN cana-3613 50 46 if if SCONJ cana-3613 50 47 π‘Šπ‘‰ π‘Šπ‘‰ PROPN cana-3613 50 48 finishes finish VERB cana-3613 50 49 before before SCONJ cana-3613 50 50 the the DET cana-3613 50 51 impatient impatient ADJ cana-3613 50 52 timer timer NOUN cana-3613 50 53 expires expire VERB cana-3613 50 54 , , PUNCT cana-3613 50 55 the the DET cana-3613 50 56 server server NOUN cana-3613 50 57 switches switch NOUN cana-3613 50 58 to to ADP cana-3613 50 59 normal normal ADJ cana-3613 50 60 working working NOUN cana-3613 50 61 period period NOUN cana-3613 50 62 , , PUNCT cana-3613 50 63 and and CCONJ cana-3613 50 64 the the DET cana-3613 50 65 customer customer NOUN cana-3613 50 66 is be AUX cana-3613 50 67 served serve VERB cana-3613 50 68 with with ADP cana-3613 50 69 rate rate NOUN cana-3613 50 70 πœ‡. πœ‡. NOUN cana-3613 50 71 since since SCONJ cana-3613 50 72 the the DET cana-3613 50 73 arrival arrival NOUN cana-3613 50 74 and and CCONJ cana-3613 50 75 departure departure NOUN cana-3613 50 76 of of ADP cana-3613 50 77 an an DET cana-3613 50 78 impatient impatient ADJ cana-3613 50 79 customer customer NOUN cana-3613 50 80 without without ADP cana-3613 50 81 service service NOUN cana-3613 50 82 are be AUX cana-3613 50 83 independent independent ADJ cana-3613 50 84 the the DET cana-3613 50 85 average average ADJ cana-3613 50 86 reneging renege VERB cana-3613 50 87 rate rate NOUN cana-3613 50 88 of of ADP cana-3613 50 89 a a DET cana-3613 50 90 customer customer NOUN cana-3613 50 91 is be AUX cana-3613 50 92 given give VERB cana-3613 50 93 by by ADP cana-3613 50 94 𝑛𝛼 𝑛𝛼 PROPN cana-3613 50 95 , , PUNCT cana-3613 50 96 where where SCONJ cana-3613 50 97 𝑛 𝑛 PROPN cana-3613 50 98 is be AUX cana-3613 50 99 the the DET cana-3613 50 100 number number NOUN cana-3613 50 101 of of ADP cana-3613 50 102 customers customer NOUN cana-3613 50 103 . . PUNCT cana-3613 51 1 3 3 NUM cana-3613 51 2 steady steady ADJ cana-3613 51 3 - - PUNCT cana-3613 51 4 state state NOUN cana-3613 51 5 probabilities probability NOUN cana-3613 51 6 at at ADP cana-3613 51 7 time time NOUN cana-3613 51 8 𝑑 𝑑 PROPN cana-3613 51 9 , , PUNCT cana-3613 51 10 let let AUX cana-3613 51 11 𝐿(𝑑 𝐿(𝑑 NOUN cana-3613 51 12 ) ) PUNCT cana-3613 51 13 denote denote VERB cana-3613 51 14 the the DET cana-3613 51 15 number number NOUN cana-3613 51 16 of of ADP cana-3613 51 17 customers customer NOUN cana-3613 51 18 in in ADP cana-3613 51 19 the the DET cana-3613 51 20 system system NOUN cana-3613 51 21 and and CCONJ cana-3613 51 22 𝐽(𝑑 𝐽(𝑑 PRON cana-3613 51 23 ) ) PUNCT cana-3613 51 24 be be VERB cana-3613 51 25 the the DET cana-3613 51 26 status status NOUN cana-3613 51 27 of of ADP cana-3613 51 28 the the DET cana-3613 51 29 server server NOUN cana-3613 51 30 , , PUNCT cana-3613 51 31 which which PRON cana-3613 51 32 is be AUX cana-3613 51 33 defined define VERB cana-3613 51 34 as as ADP cana-3613 51 35 𝐽(𝑑 𝐽(𝑑 NOUN cana-3613 51 36 ) ) PUNCT cana-3613 52 1 = = SYM cana-3613 52 2 0 0 NUM cana-3613 52 3 , , PUNCT cana-3613 52 4 when when SCONJ cana-3613 52 5 the the DET cana-3613 52 6 server server NOUN cana-3613 52 7 is be AUX cana-3613 52 8 in in ADP cana-3613 52 9 π‘Šπ‘‰ π‘Šπ‘‰ PROPN cana-3613 52 10 and and CCONJ cana-3613 52 11 𝐽(𝑑 𝐽(𝑑 PRON cana-3613 52 12 ) ) PUNCT cana-3613 52 13 = = SYM cana-3613 52 14 1 1 NUM cana-3613 52 15 , , PUNCT cana-3613 52 16 when when SCONJ cana-3613 52 17 server server NOUN cana-3613 52 18 is be AUX cana-3613 52 19 in in ADP cana-3613 52 20 normal normal ADJ cana-3613 52 21 working working NOUN cana-3613 52 22 period period NOUN cana-3613 52 23 . . PUNCT cana-3613 53 1 the the DET cana-3613 53 2 { { PUNCT cana-3613 53 3 ( ( PUNCT cana-3613 53 4 𝐽(𝑑 𝐽(𝑑 NOUN cana-3613 53 5 ) ) PUNCT cana-3613 53 6 , , PUNCT cana-3613 53 7 𝐿(𝑑 𝐿(𝑑 NOUN cana-3613 53 8 ) ) PUNCT cana-3613 53 9 ) ) PUNCT cana-3613 53 10 , , PUNCT cana-3613 53 11 𝑑 𝑑 PROPN cana-3613 53 12 β‰₯ β‰₯ NOUN cana-3613 53 13 0 0 NUM cana-3613 53 14 } } PUNCT cana-3613 53 15 is be AUX cana-3613 53 16 a a DET cana-3613 53 17 markov markov NOUN cana-3613 53 18 process process NOUN cana-3613 53 19 with with ADP cana-3613 53 20 the the DET cana-3613 53 21 state state NOUN cana-3613 53 22 space space NOUN cana-3613 53 23 Ο‰ Ο‰ PROPN cana-3613 53 24 = = SYM cana-3613 53 25 { { PUNCT cana-3613 53 26 ( ( PUNCT cana-3613 53 27 𝑗 𝑗 PROPN cana-3613 53 28 , , PUNCT cana-3613 53 29 𝑛 𝑛 NOUN cana-3613 53 30 ): ): PUNCT cana-3613 53 31 𝑛 𝑛 PRON cana-3613 53 32 β‰₯ β‰₯ NOUN cana-3613 53 33 0 0 NUM cana-3613 53 34 , , PUNCT cana-3613 53 35 𝑗 𝑗 NOUN cana-3613 53 36 = = SYM cana-3613 53 37 0,1 0,1 NUM cana-3613 53 38 } } PUNCT cana-3613 53 39 . . PUNCT cana-3613 54 1 let let VERB cana-3613 54 2 πœ‹π‘—,𝑛 πœ‹π‘—,𝑛 PUNCT cana-3613 54 3 = = SYM cana-3613 54 4 lim lim PROPN cana-3613 54 5 π‘‘β†’βˆž π‘‘β†’βˆž NUM cana-3613 54 6 πœ‹{𝐽(𝑑 πœ‹{𝐽(𝑑 PROPN cana-3613 54 7 ) ) PUNCT cana-3613 54 8 = = SYM cana-3613 54 9 𝑗 𝑗 PROPN cana-3613 54 10 , , PUNCT cana-3613 54 11 𝐿(𝑑 𝐿(𝑑 ADV cana-3613 54 12 ) ) PUNCT cana-3613 54 13 = = SYM cana-3613 54 14 𝑛 𝑛 PROPN cana-3613 54 15 } } PUNCT cana-3613 54 16 , , PUNCT cana-3613 54 17 𝑛 𝑛 DET cana-3613 54 18 β‰₯ β‰₯ NOUN cana-3613 54 19 0 0 NUM cana-3613 54 20 , , PUNCT cana-3613 54 21 𝑗 𝑗 NOUN cana-3613 54 22 = = SYM cana-3613 54 23 0,1 0,1 NUM cana-3613 54 24 , , PUNCT cana-3613 54 25 denote denote VERB cana-3613 54 26 the the DET cana-3613 54 27 steady steady ADJ cana-3613 54 28 - - PUNCT cana-3613 54 29 state state NOUN cana-3613 54 30 probabilities probability NOUN cana-3613 54 31 of of ADP cana-3613 54 32 the the DET cana-3613 54 33 process process NOUN cana-3613 54 34 { { PUNCT cana-3613 54 35 ( ( PUNCT cana-3613 54 36 𝐽(𝑑 𝐽(𝑑 NOUN cana-3613 54 37 ) ) PUNCT cana-3613 54 38 , , PUNCT cana-3613 54 39 𝐿(𝑑 𝐿(𝑑 NOUN cana-3613 54 40 ) ) PUNCT cana-3613 54 41 ) ) PUNCT cana-3613 54 42 , , PUNCT cana-3613 54 43 𝑑 𝑑 PROPN cana-3613 54 44 β‰₯ β‰₯ NOUN cana-3613 54 45 0 0 NUM cana-3613 54 46 } } PUNCT cana-3613 54 47 . . PUNCT cana-3613 55 1 then then ADV cana-3613 55 2 , , PUNCT cana-3613 55 3 the the DET cana-3613 55 4 set set NOUN cana-3613 55 5 of of ADP cana-3613 55 6 balance balance NOUN cana-3613 55 7 equations equation NOUN cana-3613 55 8 are be AUX cana-3613 55 9 given give VERB cana-3613 55 10 as as SCONJ cana-3613 55 11 follows follow VERB cana-3613 55 12 : : PUNCT cana-3613 55 13 ( ( PUNCT cana-3613 55 14 + + NOUN cana-3613 55 15 ) ) PUNCT cana-3613 56 1 _ _ NOUN cana-3613 56 2 0,0 0,0 NUM cana-3613 56 3 = = SYM cana-3613 56 4 ( ( PUNCT cana-3613 56 5 + + NOUN cana-3613 56 6 ) ) PUNCT cana-3613 56 7 _ _ NOUN cana-3613 56 8 0,1+_1,1 0,1+_1,1 NUM cana-3613 56 9 , , PUNCT cana-3613 56 10 ( ( PUNCT cana-3613 56 11 + + ADJ cana-3613 56 12 + + ADJ cana-3613 56 13 + + NOUN cana-3613 56 14 ) ) PUNCT cana-3613 56 15 _ _ NOUN cana-3613 56 16 0,1 0,1 NUM cana-3613 57 1 = = SYM cana-3613 57 2 _ _ NOUN cana-3613 57 3 0,0+(+2)_0,2 0,0+(+2)_0,2 NUM cana-3613 57 4 , , PUNCT cana-3613 57 5 ( ( PUNCT cana-3613 57 6 + + ADJ cana-3613 57 7 + + ADJ cana-3613 57 8 + + NOUN cana-3613 57 9 n)_0,n n)_0,n ADJ cana-3613 57 10 = = X cana-3613 58 1 _ _ NOUN cana-3613 58 2 0,n-1+(+(n+1))_0,n+1 0,n-1+(+(n+1))_0,n+1 ADJ cana-3613 58 3 ; ; PUNCT cana-3613 58 4 n n PROPN cana-3613 58 5 2 2 NUM cana-3613 58 6 , , PUNCT cana-3613 58 7 communications communication NOUN cana-3613 58 8 on on ADP cana-3613 58 9 applied apply VERB cana-3613 58 10 nonlinear nonlinear ADJ cana-3613 58 11 analysis analysis NOUN cana-3613 58 12 issn issn NOUN cana-3613 58 13 : : PUNCT cana-3613 58 14 1074 1074 NUM cana-3613 58 15 - - PUNCT cana-3613 58 16 133x 133x NUM cana-3613 58 17 vol vol NOUN cana-3613 58 18 32 32 NUM cana-3613 58 19 no no NOUN cana-3613 58 20 . . PUNCT cana-3613 59 1 8s 8s PROPN cana-3613 59 2 ( ( PUNCT cana-3613 59 3 2025 2025 NUM cana-3613 59 4 ) ) PUNCT cana-3613 59 5 125 125 NUM cana-3613 59 6 https://internationalpubls.com https://internationalpubls.com X cana-3613 60 1 _ _ PUNCT cana-3613 60 2 1,0 1,0 NUM cana-3613 60 3 = = PUNCT cana-3613 60 4 _ _ NOUN cana-3613 60 5 0,0 0,0 NOUN cana-3613 60 6 , , PUNCT cana-3613 60 7 ( ( PUNCT cana-3613 60 8 + + NOUN cana-3613 60 9 ) ) PUNCT cana-3613 60 10 _ _ NOUN cana-3613 61 1 1,1 1,1 NUM cana-3613 62 1 = = PUNCT cana-3613 63 1 _ _ PUNCT cana-3613 63 2 1,0+_1,2+_0,1 1,0+_1,2+_0,1 NOUN cana-3613 63 3 , , PUNCT cana-3613 63 4 ( ( PUNCT cana-3613 63 5 + + NOUN cana-3613 63 6 ) ) PUNCT cana-3613 63 7 _ _ SYM cana-3613 63 8 1,n 1,n X cana-3613 64 1 = = PUNCT cana-3613 64 2 _ _ NOUN cana-3613 64 3 1,n-1+_1,n+1+_0,n 1,n-1+_1,n+1+_0,n NUM cana-3613 64 4 ; ; PUNCT cana-3613 64 5 n2 n2 ADJ cana-3613 64 6 . . PUNCT cana-3613 65 1 the the DET cana-3613 65 2 steady steady ADJ cana-3613 65 3 state state NOUN cana-3613 65 4 probabilities probability NOUN cana-3613 65 5 are be AUX cana-3613 65 6 obtained obtain VERB cana-3613 65 7 by by ADP cana-3613 65 8 solving solve VERB cana-3613 65 9 the the DET cana-3613 65 10 above above ADJ cana-3613 65 11 system system NOUN cana-3613 65 12 of of ADP cana-3613 65 13 equations equation NOUN cana-3613 65 14 ( ( PUNCT cana-3613 65 15 3)-(3 3)-(3 NUM cana-3613 65 16 ) ) PUNCT cana-3613 65 17 using use VERB cana-3613 65 18 probability probability NOUN cana-3613 65 19 generating generating NOUN cana-3613 65 20 function function NOUN cana-3613 65 21 . . PUNCT cana-3613 66 1 define define VERB cana-3613 66 2 𝐺0(𝑧 𝐺0(𝑧 NOUN cana-3613 66 3 ) ) PUNCT cana-3613 66 4 and and CCONJ cana-3613 66 5 𝐺1(𝑧 𝐺1(𝑧 NOUN cana-3613 66 6 ) ) PUNCT cana-3613 66 7 as as ADP cana-3613 66 8 𝐺0(𝑧 𝐺0(𝑧 NOUN cana-3613 66 9 ) ) PUNCT cana-3613 66 10 = = PUNCT cana-3613 66 11 βˆ‘βˆž βˆ‘βˆž X cana-3613 66 12 𝑛=0 𝑛=0 PROPN cana-3613 66 13 π‘§π‘›πœ‹0,𝑛 π‘§π‘›πœ‹0,𝑛 PROPN cana-3613 66 14 , , PUNCT cana-3613 66 15 𝐺1(𝑍 𝐺1(𝑍 PROPN cana-3613 66 16 ) ) PUNCT cana-3613 66 17 = = PUNCT cana-3613 67 1 βˆ‘βˆž βˆ‘βˆž NOUN cana-3613 67 2 𝑛=0 𝑛=0 PROPN cana-3613 68 1 π‘§π‘›πœ‹1,𝑛 π‘§π‘›πœ‹1,𝑛 PROPN cana-3613 68 2 , , PUNCT cana-3613 68 3 with with ADP cana-3613 68 4 𝐺0(1 𝐺0(1 NOUN cana-3613 68 5 ) ) PUNCT cana-3613 68 6 + + PUNCT cana-3613 68 7 𝐺1(1 𝐺1(1 NUM cana-3613 68 8 ) ) PUNCT cana-3613 68 9 = = SYM cana-3613 68 10 1 1 X cana-3613 68 11 . . PUNCT cana-3613 68 12 and and CCONJ cana-3613 68 13 𝐺0 𝐺0 NUM cana-3613 68 14 β€² β€² NUM cana-3613 68 15 ( ( PUNCT cana-3613 68 16 𝑧 𝑧 NOUN cana-3613 68 17 ) ) PUNCT cana-3613 68 18 = = SYM cana-3613 68 19 ( ( PUNCT cana-3613 68 20 𝑑/𝑑𝑧)𝐺0(𝑧 𝑑/𝑑𝑧)𝐺0(𝑧 ADJ cana-3613 68 21 ) ) PUNCT cana-3613 68 22 = = SYM cana-3613 68 23 βˆ‘βˆž βˆ‘βˆž X cana-3613 68 24 𝑛=1 𝑛=1 NOUN cana-3613 68 25 π‘›π‘§π‘›βˆ’1πœ‹0,𝑛 π‘›π‘§π‘›βˆ’1πœ‹0,𝑛 X cana-3613 68 26 . . PUNCT cana-3613 69 1 multiplying multiply VERB cana-3613 69 2 equations equation NOUN cana-3613 69 3 ( ( PUNCT cana-3613 69 4 3)-(3 3)-(3 NUM cana-3613 69 5 ) ) PUNCT cana-3613 69 6 by by ADP cana-3613 69 7 1 1 NUM cana-3613 69 8 , , PUNCT cana-3613 69 9 𝑧 𝑧 PRON cana-3613 69 10 , , PUNCT cana-3613 69 11 𝑧𝑛 𝑧𝑛 INTJ cana-3613 69 12 ; ; PUNCT cana-3613 69 13 respectively respectively ADV cana-3613 69 14 , , PUNCT cana-3613 69 15 summing sum VERB cana-3613 69 16 over over ADP cana-3613 69 17 n n ADV cana-3613 69 18 and and CCONJ cana-3613 69 19 rearranging rearrange VERB cana-3613 69 20 the the DET cana-3613 69 21 terms term NOUN cana-3613 69 22 . . PUNCT cana-3613 70 1 we we PRON cana-3613 70 2 get get VERB cana-3613 70 3 𝛼𝑧(1 𝛼𝑧(1 ADJ cana-3613 70 4 βˆ’ βˆ’ NOUN cana-3613 70 5 𝑧)𝐺0 𝑧)𝐺0 NOUN cana-3613 70 6 β€² β€² NUM cana-3613 70 7 ( ( PUNCT cana-3613 70 8 𝑧 𝑧 X cana-3613 70 9 ) ) PUNCT cana-3613 70 10 + + CCONJ cana-3613 70 11 ( ( PUNCT cana-3613 70 12 πœ†π‘§2 πœ†π‘§2 NOUN cana-3613 70 13 βˆ’ βˆ’ PROPN cana-3613 70 14 ( ( PUNCT cana-3613 70 15 πœ† πœ† ADP cana-3613 70 16 + + NUM cana-3613 70 17 πœ™ πœ™ NOUN cana-3613 70 18 + + CCONJ cana-3613 70 19 πœ‚)𝑧 πœ‚)𝑧 PUNCT cana-3613 70 20 + + CCONJ cana-3613 70 21 πœ‚)𝐺0(𝑧 πœ‚)𝐺0(𝑧 X cana-3613 70 22 ) ) PUNCT cana-3613 70 23 + + CCONJ cana-3613 70 24 πœ‡πœ‹1,1𝑧 πœ‡πœ‹1,1𝑧 PROPN cana-3613 70 25 βˆ’ βˆ’ PROPN cana-3613 70 26 ( ( PUNCT cana-3613 70 27 1 1 NUM cana-3613 70 28 βˆ’ βˆ’ PROPN cana-3613 70 29 𝑧)πœ‚πœ‹0,0 𝑧)πœ‚πœ‹0,0 NOUN cana-3613 70 30 = = SYM cana-3613 70 31 0 0 NUM cana-3613 70 32 . . PUNCT cana-3613 71 1 ( ( PUNCT cana-3613 71 2 1 1 X cana-3613 71 3 ) ) PUNCT cana-3613 71 4 in in ADP cana-3613 71 5 similar similar ADJ cana-3613 71 6 manner manner NOUN cana-3613 71 7 , , PUNCT cana-3613 71 8 from from ADP cana-3613 71 9 equations equation NOUN cana-3613 71 10 ( ( PUNCT cana-3613 71 11 3)-(3 3)-(3 NUM cana-3613 71 12 ) ) PUNCT cana-3613 71 13 , , PUNCT cana-3613 71 14 we we PRON cana-3613 71 15 have have VERB cana-3613 71 16 ( ( PUNCT cana-3613 71 17 πœ†π‘§ πœ†π‘§ NOUN cana-3613 71 18 βˆ’ βˆ’ NOUN cana-3613 71 19 πœ‡)(1 πœ‡)(1 NOUN cana-3613 72 1 βˆ’ βˆ’ PROPN cana-3613 72 2 𝑧)𝐺1(𝑧 𝑧)𝐺1(𝑧 PROPN cana-3613 72 3 ) ) PUNCT cana-3613 72 4 = = SYM cana-3613 72 5 πœ™π‘§πΊ0(𝑧 πœ™π‘§πΊ0(𝑧 PROPN cana-3613 72 6 ) ) PUNCT cana-3613 72 7 βˆ’ βˆ’ PROPN cana-3613 73 1 πœ‡(1 πœ‡(1 PROPN cana-3613 73 2 βˆ’ βˆ’ PROPN cana-3613 73 3 𝑧)πœ‹1,0 𝑧)πœ‹1,0 PROPN cana-3613 73 4 βˆ’ βˆ’ PROPN cana-3613 73 5 πœ‡πœ‹1,1𝑧. πœ‡πœ‹1,1𝑧. NOUN cana-3613 73 6 ( ( PUNCT cana-3613 73 7 2 2 NUM cana-3613 73 8 ) ) PUNCT cana-3613 73 9 from from ADP cana-3613 73 10 equation equation NOUN cana-3613 73 11 ( ( PUNCT cana-3613 73 12 1 1 X cana-3613 73 13 ) ) PUNCT cana-3613 73 14 can can AUX cana-3613 73 15 be be AUX cana-3613 73 16 written write VERB cana-3613 73 17 as as ADP cana-3613 73 18 𝐺0 𝐺0 NOUN cana-3613 73 19 β€² β€² NUM cana-3613 73 20 ( ( PUNCT cana-3613 73 21 𝑧 𝑧 NOUN cana-3613 73 22 ) ) PUNCT cana-3613 73 23 βˆ’ βˆ’ PROPN cana-3613 74 1 ( ( PUNCT cana-3613 74 2 πœ† πœ† ADP cana-3613 74 3 𝛼 𝛼 X cana-3613 74 4 + + X cana-3613 74 5 ( ( PUNCT cana-3613 74 6 πœ™+πœ‚ πœ™+πœ‚ NUM cana-3613 74 7 ) ) PUNCT cana-3613 74 8 𝛼(1βˆ’π‘§ 𝛼(1βˆ’π‘§ NOUN cana-3613 74 9 ) ) PUNCT cana-3613 75 1 βˆ’ βˆ’ NOUN cana-3613 75 2 πœ‚ πœ‚ NOUN cana-3613 75 3 𝛼𝑧(1βˆ’π‘§ 𝛼𝑧(1βˆ’π‘§ NOUN cana-3613 75 4 ) ) PUNCT cana-3613 75 5 ) ) PUNCT cana-3613 76 1 𝐺0(𝑧 𝐺0(𝑧 X cana-3613 76 2 ) ) PUNCT cana-3613 76 3 = = SYM cana-3613 77 1 πœ‚ πœ‚ NOUN cana-3613 77 2 𝛼𝑧 𝛼𝑧 NUM cana-3613 77 3 πœ‹0,0 πœ‹0,0 NOUN cana-3613 77 4 βˆ’ βˆ’ PROPN cana-3613 77 5 πœ‡ πœ‡ ADP cana-3613 77 6 𝛼(1βˆ’π‘§ 𝛼(1βˆ’π‘§ NOUN cana-3613 77 7 ) ) PUNCT cana-3613 77 8 πœ‹1,1 πœ‹1,1 PROPN cana-3613 77 9 for for ADP cana-3613 77 10 𝑧 𝑧 DET cana-3613 77 11 β‰  β‰  PROPN cana-3613 77 12 0 0 NUM cana-3613 77 13 and and CCONJ cana-3613 77 14 𝑧 𝑧 DET cana-3613 77 15 β‰  β‰  PROPN cana-3613 77 16 1 1 NUM cana-3613 77 17 . . X cana-3613 77 18 multiplying multiply VERB cana-3613 77 19 with with ADP cana-3613 77 20 π‘’βˆ’(πœ†/𝛼)𝑧(1 π‘’βˆ’(πœ†/𝛼)𝑧(1 NOUN cana-3613 77 21 βˆ’ βˆ’ PROPN cana-3613 77 22 𝑧)πœ™/π›Όπ‘§πœ‚/𝛼 𝑧)πœ™/π›Όπ‘§πœ‚/𝛼 PROPN cana-3613 77 23 on on ADP cana-3613 77 24 both both DET cana-3613 77 25 sides side NOUN cana-3613 77 26 in in ADP cana-3613 77 27 the the DET cana-3613 77 28 above above ADJ cana-3613 77 29 equation equation NOUN cana-3613 77 30 and and CCONJ cana-3613 77 31 integrating integrate VERB cana-3613 77 32 from from ADP cana-3613 77 33 0 0 NUM cana-3613 77 34 to to ADP cana-3613 77 35 𝑧 𝑧 DET cana-3613 77 36 yields yield NOUN cana-3613 77 37 , , PUNCT cana-3613 77 38 g_0(z)=-_1,1k_1(z)+_0,0k_2(z g_0(z)=-_1,1k_1(z)+_0,0k_2(z VERB cana-3613 77 39 ) ) PUNCT cana-3613 77 40 e^-(/)z(1 e^-(/)z(1 ADJ cana-3613 77 41 - - PUNCT cana-3613 77 42 z)^/ z)^/ X cana-3613 77 43 z^/ z^/ NUM cana-3613 77 44 , , PUNCT cana-3613 77 45 where where SCONJ cana-3613 77 46 k_1(z)=_0^ze^-(/)x(1 k_1(z)=_0^ze^-(/)x(1 PROPN cana-3613 77 47 - - PUNCT cana-3613 77 48 x)^(/)-1x^/dx x)^(/)-1x^/dx PROPN cana-3613 77 49 , , PUNCT cana-3613 77 50 k_2(z)=_0^ze^-(/)x(1 k_2(z)=_0^ze^-(/)x(1 PROPN cana-3613 77 51 - - PUNCT cana-3613 77 52 x)^/x^(/)-1dx x)^/x^(/)-1dx PROPN cana-3613 77 53 . . PUNCT cana-3613 78 1 let let VERB cana-3613 78 2 𝐺0(1 𝐺0(1 NOUN cana-3613 78 3 ) ) PUNCT cana-3613 78 4 and and CCONJ cana-3613 78 5 𝐺1(1 𝐺1(1 ADJ cana-3613 78 6 ) ) PUNCT cana-3613 78 7 denotes denote VERB cana-3613 78 8 the the DET cana-3613 78 9 sum sum NOUN cana-3613 78 10 of of ADP cana-3613 78 11 probabilities probability NOUN cana-3613 78 12 when when SCONJ cana-3613 78 13 the the DET cana-3613 78 14 server server NOUN cana-3613 78 15 is be AUX cana-3613 78 16 in in ADP cana-3613 78 17 working work VERB cana-3613 78 18 vacation vacation NOUN cana-3613 78 19 and and CCONJ cana-3613 78 20 normal normal ADJ cana-3613 78 21 busy busy ADJ cana-3613 78 22 period period NOUN cana-3613 78 23 and and CCONJ cana-3613 78 24 define define VERB cana-3613 78 25 𝐺0(1 𝐺0(1 NOUN cana-3613 78 26 ) ) PUNCT cana-3613 78 27 = = NOUN cana-3613 79 1 βˆ‘βˆž βˆ‘βˆž X cana-3613 79 2 𝑛=0 𝑛=0 PROPN cana-3613 79 3 πœ‹0,𝑛 πœ‹0,𝑛 ADJ cana-3613 79 4 and and CCONJ cana-3613 79 5 𝐺1(1 𝐺1(1 NUM cana-3613 79 6 ) ) PUNCT cana-3613 79 7 = = NOUN cana-3613 79 8 βˆ‘βˆž βˆ‘βˆž X cana-3613 79 9 𝑛=0 𝑛=0 X cana-3613 79 10 πœ‹1,𝑛 πœ‹1,𝑛 PROPN cana-3613 79 11 , , PUNCT cana-3613 79 12 respectively respectively ADV cana-3613 79 13 . . PUNCT cana-3613 80 1 taking take VERB cana-3613 80 2 𝑧 𝑧 X cana-3613 80 3 = = NOUN cana-3613 80 4 1 1 NUM cana-3613 80 5 in in ADP cana-3613 80 6 equation equation NOUN cana-3613 80 7 ( ( PUNCT cana-3613 80 8 3 3 NUM cana-3613 80 9 ) ) PUNCT cana-3613 80 10 , , PUNCT cana-3613 80 11 we we PRON cana-3613 80 12 get get VERB cana-3613 80 13 πœ‡πœ‹1,1π‘˜1(1 πœ‡πœ‹1,1π‘˜1(1 NOUN cana-3613 80 14 ) ) PUNCT cana-3613 80 15 = = SYM cana-3613 80 16 πœ‚πœ‹0,0π‘˜2(1 πœ‚πœ‹0,0π‘˜2(1 NOUN cana-3613 80 17 ) ) PUNCT cana-3613 80 18 . . PUNCT cana-3613 81 1 ( ( PUNCT cana-3613 81 2 3 3 X cana-3613 81 3 ) ) PUNCT cana-3613 81 4 therefore therefore ADV cana-3613 81 5 equation equation NOUN cana-3613 81 6 ( ( PUNCT cana-3613 81 7 3 3 X cana-3613 81 8 ) ) PUNCT cana-3613 81 9 becomes become VERB cana-3613 81 10 as as ADP cana-3613 81 11 𝐺0(𝑧 𝐺0(𝑧 NOUN cana-3613 81 12 ) ) PUNCT cana-3613 81 13 = = PUNCT cana-3613 82 1 𝑒(πœ†/𝛼)𝑧 𝑒(πœ†/𝛼)𝑧 X cana-3613 82 2 ( ( PUNCT cana-3613 82 3 1βˆ’π‘§)πœ™/π›Όπ‘§πœ‚/𝛼 1βˆ’π‘§)πœ™/π›Όπ‘§πœ‚/𝛼 X cana-3613 82 4 [ [ X cana-3613 82 5 π‘˜2(𝑧 π‘˜2(𝑧 NOUN cana-3613 82 6 ) ) PUNCT cana-3613 82 7 βˆ’ βˆ’ PROPN cana-3613 82 8 π‘˜2(1 π‘˜2(1 NOUN cana-3613 82 9 ) ) PUNCT cana-3613 82 10 π‘˜1(1 π‘˜1(1 NOUN cana-3613 82 11 ) ) PUNCT cana-3613 82 12 π‘˜1(𝑧 π‘˜1(𝑧 PROPN cana-3613 82 13 ) ) PUNCT cana-3613 82 14 ] ] PUNCT cana-3613 82 15 πœ‚ πœ‚ X cana-3613 82 16 𝛼 𝛼 NOUN cana-3613 82 17 πœ‹0,0 πœ‹0,0 PROPN cana-3613 82 18 . . PUNCT cana-3613 82 19 ( ( PUNCT cana-3613 82 20 4 4 X cana-3613 82 21 ) ) PUNCT cana-3613 82 22 the the DET cana-3613 82 23 average average ADJ cana-3613 82 24 number number NOUN cana-3613 82 25 of of ADP cana-3613 82 26 customers customer NOUN cana-3613 82 27 in in ADP cana-3613 82 28 the the DET cana-3613 82 29 system system NOUN cana-3613 82 30 during during ADP cana-3613 82 31 a a DET cana-3613 82 32 working work VERB cana-3613 82 33 vacation vacation NOUN cana-3613 82 34 is be AUX cana-3613 82 35 dinotes dinote NOUN cana-3613 82 36 𝐸[𝐿0 𝐸[𝐿0 X cana-3613 82 37 ] ] PUNCT cana-3613 82 38 and and CCONJ cana-3613 82 39 define define VERB cana-3613 82 40 𝐸[𝐿0 𝐸[𝐿0 X cana-3613 82 41 ] ] X cana-3613 82 42 = = X cana-3613 82 43 𝐺0 𝐺0 X cana-3613 82 44 β€² β€² NUM cana-3613 82 45 ( ( PUNCT cana-3613 82 46 1 1 NUM cana-3613 82 47 ) ) PUNCT cana-3613 82 48 = = NOUN cana-3613 82 49 βˆ‘βˆž βˆ‘βˆž NOUN cana-3613 82 50 𝑛=1 𝑛=1 NOUN cana-3613 82 51 π‘›πœ‹0,𝑛. π‘›πœ‹0,𝑛. NUM cana-3613 82 52 from from ADP cana-3613 82 53 the the DET cana-3613 82 54 equation(1 equation(1 NOUN cana-3613 82 55 ) ) PUNCT cana-3613 82 56 , , PUNCT cana-3613 82 57 𝐺0 𝐺0 PROPN cana-3613 82 58 β€² β€² NUM cana-3613 82 59 ( ( PUNCT cana-3613 82 60 𝑧 𝑧 NOUN cana-3613 82 61 ) ) PUNCT cana-3613 82 62 = = SYM cana-3613 82 63 ( ( PUNCT cana-3613 82 64 1βˆ’π‘§)πœ‚πœ‹0,0βˆ’(πœ†π‘§2βˆ’(πœ†+πœ™+πœ‚)𝑧+πœ‚)𝐺0(𝑧)βˆ’πœ‡πœ‹1,1𝑧 1βˆ’π‘§)πœ‚πœ‹0,0βˆ’(πœ†π‘§2βˆ’(πœ†+πœ™+πœ‚)𝑧+πœ‚)𝐺0(𝑧)βˆ’πœ‡πœ‹1,1𝑧 NUM cana-3613 82 65 𝛼𝑧(1βˆ’π‘§ 𝛼𝑧(1βˆ’π‘§ NOUN cana-3613 82 66 ) ) PUNCT cana-3613 82 67 . . PUNCT cana-3613 83 1 take take VERB cana-3613 83 2 𝑧 𝑧 NOUN cana-3613 83 3 = = NOUN cana-3613 83 4 1 1 NUM cana-3613 83 5 and and CCONJ cana-3613 83 6 using use VERB cana-3613 83 7 l’hospital l’hospital NOUN cana-3613 83 8 rule rule NOUN cana-3613 83 9 , , PUNCT cana-3613 83 10 𝐺0 𝐺0 NUM cana-3613 83 11 β€² β€² NUM cana-3613 83 12 ( ( PUNCT cana-3613 83 13 1 1 X cana-3613 83 14 ) ) PUNCT cana-3613 83 15 can can AUX cana-3613 83 16 be be AUX cana-3613 83 17 obtained obtain VERB cana-3613 83 18 as as ADP cana-3613 83 19 𝐺0 𝐺0 NOUN cana-3613 83 20 β€² β€² NUM cana-3613 83 21 ( ( PUNCT cana-3613 83 22 1 1 NUM cana-3613 83 23 ) ) PUNCT cana-3613 83 24 = = SYM cana-3613 83 25 ( ( PUNCT cana-3613 83 26 πœ†βˆ’πœ‚)𝐺0(1)+πœ‚πœ‹0,0 πœ†βˆ’πœ‚)𝐺0(1)+πœ‚πœ‹0,0 NOUN cana-3613 83 27 ( ( PUNCT cana-3613 83 28 𝛼+πœ™ 𝛼+πœ™ PROPN cana-3613 83 29 ) ) PUNCT cana-3613 83 30 . . PUNCT cana-3613 84 1 ( ( PUNCT cana-3613 84 2 5 5 X cana-3613 84 3 ) ) PUNCT cana-3613 84 4 now now ADV cana-3613 84 5 we we PRON cana-3613 84 6 obtained obtain VERB cana-3613 84 7 𝐺0(1 𝐺0(1 NOUN cana-3613 84 8 ) ) PUNCT cana-3613 84 9 and and CCONJ cana-3613 84 10 πœ‹0,0 πœ‹0,0 NOUN cana-3613 84 11 . . PUNCT cana-3613 85 1 taking take VERB cana-3613 85 2 𝑧 𝑧 X cana-3613 85 3 = = NOUN cana-3613 85 4 1 1 NUM cana-3613 85 5 in in ADP cana-3613 85 6 equation equation NOUN cana-3613 85 7 ( ( PUNCT cana-3613 85 8 2 2 NUM cana-3613 85 9 ) ) PUNCT cana-3613 85 10 , , PUNCT cana-3613 85 11 we we PRON cana-3613 85 12 have have VERB cana-3613 85 13 𝐺0(1 𝐺0(1 NUM cana-3613 85 14 ) ) PUNCT cana-3613 86 1 = = PRON cana-3613 86 2 πœ‡πœ‹1,1 πœ‡πœ‹1,1 VERB cana-3613 86 3 πœ™ πœ™ X cana-3613 86 4 . . PUNCT cana-3613 87 1 ( ( PUNCT cana-3613 87 2 6 6 X cana-3613 87 3 ) ) PUNCT cana-3613 87 4 communications communication NOUN cana-3613 87 5 on on ADP cana-3613 87 6 applied apply VERB cana-3613 87 7 nonlinear nonlinear ADJ cana-3613 87 8 analysis analysis NOUN cana-3613 87 9 issn issn NOUN cana-3613 87 10 : : PUNCT cana-3613 87 11 1074 1074 NUM cana-3613 87 12 - - PUNCT cana-3613 87 13 133x 133x NUM cana-3613 87 14 vol vol NOUN cana-3613 87 15 32 32 NUM cana-3613 87 16 no no NOUN cana-3613 87 17 . . PUNCT cana-3613 88 1 8s 8s PROPN cana-3613 88 2 ( ( PUNCT cana-3613 88 3 2025 2025 NUM cana-3613 88 4 ) ) PUNCT cana-3613 88 5 126 126 NUM cana-3613 88 6 https://internationalpubls.com https://internationalpubls.com X cana-3613 88 7 from from ADP cana-3613 88 8 equation equation NOUN cana-3613 88 9 ( ( PUNCT cana-3613 88 10 2 2 NUM cana-3613 88 11 ) ) PUNCT cana-3613 88 12 , , PUNCT cana-3613 88 13 𝐺1(𝑧 𝐺1(𝑧 PROPN cana-3613 88 14 ) ) PUNCT cana-3613 88 15 = = SYM cana-3613 88 16 πœ™π‘§πΊ0(𝑧)βˆ’πœ‡(1βˆ’π‘§)πœ‹1,0βˆ’πœ‡πœ‹1,1𝑧 πœ™π‘§πΊ0(𝑧)βˆ’πœ‡(1βˆ’π‘§)πœ‹1,0βˆ’πœ‡πœ‹1,1𝑧 NOUN cana-3613 88 17 ( ( PUNCT cana-3613 88 18 πœ†π‘§βˆ’πœ‡)(1βˆ’π‘§ πœ†π‘§βˆ’πœ‡)(1βˆ’π‘§ PROPN cana-3613 88 19 ) ) PUNCT cana-3613 88 20 , , PUNCT cana-3613 88 21 and and CCONJ cana-3613 88 22 using use VERB cana-3613 88 23 l’hospital l’hospital NOUN cana-3613 88 24 rule rule NOUN cana-3613 88 25 by by ADP cana-3613 88 26 taking take VERB cana-3613 88 27 𝑧 𝑧 X cana-3613 88 28 = = ADJ cana-3613 88 29 1 1 NUM cana-3613 88 30 , , PUNCT cana-3613 88 31 then then ADV cana-3613 88 32 𝐺1(1 𝐺1(1 NUM cana-3613 88 33 ) ) PUNCT cana-3613 88 34 can can AUX cana-3613 88 35 be be AUX cana-3613 88 36 obtained obtain VERB cana-3613 88 37 as as ADP cana-3613 88 38 𝐺1(1 𝐺1(1 ADJ cana-3613 88 39 ) ) PUNCT cana-3613 89 1 = = SYM cana-3613 89 2 πœ™πΊ0 πœ™πΊ0 NOUN cana-3613 89 3 β€² β€² NUM cana-3613 90 1 ( ( PUNCT cana-3613 90 2 1)+πœ‡πœ‹1,0 1)+πœ‡πœ‹1,0 NUM cana-3613 90 3 ( ( PUNCT cana-3613 90 4 πœ‡βˆ’πœ† πœ‡βˆ’πœ† NUM cana-3613 90 5 ) ) PUNCT cana-3613 90 6 . . PUNCT cana-3613 91 1 ( ( PUNCT cana-3613 91 2 7 7 NUM cana-3613 91 3 ) ) PUNCT cana-3613 91 4 from from ADP cana-3613 91 5 the the DET cana-3613 91 6 equations equation NOUN cana-3613 91 7 ( ( PUNCT cana-3613 91 8 3 3 NUM cana-3613 91 9 ) ) PUNCT cana-3613 91 10 and and CCONJ cana-3613 91 11 ( ( PUNCT cana-3613 91 12 6 6 NUM cana-3613 91 13 ) ) PUNCT cana-3613 91 14 , , PUNCT cana-3613 91 15 𝐺0(1 𝐺0(1 NUM cana-3613 91 16 ) ) PUNCT cana-3613 91 17 can can AUX cana-3613 91 18 be be AUX cana-3613 91 19 written write VERB cana-3613 91 20 as as ADP cana-3613 91 21 𝐺0(1 𝐺0(1 NOUN cana-3613 91 22 ) ) PUNCT cana-3613 91 23 = = SYM cana-3613 91 24 π›½πœ‹0,0 π›½πœ‹0,0 NOUN cana-3613 91 25 , , PUNCT cana-3613 91 26 where where SCONJ cana-3613 91 27 𝛽 𝛽 NOUN cana-3613 91 28 = = SYM cana-3613 91 29 πœ‚π‘˜2(1 πœ‚π‘˜2(1 NOUN cana-3613 91 30 ) ) PUNCT cana-3613 91 31 πœ™π‘˜1(1 πœ™π‘˜1(1 NOUN cana-3613 91 32 ) ) PUNCT cana-3613 91 33 . . PUNCT cana-3613 92 1 using use VERB cana-3613 92 2 equation equation NOUN cana-3613 92 3 ( ( PUNCT cana-3613 92 4 3 3 NUM cana-3613 92 5 ) ) PUNCT cana-3613 92 6 and and CCONJ cana-3613 92 7 the the DET cana-3613 92 8 normalizing normalizing ADJ cana-3613 92 9 condition condition NOUN cana-3613 92 10 i.e. i.e. X cana-3613 92 11 𝐺0(1 𝐺0(1 NOUN cana-3613 92 12 ) ) PUNCT cana-3613 92 13 + + PUNCT cana-3613 92 14 𝐺1(1 𝐺1(1 ADJ cana-3613 92 15 ) ) PUNCT cana-3613 92 16 = = SYM cana-3613 92 17 1 1 NUM cana-3613 92 18 , , PUNCT cana-3613 92 19 we we PRON cana-3613 92 20 get get VERB cana-3613 92 21 πœ‹0,0 πœ‹0,0 NOUN cana-3613 92 22 = = SYM cana-3613 92 23 πœ†=(𝛼+πœ™)(πœ‡βˆ’πœ† πœ†=(𝛼+πœ™)(πœ‡βˆ’πœ† ADJ cana-3613 92 24 ) ) PUNCT cana-3613 92 25 ( ( PUNCT cana-3613 92 26 𝛼+πœ™)(π›½πœ†(πœ‡βˆ’πœ†)+πœ‡πœ™)+πœ†πœ™(𝛽(πœ†βˆ’πœ‚)+πœ‚ 𝛼+πœ™)(π›½πœ†(πœ‡βˆ’πœ†)+πœ‡πœ™)+πœ†πœ™(𝛽(πœ†βˆ’πœ‚)+πœ‚ PROPN cana-3613 92 27 ) ) PUNCT cana-3613 92 28 . . PUNCT cana-3613 93 1 ( ( PUNCT cana-3613 93 2 8) 8) NUM cana-3613 93 3 4 4 NUM cana-3613 93 4 performance performance NOUN cana-3613 93 5 measures measure NOUN cana-3613 93 6 in in ADP cana-3613 93 7 this this DET cana-3613 93 8 section section NOUN cana-3613 93 9 , , PUNCT cana-3613 93 10 we we PRON cana-3613 93 11 present present VERB cana-3613 93 12 some some DET cana-3613 93 13 important important ADJ cana-3613 93 14 performance performance NOUN cana-3613 93 15 measures measure NOUN cana-3613 93 16 of of ADP cana-3613 93 17 the the DET cana-3613 93 18 model model NOUN cana-3613 93 19 . . PUNCT cana-3613 94 1 let let VERB cana-3613 94 2 𝐸[𝐿1 𝐸[𝐿1 PROPN cana-3613 94 3 ] ] PUNCT cana-3613 94 4 denote denote VERB cana-3613 94 5 the the DET cana-3613 94 6 average average ADJ cana-3613 94 7 number number NOUN cana-3613 94 8 of of ADP cana-3613 94 9 customers customer NOUN cana-3613 94 10 in in ADP cana-3613 94 11 the the DET cana-3613 94 12 system system NOUN cana-3613 94 13 when when SCONJ cana-3613 94 14 the the DET cana-3613 94 15 server server NOUN cana-3613 94 16 is be AUX cana-3613 94 17 in in ADP cana-3613 94 18 normal normal ADJ cana-3613 94 19 working working NOUN cana-3613 94 20 period period NOUN cana-3613 94 21 . . PUNCT cana-3613 95 1 using use VERB cana-3613 95 2 equation equation NOUN cana-3613 95 3 ( ( PUNCT cana-3613 95 4 3 3 NUM cana-3613 95 5 ) ) PUNCT cana-3613 95 6 , , PUNCT cana-3613 95 7 and and CCONJ cana-3613 95 8 differentiating differentiate VERB cana-3613 95 9 equation equation NOUN cana-3613 95 10 ( ( PUNCT cana-3613 95 11 2 2 NUM cana-3613 95 12 ) ) PUNCT cana-3613 95 13 with with ADP cana-3613 95 14 respect respect NOUN cana-3613 95 15 to to ADP cana-3613 95 16 𝑧 𝑧 PROPN cana-3613 95 17 and and CCONJ cana-3613 95 18 using use VERB cana-3613 95 19 l’hospital l’hospital NOUN cana-3613 95 20 rule rule NOUN cana-3613 95 21 twice twice ADV cana-3613 95 22 , , PUNCT cana-3613 95 23 the the DET cana-3613 95 24 expression expression NOUN cana-3613 95 25 for for ADP cana-3613 95 26 𝐸[𝐿1 𝐸[𝐿1 PROPN cana-3613 95 27 ] ] PUNCT cana-3613 95 28 is be AUX cana-3613 95 29 obtained obtain VERB cana-3613 95 30 as as ADP cana-3613 95 31 𝐸[𝐿1 𝐸[𝐿1 NOUN cana-3613 95 32 ] ] PUNCT cana-3613 95 33 = = PUNCT cana-3613 95 34 𝐺1 𝐺1 NOUN cana-3613 95 35 β€² β€² NUM cana-3613 95 36 ( ( PUNCT cana-3613 95 37 1 1 NUM cana-3613 95 38 ) ) PUNCT cana-3613 95 39 = = SYM cana-3613 95 40 πœ™πΊβ€²β€²0(1 πœ™πΊβ€²β€²0(1 NUM cana-3613 95 41 ) ) PUNCT cana-3613 95 42 2(πœ‡βˆ’πœ† 2(πœ‡βˆ’πœ† NUM cana-3613 95 43 ) ) PUNCT cana-3613 96 1 + + CCONJ cana-3613 96 2 πœ‡πœ™ πœ‡πœ™ INTJ cana-3613 96 3 ( ( PUNCT cana-3613 96 4 πœ‡βˆ’πœ†)2 πœ‡βˆ’πœ†)2 VERB cana-3613 96 5 𝐸[𝐿0 𝐸[𝐿0 PART cana-3613 96 6 ] ] X cana-3613 96 7 + + CCONJ cana-3613 96 8 πœ‡πœ™ πœ‡πœ™ INTJ cana-3613 96 9 ( ( PUNCT cana-3613 96 10 πœ‡βˆ’πœ†)2 πœ‡βˆ’πœ†)2 PROPN cana-3613 96 11 πœ‹0,0 πœ‹0,0 NOUN cana-3613 96 12 . . PUNCT cana-3613 97 1 ( ( PUNCT cana-3613 97 2 9 9 X cana-3613 97 3 ) ) PUNCT cana-3613 97 4 differentiating differentiate VERB cana-3613 97 5 equation equation NOUN cana-3613 97 6 ( ( PUNCT cana-3613 97 7 1 1 NUM cana-3613 97 8 ) ) PUNCT cana-3613 97 9 with with ADP cana-3613 97 10 respect respect NOUN cana-3613 97 11 to to ADP cana-3613 97 12 𝑧 𝑧 PROPN cana-3613 97 13 and and CCONJ cana-3613 97 14 using use VERB cana-3613 97 15 l’hospital l’hospital NOUN cana-3613 97 16 rule rule NOUN cana-3613 97 17 , , PUNCT cana-3613 97 18 taking take VERB cana-3613 97 19 𝑧 𝑧 X cana-3613 97 20 = = ADJ cana-3613 97 21 1 1 NUM cana-3613 97 22 , , PUNCT cana-3613 97 23 we we PRON cana-3613 97 24 have have VERB cana-3613 97 25 𝐺′′0(1 𝐺′′0(1 NOUN cana-3613 97 26 ) ) PUNCT cana-3613 97 27 = = SYM cana-3613 97 28 2((πœ†βˆ’πœ™βˆ’πœ‚βˆ’π›Ό)𝐸[𝐿0]+πœ†πΊ0(1 2((πœ†βˆ’πœ™βˆ’πœ‚βˆ’π›Ό)𝐸[𝐿0]+πœ†πΊ0(1 NUM cana-3613 97 29 ) ) PUNCT cana-3613 97 30 ) ) PUNCT cana-3613 97 31 2𝛼+πœ™ 2𝛼+πœ™ NUM cana-3613 97 32 , , PUNCT cana-3613 97 33 substituting substitute VERB cana-3613 97 34 𝐺′′0(1 𝐺′′0(1 NOUN cana-3613 97 35 ) ) PUNCT cana-3613 97 36 and and CCONJ cana-3613 97 37 𝐸[𝐿0 𝐸[𝐿0 X cana-3613 97 38 ] ] X cana-3613 97 39 in in ADP cana-3613 97 40 equation equation NOUN cana-3613 97 41 ( ( PUNCT cana-3613 97 42 4 4 X cana-3613 97 43 ) ) PUNCT cana-3613 97 44 yields yield NOUN cana-3613 97 45 𝐸[𝐿1 𝐸[𝐿1 NOUN cana-3613 97 46 ] ] PUNCT cana-3613 97 47 . . PUNCT cana-3613 98 1 therefore therefore ADV cana-3613 98 2 , , PUNCT cana-3613 98 3 the the DET cana-3613 98 4 average average ADJ cana-3613 98 5 system system NOUN cana-3613 98 6 length length NOUN cana-3613 98 7 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 98 8 ] ] PUNCT cana-3613 98 9 is be AUX cana-3613 98 10 given give VERB cana-3613 98 11 by by ADP cana-3613 98 12 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 98 13 ] ] X cana-3613 98 14 = = PUNCT cana-3613 98 15 𝐸[𝐿0 𝐸[𝐿0 X cana-3613 98 16 ] ] X cana-3613 99 1 + + PUNCT cana-3613 99 2 𝐸[𝐿1 𝐸[𝐿1 NOUN cana-3613 99 3 ] ] PUNCT cana-3613 99 4 . . PUNCT cana-3613 100 1 as as SCONJ cana-3613 100 2 the the DET cana-3613 100 3 instantaneous instantaneous ADJ cana-3613 100 4 reneging renege VERB cana-3613 100 5 rate rate NOUN cana-3613 100 6 during during ADP cana-3613 100 7 π‘Šπ‘‰ π‘Šπ‘‰ PROPN cana-3613 100 8 is be AUX cana-3613 100 9 𝑛𝛼 𝑛𝛼 PROPN cana-3613 100 10 , , PUNCT cana-3613 100 11 the the DET cana-3613 100 12 average average ADJ cana-3613 100 13 reneging renege VERB cana-3613 100 14 rate rate NOUN cana-3613 100 15 ( ( PUNCT cana-3613 100 16 𝑅. 𝑅. PROPN cana-3613 100 17 𝑅 𝑅 NOUN cana-3613 100 18 ) ) PUNCT cana-3613 100 19 is be AUX cana-3613 100 20 𝑅. 𝑅. PROPN cana-3613 100 21 𝑅 𝑅 NOUN cana-3613 100 22 = = PUNCT cana-3613 100 23 βˆ‘βˆž βˆ‘βˆž NOUN cana-3613 100 24 𝑛=1 𝑛=1 NOUN cana-3613 100 25 π‘›π›Όπœ‹0,𝑛 π‘›π›Όπœ‹0,𝑛 NOUN cana-3613 100 26 = = SYM cana-3613 100 27 𝛼𝐸[𝐿0 𝛼𝐸[𝐿0 NOUN cana-3613 100 28 ] ] X cana-3613 100 29 5 5 NUM cana-3613 100 30 numerical numerical ADJ cana-3613 100 31 results result NOUN cana-3613 100 32 in in ADP cana-3613 100 33 this this DET cana-3613 100 34 section section NOUN cana-3613 100 35 , , PUNCT cana-3613 100 36 we we PRON cana-3613 100 37 present present VERB cana-3613 100 38 the the DET cana-3613 100 39 effect effect NOUN cana-3613 100 40 of of ADP cana-3613 100 41 some some DET cana-3613 100 42 parameters parameter NOUN cana-3613 100 43 on on ADP cana-3613 100 44 the the DET cana-3613 100 45 system system NOUN cana-3613 100 46 performance performance NOUN cana-3613 100 47 measures measure NOUN cana-3613 100 48 through through ADP cana-3613 100 49 some some DET cana-3613 100 50 numerical numerical ADJ cana-3613 100 51 results result NOUN cana-3613 100 52 . . PUNCT cana-3613 101 1 the the DET cana-3613 101 2 various various ADJ cana-3613 101 3 parameters parameter NOUN cana-3613 101 4 of of ADP cana-3613 101 5 the the DET cana-3613 101 6 model model NOUN cana-3613 101 7 are be AUX cana-3613 101 8 chosen choose VERB cana-3613 101 9 as as ADP cana-3613 101 10 πœ† πœ† NOUN cana-3613 101 11 = = SYM cana-3613 101 12 1.7 1.7 NUM cana-3613 101 13 ; ; PUNCT cana-3613 101 14 πœ‡ πœ‡ X cana-3613 101 15 = = PROPN cana-3613 101 16 2.5 2.5 NUM cana-3613 101 17 ; ; PUNCT cana-3613 101 18 πœ‚ πœ‚ X cana-3613 101 19 = = SYM cana-3613 101 20 1.9 1.9 NUM cana-3613 101 21 ; ; PUNCT cana-3613 102 1 πœ™ πœ™ X cana-3613 102 2 = = SYM cana-3613 102 3 1.5 1.5 NUM cana-3613 102 4 ; ; PUNCT cana-3613 102 5 𝛼 𝛼 X cana-3613 102 6 = = NOUN cana-3613 102 7 1.1 1.1 NUM cana-3613 102 8 ; ; PUNCT cana-3613 102 9 unless unless SCONJ cana-3613 102 10 they they PRON cana-3613 102 11 are be AUX cana-3613 102 12 considered consider VERB cana-3613 102 13 as as ADP cana-3613 102 14 variables variable NOUN cana-3613 102 15 or or CCONJ cana-3613 102 16 their their PRON cana-3613 102 17 values value NOUN cana-3613 102 18 are be AUX cana-3613 102 19 mentioned mention VERB cana-3613 102 20 in in ADP cana-3613 102 21 the the DET cana-3613 102 22 respective respective ADJ cana-3613 102 23 figures figure NOUN cana-3613 102 24 . . PUNCT cana-3613 103 1 figure figure VERB cana-3613 103 2 1 1 NUM cana-3613 103 3 : : PUNCT cana-3613 103 4 effect effect VERB cana-3613 103 5 πœ† πœ† ADP cana-3613 103 6 on on ADP cana-3613 103 7 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 103 8 ] ] PUNCT cana-3613 103 9 communications communication NOUN cana-3613 103 10 on on ADP cana-3613 103 11 applied apply VERB cana-3613 103 12 nonlinear nonlinear ADJ cana-3613 103 13 analysis analysis NOUN cana-3613 103 14 issn issn NOUN cana-3613 103 15 : : PUNCT cana-3613 103 16 1074 1074 NUM cana-3613 103 17 - - PUNCT cana-3613 103 18 133x 133x NUM cana-3613 103 19 vol vol NOUN cana-3613 103 20 32 32 NUM cana-3613 103 21 no no NOUN cana-3613 103 22 . . PUNCT cana-3613 104 1 8s 8s PROPN cana-3613 104 2 ( ( PUNCT cana-3613 104 3 2025 2025 NUM cana-3613 104 4 ) ) PUNCT cana-3613 104 5 127 127 NUM cana-3613 104 6 https://internationalpubls.com https://internationalpubls.com NUM cana-3613 104 7 figure figure NOUN cana-3613 104 8 2 2 NUM cana-3613 104 9 presents present VERB cana-3613 104 10 the the DET cana-3613 104 11 effect effect NOUN cana-3613 104 12 of of ADP cana-3613 104 13 arrival arrival NOUN cana-3613 104 14 rate rate NOUN cana-3613 104 15 ( ( PUNCT cana-3613 104 16 πœ† πœ† X cana-3613 104 17 ) ) PUNCT cana-3613 104 18 on on ADP cana-3613 104 19 the the DET cana-3613 104 20 average average ADJ cana-3613 104 21 system system NOUN cana-3613 104 22 length length NOUN cana-3613 104 23 ( ( PUNCT cana-3613 104 24 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 104 25 ] ] PUNCT cana-3613 104 26 ) ) PUNCT cana-3613 104 27 for for ADP cana-3613 104 28 different different ADJ cana-3613 104 29 vacation vacation NOUN cana-3613 104 30 rates rate NOUN cana-3613 104 31 ( ( PUNCT cana-3613 104 32 πœ™ πœ™ NOUN cana-3613 104 33 ) ) PUNCT cana-3613 104 34 . . PUNCT cana-3613 105 1 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 105 2 ] ] PUNCT cana-3613 105 3 increase increase NOUN cana-3613 105 4 with with ADP cana-3613 105 5 the the DET cana-3613 105 6 increase increase NOUN cana-3613 105 7 of of ADP cana-3613 105 8 πœ† πœ† PRON cana-3613 105 9 for for ADP cana-3613 105 10 fixed fix VERB cana-3613 105 11 πœ™ πœ™ NOUN cana-3613 105 12 and and CCONJ cana-3613 105 13 it it PRON cana-3613 105 14 decreases decrease VERB cana-3613 105 15 with with ADP cana-3613 105 16 the the DET cana-3613 105 17 increase increase NOUN cana-3613 105 18 of of ADP cana-3613 105 19 πœ™ πœ™ NOUN cana-3613 105 20 for for ADP cana-3613 105 21 fixed fix VERB cana-3613 105 22 πœ† πœ† PRON cana-3613 105 23 as as SCONJ cana-3613 105 24 it it PRON cana-3613 105 25 should should AUX cana-3613 105 26 be be AUX cana-3613 105 27 . . PUNCT cana-3613 105 28 figure figure VERB cana-3613 105 29 2 2 NUM cana-3613 105 30 : : PUNCT cana-3613 105 31 effect effect NOUN cana-3613 105 32 𝑅. 𝑅. ADV cana-3613 105 33 𝑅. 𝑅. NOUN cana-3613 105 34 for for ADP cana-3613 105 35 different different ADJ cana-3613 105 36 πœ™ πœ™ PRON cana-3613 105 37 figure figure NOUN cana-3613 105 38 2 2 NUM cana-3613 105 39 shows show VERB cana-3613 105 40 the the DET cana-3613 105 41 effect effect NOUN cana-3613 105 42 of of ADP cana-3613 105 43 𝛼 𝛼 PRON cana-3613 105 44 on on ADP cana-3613 105 45 the the DET cana-3613 105 46 reneging renege VERB cana-3613 105 47 rate rate NOUN cana-3613 105 48 ( ( PUNCT cana-3613 105 49 𝑅. 𝑅. ADV cana-3613 105 50 𝑅. 𝑅. NOUN cana-3613 105 51 ) ) PUNCT cana-3613 105 52 for for ADP cana-3613 105 53 different different ADJ cana-3613 105 54 vacation vacation NOUN cana-3613 105 55 rates rate NOUN cana-3613 105 56 ( ( PUNCT cana-3613 105 57 πœ™ πœ™ NOUN cana-3613 105 58 ) ) PUNCT cana-3613 105 59 . . PUNCT cana-3613 106 1 as as SCONJ cana-3613 106 2 expected expect VERB cana-3613 106 3 in in ADP cana-3613 106 4 real real ADJ cana-3613 106 5 life life NOUN cana-3613 106 6 , , PUNCT cana-3613 106 7 𝑅. 𝑅. ADV cana-3613 106 8 𝑅. 𝑅. NOUN cana-3613 106 9 increases increase NOUN cana-3613 106 10 with with ADP cana-3613 106 11 the the DET cana-3613 106 12 increase increase NOUN cana-3613 106 13 of of ADP cana-3613 106 14 𝛼. 𝛼. NOUN cana-3613 106 15 in in ADP cana-3613 106 16 this this DET cana-3613 106 17 paper paper NOUN cana-3613 106 18 we we PRON cana-3613 106 19 considered consider VERB cana-3613 106 20 that that SCONJ cana-3613 106 21 , , PUNCT cana-3613 106 22 the the DET cana-3613 106 23 arrived arrive VERB cana-3613 106 24 customer customer NOUN cana-3613 106 25 may may AUX cana-3613 106 26 renege renege VERB cana-3613 106 27 due due ADJ cana-3613 106 28 to to ADP cana-3613 106 29 impatience impatience NOUN cana-3613 106 30 whenever whenever SCONJ cana-3613 106 31 the the DET cana-3613 106 32 server server NOUN cana-3613 106 33 is be AUX cana-3613 106 34 in in ADP cana-3613 106 35 π‘Šπ‘‰. π‘Šπ‘‰. X cana-3613 106 36 however however ADV cana-3613 106 37 , , PUNCT cana-3613 106 38 the the DET cana-3613 106 39 server server NOUN cana-3613 106 40 spends spend VERB cana-3613 106 41 more more ADJ cana-3613 106 42 time time NOUN cana-3613 106 43 in in ADP cana-3613 106 44 normal normal ADJ cana-3613 106 45 working working NOUN cana-3613 106 46 period period NOUN cana-3613 106 47 with with ADP cana-3613 106 48 the the DET cana-3613 106 49 increase increase NOUN cana-3613 106 50 of of ADP cana-3613 106 51 πœ™ πœ™ NOUN cana-3613 106 52 and and CCONJ cana-3613 106 53 hence hence ADV cana-3613 106 54 𝑅. 𝑅. ADV cana-3613 106 55 𝑅. 𝑅. NOUN cana-3613 106 56 decrease decrease NOUN cana-3613 106 57 with with ADP cana-3613 106 58 the the DET cana-3613 106 59 increase increase NOUN cana-3613 106 60 of of ADP cana-3613 106 61 πœ™ πœ™ NOUN cana-3613 106 62 for for ADP cana-3613 106 63 fixed fix VERB cana-3613 106 64 πœ†. πœ†. NOUN cana-3613 106 65 we we PRON cana-3613 106 66 can can AUX cana-3613 106 67 clearly clearly ADV cana-3613 106 68 observe observe VERB cana-3613 106 69 this this DET cana-3613 106 70 case case NOUN cana-3613 106 71 from from ADP cana-3613 106 72 figure figure NOUN cana-3613 106 73 2 2 NUM cana-3613 106 74 . . PUNCT cana-3613 106 75 figure figure VERB cana-3613 106 76 3 3 NUM cana-3613 106 77 : : PUNCT cana-3613 106 78 effect effect VERB cana-3613 106 79 πœ‚ πœ‚ NOUN cana-3613 106 80 on on ADP cana-3613 106 81 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 106 82 ] ] PUNCT cana-3613 106 83 for for ADP cana-3613 106 84 different different ADJ cana-3613 106 85 πœ™ πœ™ NOUN cana-3613 106 86 the the DET cana-3613 106 87 effect effect NOUN cana-3613 106 88 of of ADP cana-3613 106 89 service service NOUN cana-3613 106 90 rates rate NOUN cana-3613 106 91 in in ADP cana-3613 106 92 working work VERB cana-3613 106 93 vacation vacation NOUN cana-3613 106 94 period period NOUN cana-3613 106 95 ( ( PUNCT cana-3613 106 96 πœ‚ πœ‚ NOUN cana-3613 106 97 ) ) PUNCT cana-3613 106 98 on on ADP cana-3613 106 99 the the DET cana-3613 106 100 average average ADJ cana-3613 106 101 system system NOUN cana-3613 106 102 length length NOUN cana-3613 106 103 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 106 104 ] ] PUNCT cana-3613 106 105 for for ADP cana-3613 106 106 different different ADJ cana-3613 106 107 vacation vacation NOUN cana-3613 106 108 rates rate NOUN cana-3613 106 109 πœ™ πœ™ PRON cana-3613 106 110 is be AUX cana-3613 106 111 given give VERB cana-3613 106 112 in in ADP cana-3613 106 113 figure figure NOUN cana-3613 106 114 3 3 NUM cana-3613 106 115 . . PUNCT cana-3613 107 1 we we PRON cana-3613 107 2 know know VERB cana-3613 107 3 that that SCONJ cana-3613 107 4 , , PUNCT cana-3613 107 5 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 107 6 ] ] PUNCT cana-3613 107 7 decreases decrease VERB cana-3613 107 8 with with ADP cana-3613 107 9 πœ‚ πœ‚ NOUN cana-3613 107 10 for for ADP cana-3613 107 11 fixed fix VERB cana-3613 107 12 πœ™ πœ™ NOUN cana-3613 107 13 and and CCONJ cana-3613 107 14 it it PRON cana-3613 107 15 increases increase VERB cana-3613 107 16 with with ADP cana-3613 107 17 the the DET cana-3613 107 18 increase increase NOUN cana-3613 107 19 of of ADP cana-3613 107 20 πœ™ πœ™ NOUN cana-3613 107 21 for for ADP cana-3613 107 22 fixed fixed ADJ cana-3613 107 23 πœ‚ πœ‚ NOUN cana-3613 107 24 as as SCONJ cana-3613 107 25 it it PRON cana-3613 107 26 clear clear ADJ cana-3613 107 27 from from ADP cana-3613 107 28 real real ADJ cana-3613 107 29 life life NOUN cana-3613 107 30 . . PUNCT cana-3613 108 1 figure figure VERB cana-3613 108 2 4 4 NUM cana-3613 108 3 : : PUNCT cana-3613 108 4 effect effect NOUN cana-3613 108 5 πœ‡ πœ‡ ADP cana-3613 108 6 on on ADP cana-3613 108 7 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 108 8 ] ] PUNCT cana-3613 108 9 for for SCONJ cana-3613 108 10 different different ADJ cana-3613 108 11 πœ† πœ† DET cana-3613 108 12 communications communication NOUN cana-3613 108 13 on on ADP cana-3613 108 14 applied apply VERB cana-3613 108 15 nonlinear nonlinear ADJ cana-3613 108 16 analysis analysis NOUN cana-3613 108 17 issn issn NOUN cana-3613 108 18 : : PUNCT cana-3613 108 19 1074 1074 NUM cana-3613 108 20 - - PUNCT cana-3613 108 21 133x 133x NUM cana-3613 108 22 vol vol NOUN cana-3613 108 23 32 32 NUM cana-3613 108 24 no no NOUN cana-3613 108 25 . . PUNCT cana-3613 109 1 8s 8s PROPN cana-3613 109 2 ( ( PUNCT cana-3613 109 3 2025 2025 NUM cana-3613 109 4 ) ) PUNCT cana-3613 109 5 128 128 NUM cana-3613 109 6 https://internationalpubls.com https://internationalpubls.com X cana-3613 109 7 figure figure NOUN cana-3613 109 8 4 4 NUM cana-3613 109 9 gives give VERB cana-3613 109 10 the the DET cana-3613 109 11 effect effect NOUN cana-3613 109 12 of of ADP cana-3613 109 13 service service NOUN cana-3613 109 14 rates rate NOUN cana-3613 109 15 in in ADP cana-3613 109 16 normal normal ADJ cana-3613 109 17 working working NOUN cana-3613 109 18 period period NOUN cana-3613 109 19 ( ( PUNCT cana-3613 109 20 πœ‡ πœ‡ ADP cana-3613 109 21 ) ) PUNCT cana-3613 109 22 on on ADP cana-3613 109 23 the the DET cana-3613 109 24 average average ADJ cana-3613 109 25 system system NOUN cana-3613 109 26 length length NOUN cana-3613 109 27 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 109 28 ] ] PUNCT cana-3613 109 29 for for ADP cana-3613 109 30 different different ADJ cana-3613 109 31 arrival arrival NOUN cana-3613 109 32 rates rate NOUN cana-3613 109 33 πœ†. πœ†. VERB cana-3613 109 34 as as SCONJ cana-3613 109 35 explained explain VERB cana-3613 109 36 in in ADP cana-3613 109 37 figure figure NOUN cana-3613 109 38 2 2 NUM cana-3613 109 39 , , PUNCT cana-3613 109 40 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 109 41 ] ] PUNCT cana-3613 109 42 increases increase VERB cana-3613 109 43 with with ADP cana-3613 109 44 πœ† πœ† PRON cana-3613 109 45 for for ADP cana-3613 109 46 fixed fix VERB cana-3613 109 47 πœ‡. πœ‡. NOUN cana-3613 109 48 also also ADV cana-3613 109 49 it it PRON cana-3613 109 50 decreases decrease VERB cana-3613 109 51 with with ADP cana-3613 109 52 the the DET cana-3613 109 53 increase increase NOUN cana-3613 109 54 of of ADP cana-3613 109 55 πœ‡ πœ‡ ADP cana-3613 109 56 for for ADP cana-3613 109 57 fixed fix VERB cana-3613 109 58 πœ†. πœ†. NOUN cana-3613 109 59 figure figure NOUN cana-3613 109 60 5 5 NUM cana-3613 109 61 : : PUNCT cana-3613 109 62 effect effect NOUN cana-3613 109 63 πœ‚ πœ‚ NOUN cana-3613 109 64 on on ADP cana-3613 109 65 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 109 66 ] ] PUNCT cana-3613 109 67 for for SCONJ cana-3613 109 68 different different ADJ cana-3613 109 69 πœ† πœ† DET cana-3613 109 70 figure figure NOUN cana-3613 109 71 5 5 NUM cana-3613 109 72 depicts depict VERB cana-3613 109 73 the the DET cana-3613 109 74 effect effect NOUN cana-3613 109 75 of of ADP cana-3613 109 76 service service NOUN cana-3613 109 77 rates rate NOUN cana-3613 109 78 πœ‚ πœ‚ NOUN cana-3613 109 79 on on ADP cana-3613 109 80 the the DET cana-3613 109 81 average average ADJ cana-3613 109 82 system system NOUN cana-3613 109 83 length length NOUN cana-3613 109 84 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 109 85 ] ] PUNCT cana-3613 109 86 for for ADP cana-3613 109 87 different different ADJ cana-3613 109 88 arrival arrival NOUN cana-3613 109 89 rates rate NOUN cana-3613 109 90 πœ† πœ† X cana-3613 109 91 . . PUNCT cana-3613 110 1 here here ADV cana-3613 110 2 also also ADV cana-3613 110 3 𝐸[𝐿 𝐸[𝐿 ADV cana-3613 110 4 ] ] PUNCT cana-3613 110 5 increases increase VERB cana-3613 110 6 with with ADP cana-3613 110 7 the the DET cana-3613 110 8 increase increase NOUN cana-3613 110 9 of of ADP cana-3613 110 10 πœ† πœ† PRON cana-3613 110 11 for for ADP cana-3613 110 12 fixed fixed ADJ cana-3613 110 13 πœ‚ πœ‚ NOUN cana-3613 110 14 and and CCONJ cana-3613 110 15 decreases decrease VERB cana-3613 110 16 with with ADP cana-3613 110 17 increase increase NOUN cana-3613 110 18 of of ADP cana-3613 110 19 πœ† πœ† PRON cana-3613 110 20 for for ADP cana-3613 110 21 fixed fixed ADJ cana-3613 110 22 πœ‚ πœ‚ NOUN cana-3613 110 23 as as ADP cana-3613 110 24 in in ADP cana-3613 110 25 figure figure NOUN cana-3613 110 26 4 4 NUM cana-3613 110 27 . . PUNCT cana-3613 111 1 but but CCONJ cana-3613 111 2 , , PUNCT cana-3613 111 3 the the DET cana-3613 111 4 effect effect NOUN cana-3613 111 5 of of ADP cana-3613 111 6 service service NOUN cana-3613 111 7 rate rate NOUN cana-3613 111 8 on on ADP cana-3613 111 9 𝐸[𝐿 𝐸[𝐿 NOUN cana-3613 111 10 ] ] PUNCT cana-3613 111 11 is be AUX cana-3613 111 12 more more ADV cana-3613 111 13 in in ADP cana-3613 111 14 figure figure NOUN cana-3613 111 15 4 4 NUM cana-3613 111 16 when when SCONJ cana-3613 111 17 compare compare VERB cana-3613 111 18 with with ADP cana-3613 111 19 figure figure NOUN cana-3613 111 20 5 5 NUM cana-3613 111 21 . . PUNCT cana-3613 112 1 this this PRON cana-3613 112 2 is be AUX cana-3613 112 3 due due ADJ cana-3613 112 4 to to ADP cana-3613 112 5 the the DET cana-3613 112 6 service service NOUN cana-3613 112 7 rate rate NOUN cana-3613 112 8 in in ADP cana-3613 112 9 working work VERB cana-3613 112 10 vacation vacation NOUN cana-3613 112 11 period period NOUN cana-3613 112 12 is be AUX cana-3613 112 13 lower low ADJ cana-3613 112 14 than than ADP cana-3613 112 15 the the DET cana-3613 112 16 service service NOUN cana-3613 112 17 rate rate NOUN cana-3613 112 18 in in ADP cana-3613 112 19 normal normal ADJ cana-3613 112 20 working working NOUN cana-3613 112 21 period period NOUN cana-3613 112 22 . . PUNCT cana-3613 113 1 6 6 NUM cana-3613 113 2 conclusion conclusion NOUN cana-3613 113 3 in in ADP cana-3613 113 4 this this DET cana-3613 113 5 paper paper NOUN cana-3613 113 6 , , PUNCT cana-3613 113 7 we we PRON cana-3613 113 8 have have AUX cana-3613 113 9 studied study VERB cana-3613 113 10 an an DET cana-3613 113 11 𝑀/𝑀/1 𝑀/𝑀/1 NOUN cana-3613 113 12 queueing queue VERB cana-3613 113 13 system system NOUN cana-3613 113 14 with with ADP cana-3613 113 15 single single ADJ cana-3613 113 16 working work VERB cana-3613 113 17 vacation vacation NOUN cana-3613 113 18 and and CCONJ cana-3613 113 19 customers customer NOUN cana-3613 113 20 ’ ' PUNCT cana-3613 113 21 impatience impatience NOUN cana-3613 113 22 . . PUNCT cana-3613 114 1 we we PRON cana-3613 114 2 have have AUX cana-3613 114 3 obtained obtain VERB cana-3613 114 4 the the DET cana-3613 114 5 closed closed ADJ cana-3613 114 6 form form NOUN cana-3613 114 7 expressions expression NOUN cana-3613 114 8 of of ADP cana-3613 114 9 the the DET cana-3613 114 10 steady steady ADJ cana-3613 114 11 state state NOUN cana-3613 114 12 probabilities probability NOUN cana-3613 114 13 . . PUNCT cana-3613 115 1 some some DET cana-3613 115 2 important important ADJ cana-3613 115 3 performance performance NOUN cana-3613 115 4 measures measure NOUN cana-3613 115 5 of of ADP cana-3613 115 6 the the DET cana-3613 115 7 model model NOUN cana-3613 115 8 such such ADJ cana-3613 115 9 as as ADP cana-3613 115 10 average average ADJ cana-3613 115 11 system system NOUN cana-3613 115 12 length length NOUN cana-3613 115 13 and and CCONJ cana-3613 115 14 average average ADJ cana-3613 115 15 reneging renege VERB cana-3613 115 16 rate rate NOUN cana-3613 115 17 . . PUNCT cana-3613 116 1 the the DET cana-3613 116 2 effects effect NOUN cana-3613 116 3 of of ADP cana-3613 116 4 some some DET cana-3613 116 5 parameters parameter NOUN cana-3613 116 6 on on ADP cana-3613 116 7 the the DET cana-3613 116 8 performance performance NOUN cana-3613 116 9 measures measure NOUN cana-3613 116 10 of of ADP cana-3613 116 11 the the DET cana-3613 116 12 system system NOUN cana-3613 116 13 have have AUX cana-3613 116 14 been be AUX cana-3613 116 15 investigated investigate VERB cana-3613 116 16 numerically numerically ADV cana-3613 116 17 and and CCONJ cana-3613 116 18 presented present VERB cana-3613 116 19 through through ADP cana-3613 116 20 graphically graphically ADV cana-3613 116 21 . . PUNCT cana-3613 117 1 the the DET cana-3613 117 2 techniques technique NOUN cana-3613 117 3 adopted adopt VERB cana-3613 117 4 in in ADP cana-3613 117 5 this this DET cana-3613 117 6 paper paper NOUN cana-3613 117 7 can can AUX cana-3613 117 8 be be AUX cana-3613 117 9 applied apply VERB cana-3613 117 10 to to PART cana-3613 117 11 analyze analyze VERB cana-3613 117 12 models model NOUN cana-3613 117 13 like like ADP cana-3613 117 14 impatient impatient ADJ cana-3613 117 15 customer customer NOUN cana-3613 117 16 𝑀/𝑀/1 𝑀/𝑀/1 NOUN cana-3613 117 17 queue queue NOUN cana-3613 117 18 with with ADP cana-3613 117 19 variant variant ADJ cana-3613 117 20 working working NOUN cana-3613 117 21 vacation vacation NOUN cana-3613 117 22 . . PUNCT cana-3613 118 1 references reference NOUN cana-3613 118 2 [ [ X cana-3613 118 3 1 1 NUM cana-3613 118 4 ] ] PUNCT cana-3613 118 5 baba baba PROPN cana-3613 118 6 , , PUNCT cana-3613 118 7 y. y. PROPN cana-3613 118 8 ( ( PUNCT cana-3613 118 9 2005 2005 NUM cana-3613 118 10 ) ) PUNCT cana-3613 118 11 analysis analysis NOUN cana-3613 118 12 of of ADP cana-3613 118 13 a a DET cana-3613 118 14 𝐺𝐼/𝑀/1 𝐺𝐼/𝑀/1 NOUN cana-3613 118 15 queue queue NOUN cana-3613 118 16 with with ADP cana-3613 118 17 multiple multiple ADJ cana-3613 118 18 working work VERB cana-3613 118 19 vacations vacation NOUN cana-3613 118 20 . . PUNCT cana-3613 119 1 operation operation NOUN cana-3613 119 2 research research NOUN cana-3613 119 3 lett lett PROPN cana-3613 119 4 33 33 NUM cana-3613 119 5 , , PUNCT cana-3613 119 6 pp pp ADJ cana-3613 119 7 . . PUNCT cana-3613 120 1 201–9 201–9 X cana-3613 120 2 . . PUNCT cana-3613 121 1 [ [ X cana-3613 121 2 2 2 NUM cana-3613 121 3 ] ] X cana-3613 121 4 doshi doshi PROPN cana-3613 121 5 , , PUNCT cana-3613 121 6 b.t b.t PROPN cana-3613 121 7 . . PROPN cana-3613 121 8 , , PUNCT cana-3613 121 9 ( ( PUNCT cana-3613 121 10 1986 1986 NUM cana-3613 121 11 ) ) PUNCT cana-3613 121 12 queueing queue VERB cana-3613 121 13 systems system NOUN cana-3613 121 14 with with ADP cana-3613 121 15 vacations vacation NOUN cana-3613 121 16 - - PUNCT cana-3613 121 17 a a DET cana-3613 121 18 survey survey NOUN cana-3613 121 19 . . PUNCT cana-3613 122 1 queueing queue VERB cana-3613 122 2 systems system NOUN cana-3613 122 3 1 1 NUM cana-3613 122 4 , , PUNCT cana-3613 122 5 pp pp ADJ cana-3613 122 6 . . PUNCT cana-3613 123 1 29–66 29–66 NUM cana-3613 123 2 . . PUNCT cana-3613 124 1 [ [ X cana-3613 124 2 3 3 NUM cana-3613 124 3 ] ] X cana-3613 124 4 haight haight NOUN cana-3613 124 5 , , PUNCT cana-3613 124 6 f. f. PROPN cana-3613 124 7 a. a. PROPN cana-3613 124 8 , , PUNCT cana-3613 124 9 ( ( PUNCT cana-3613 124 10 1959 1959 NUM cana-3613 124 11 ) ) PUNCT cana-3613 124 12 queing quee VERB cana-3613 124 13 with with ADP cana-3613 124 14 reneging renege VERB cana-3613 124 15 . . PUNCT cana-3613 125 1 metrika metrika NOUN cana-3613 125 2 2 2 NUM cana-3613 125 3 , , PUNCT cana-3613 125 4 pp.186–197 pp.186–197 PROPN cana-3613 125 5 . . PUNCT cana-3613 126 1 [ [ X cana-3613 126 2 4 4 NUM cana-3613 126 3 ] ] X cana-3613 126 4 ke ke PROPN cana-3613 126 5 , , PUNCT cana-3613 126 6 j.c j.c PROPN cana-3613 126 7 . . PROPN cana-3613 126 8 , , PUNCT cana-3613 126 9 wu wu PROPN cana-3613 126 10 , , PUNCT cana-3613 126 11 c. c. PROPN cana-3613 126 12 h. h. PROPN cana-3613 126 13 , , PUNCT cana-3613 126 14 and and CCONJ cana-3613 126 15 zhang zhang PROPN cana-3613 126 16 , , PUNCT cana-3613 126 17 z.g z.g PROPN cana-3613 126 18 . . PROPN cana-3613 126 19 , , PUNCT cana-3613 126 20 ( ( PUNCT cana-3613 126 21 2010 2010 NUM cana-3613 126 22 ) ) PUNCT cana-3613 126 23 recent recent ADJ cana-3613 126 24 developments development NOUN cana-3613 126 25 in in ADP cana-3613 126 26 vacation vacation NOUN cana-3613 126 27 queueing queue VERB cana-3613 126 28 models model NOUN cana-3613 126 29 : : PUNCT cana-3613 126 30 a a DET cana-3613 126 31 short short ADJ cana-3613 126 32 survey.international survey.international ADJ cana-3613 126 33 journal journal NOUN cana-3613 126 34 of of ADP cana-3613 126 35 operation operation NOUN cana-3613 126 36 research research NOUN cana-3613 126 37 7 7 NUM cana-3613 126 38 , , PUNCT cana-3613 126 39 pp pp ADJ cana-3613 126 40 . . PUNCT cana-3613 127 1 3–8 3–8 X cana-3613 127 2 . . PUNCT cana-3613 128 1 [ [ X cana-3613 128 2 5 5 NUM cana-3613 128 3 ] ] SYM cana-3613 128 4 li li PROPN cana-3613 128 5 , , PUNCT cana-3613 128 6 j. j. PROPN cana-3613 128 7 and and CCONJ cana-3613 128 8 tian tian PROPN cana-3613 128 9 , , PUNCT cana-3613 128 10 n. n. PROPN cana-3613 128 11 ( ( PUNCT cana-3613 128 12 2011 2011 NUM cana-3613 128 13 ) ) PUNCT cana-3613 128 14 performance performance NOUN cana-3613 128 15 analysis analysis NOUN cana-3613 128 16 of of ADP cana-3613 128 17 a a DET cana-3613 128 18 𝐺𝐼/𝑀/1 𝐺𝐼/𝑀/1 NOUN cana-3613 128 19 queue queue NOUN cana-3613 128 20 with with ADP cana-3613 128 21 single single ADJ cana-3613 128 22 working work VERB cana-3613 128 23 vacation vacation NOUN cana-3613 128 24 . . PUNCT cana-3613 129 1 applied apply VERB cana-3613 129 2 maths math NOUN cana-3613 129 3 computation computation NOUN cana-3613 129 4 217 217 NUM cana-3613 129 5 , , PUNCT cana-3613 129 6 pp pp ADV cana-3613 129 7 . . PUNCT cana-3613 130 1 4960–71 4960–71 NOUN cana-3613 130 2 . . PUNCT cana-3613 131 1 [ [ X cana-3613 131 2 6 6 NUM cana-3613 131 3 ] ] X cana-3613 131 4 vijaya vijaya PROPN cana-3613 131 5 laxmi laxmi PROPN cana-3613 131 6 , , PUNCT cana-3613 131 7 p. p. NOUN cana-3613 131 8 , , PUNCT cana-3613 131 9 goswani goswani PROPN cana-3613 131 10 , , PUNCT cana-3613 131 11 v. v. PROPN cana-3613 131 12 and and CCONJ cana-3613 131 13 jyothsna jyothsna PROPN cana-3613 131 14 , , PUNCT cana-3613 131 15 k. k. PROPN cana-3613 131 16 ( ( PUNCT cana-3613 131 17 2013 2013 NUM cana-3613 131 18 ) ) PUNCT cana-3613 131 19 analysis analysis NOUN cana-3613 131 20 of of ADP cana-3613 131 21 finite finite ADJ cana-3613 131 22 buffer buffer NOUN cana-3613 131 23 markovian markovian PROPN cana-3613 131 24 queue queue NOUN cana-3613 131 25 with with ADP cana-3613 131 26 balking balk VERB cana-3613 131 27 , , PUNCT cana-3613 131 28 reneging renege VERB cana-3613 131 29 and and CCONJ cana-3613 131 30 working working NOUN cana-3613 131 31 vacations vacation NOUN cana-3613 131 32 . . PUNCT cana-3613 132 1 international international ADJ cana-3613 132 2 journal journal NOUN cana-3613 132 3 of of ADP cana-3613 132 4 strategic strategic ADJ cana-3613 132 5 decision decision NOUN cana-3613 132 6 sciences science NOUN cana-3613 132 7 4 4 NUM cana-3613 132 8 , , PUNCT cana-3613 132 9 pp pp ADJ cana-3613 132 10 . . PUNCT cana-3613 133 1 1–24 1–24 PROPN cana-3613 133 2 . . PUNCT cana-3613 134 1 communications communication NOUN cana-3613 134 2 on on ADP cana-3613 134 3 applied apply VERB cana-3613 134 4 nonlinear nonlinear ADJ cana-3613 134 5 analysis analysis NOUN cana-3613 134 6 issn issn NOUN cana-3613 134 7 : : PUNCT cana-3613 134 8 1074 1074 NUM cana-3613 134 9 - - PUNCT cana-3613 134 10 133x 133x NUM cana-3613 134 11 vol vol NOUN cana-3613 134 12 32 32 NUM cana-3613 134 13 no no NOUN cana-3613 134 14 . . PUNCT cana-3613 135 1 8s 8s PROPN cana-3613 135 2 ( ( PUNCT cana-3613 135 3 2025 2025 NUM cana-3613 135 4 ) ) PUNCT cana-3613 135 5 129 129 NUM cana-3613 135 6 https://internationalpubls.com https://internationalpubls.com X cana-3613 136 1 [ [ X cana-3613 136 2 7 7 NUM cana-3613 136 3 ] ] X cana-3613 136 4 servi servi PROPN cana-3613 136 5 , , PUNCT cana-3613 136 6 l. l. PROPN cana-3613 136 7 d. d. PROPN cana-3613 136 8 , , PUNCT cana-3613 136 9 finn finn PROPN cana-3613 136 10 , , PUNCT cana-3613 136 11 s. s. PROPN cana-3613 136 12 g. g. PROPN cana-3613 136 13 , , PUNCT cana-3613 136 14 ( ( PUNCT cana-3613 136 15 2002 2002 NUM cana-3613 136 16 ) ) PUNCT cana-3613 136 17 𝑀/𝑀/1 𝑀/𝑀/1 NOUN cana-3613 136 18 queues queue NOUN cana-3613 136 19 with with ADP cana-3613 136 20 working work VERB cana-3613 136 21 vacation vacation NOUN cana-3613 136 22 ( ( PUNCT cana-3613 136 23 𝑀/𝑀/1/π‘Šπ‘‰ 𝑀/𝑀/1/π‘Šπ‘‰ PROPN cana-3613 136 24 ) ) PUNCT cana-3613 136 25 . . PUNCT cana-3613 137 1 perform perform VERB cana-3613 137 2 evalutation evalutation NOUN cana-3613 137 3 50 50 NUM cana-3613 137 4 , , PUNCT cana-3613 137 5 pp pp ADJ cana-3613 137 6 . . PUNCT cana-3613 138 1 41 41 NUM cana-3613 138 2 - - SYM cana-3613 138 3 52 52 NUM cana-3613 138 4 . . PUNCT cana-3613 139 1 [ [ X cana-3613 139 2 8 8 NUM cana-3613 139 3 ] ] SYM cana-3613 139 4 selvaraju selvaraju NOUN cana-3613 139 5 , , PUNCT cana-3613 139 6 n. n. NOUN cana-3613 139 7 and and CCONJ cana-3613 139 8 goswami goswami PROPN cana-3613 139 9 , , PUNCT cana-3613 139 10 c. c. PROPN cana-3613 139 11 ( ( PUNCT cana-3613 139 12 2013 2013 NUM cana-3613 139 13 ) ) PUNCT cana-3613 139 14 impatient impatient ADJ cana-3613 139 15 customers customer NOUN cana-3613 139 16 in in ADP cana-3613 139 17 an an DET cana-3613 139 18 𝑀/𝑀/1 𝑀/𝑀/1 NOUN cana-3613 139 19 queue queue NOUN cana-3613 139 20 with with ADP cana-3613 139 21 single single ADJ cana-3613 139 22 and and CCONJ cana-3613 139 23 multiple multiple ADJ cana-3613 139 24 working work VERB cana-3613 139 25 vacations vacation NOUN cana-3613 139 26 . . PUNCT cana-3613 140 1 computers computer NOUN cana-3613 140 2 and and CCONJ cana-3613 140 3 industrial industrial ADJ cana-3613 140 4 engineering engineering NOUN cana-3613 140 5 65 65 NUM cana-3613 140 6 , , PUNCT cana-3613 140 7 pp pp ADJ cana-3613 140 8 . . PUNCT cana-3613 140 9 207–15 207–15 NUM cana-3613 140 10 . . PUNCT cana-3613 141 1 [ [ X cana-3613 141 2 9 9 NUM cana-3613 141 3 ] ] X cana-3613 141 4 tian tian ADJ cana-3613 141 5 , , PUNCT cana-3613 141 6 n. n. PROPN cana-3613 141 7 , , PUNCT cana-3613 141 8 zhang zhang PROPN cana-3613 141 9 , , PUNCT cana-3613 141 10 z. z. PROPN cana-3613 141 11 g. g. PROPN cana-3613 141 12 , , PUNCT cana-3613 141 13 ( ( PUNCT cana-3613 141 14 2006 2006 NUM cana-3613 141 15 ) ) PUNCT cana-3613 141 16 vacation vacation NOUN cana-3613 141 17 queueing queue VERB cana-3613 141 18 models model NOUN cana-3613 141 19 : : PUNCT cana-3613 141 20 theory theory NOUN cana-3613 141 21 and and CCONJ cana-3613 141 22 applications application NOUN cana-3613 141 23 . . PUNCT cana-3613 142 1 new new PROPN cana-3613 142 2 york york PROPN cana-3613 142 3 : : PUNCT cana-3613 142 4 springer springer NOUN cana-3613 142 5 - - PUNCT cana-3613 142 6 verlag verlag PROPN cana-3613 142 7 . . PUNCT cana-3613 143 1 [ [ X cana-3613 143 2 10 10 NUM cana-3613 143 3 ] ] X cana-3613 143 4 tian tian ADJ cana-3613 143 5 , , PUNCT cana-3613 143 6 n. n. NOUN cana-3613 143 7 , , PUNCT cana-3613 143 8 zhao zhao PROPN cana-3613 143 9 , , PUNCT cana-3613 143 10 x. x. PROPN cana-3613 143 11 and and CCONJ cana-3613 143 12 wang wang PROPN cana-3613 143 13 , , PUNCT cana-3613 143 14 k. k. PROPN cana-3613 143 15 ( ( PUNCT cana-3613 143 16 2008 2008 NUM cana-3613 143 17 ) ) PUNCT cana-3613 143 18 the the DET cana-3613 143 19 𝑀/𝑀/1 𝑀/𝑀/1 NOUN cana-3613 143 20 queue queue NOUN cana-3613 143 21 with with ADP cana-3613 143 22 single single ADJ cana-3613 143 23 working work VERB cana-3613 143 24 vacation vacation NOUN cana-3613 143 25 . . PUNCT cana-3613 144 1 international international ADJ cana-3613 144 2 journal journal PROPN cana-3613 144 3 of of ADP cana-3613 144 4 information information NOUN cana-3613 144 5 and and CCONJ cana-3613 144 6 management management NOUN cana-3613 144 7 sciences sciences PROPN cana-3613 144 8 vol vol NOUN cana-3613 144 9 . . PROPN cana-3613 144 10 19 19 NUM cana-3613 144 11 , , PUNCT cana-3613 144 12 no no INTJ cana-3613 144 13 . . NOUN cana-3613 144 14 4 4 NUM cana-3613 144 15 , , PUNCT cana-3613 144 16 pp pp ADJ cana-3613 144 17 . . PUNCT cana-3613 145 1 621–634 621–634 NUM cana-3613 145 2 . . PUNCT cana-3613 146 1 [ [ X cana-3613 146 2 11 11 NUM cana-3613 146 3 ] ] X cana-3613 146 4 vijaya vijaya PROPN cana-3613 146 5 laxmi laxmi PROPN cana-3613 146 6 , , PUNCT cana-3613 146 7 p. p. NOUN cana-3613 146 8 , , PUNCT cana-3613 146 9 and and CCONJ cana-3613 146 10 jyothsna jyothsna PROPN cana-3613 146 11 , , PUNCT cana-3613 146 12 k. k. PROPN cana-3613 146 13 ( ( PUNCT cana-3613 146 14 2015 2015 NUM cana-3613 146 15 ) ) PUNCT cana-3613 146 16 impatient impatient ADJ cana-3613 146 17 customer customer NOUN cana-3613 146 18 queue queue NOUN cana-3613 146 19 with with ADP cana-3613 146 20 bernoulli bernoulli PROPN cana-3613 146 21 schedule schedule NOUN cana-3613 146 22 vacation vacation NOUN cana-3613 146 23 interruption interruption NOUN cana-3613 146 24 . . PUNCT cana-3613 147 1 computers computer NOUN cana-3613 147 2 & & CCONJ cana-3613 147 3 operations operation NOUN cana-3613 147 4 research research VERB cana-3613 147 5 56 56 NUM cana-3613 147 6 , , PUNCT cana-3613 147 7 pp pp ADJ cana-3613 147 8 . . PUNCT cana-3613 148 1 1–7 1–7 X cana-3613 148 2 . . PUNCT cana-3613 149 1 [ [ X cana-3613 149 2 12 12 NUM cana-3613 149 3 ] ] SYM cana-3613 149 4 wu wu PROPN cana-3613 149 5 , , PUNCT cana-3613 149 6 d. d. PROPN cana-3613 149 7 takagi takagi PROPN cana-3613 149 8 , , PUNCT cana-3613 149 9 h. h. PROPN cana-3613 149 10 ( ( PUNCT cana-3613 149 11 2006 2006 NUM cana-3613 149 12 ) ) PUNCT cana-3613 149 13 𝑀/𝐺/1 𝑀/𝐺/1 NOUN cana-3613 149 14 queue queue NOUN cana-3613 149 15 with with ADP cana-3613 149 16 myltiple myltiple NOUN cana-3613 149 17 working working NOUN cana-3613 149 18 vacations vacation NOUN cana-3613 149 19 . . PUNCT cana-3613 150 1 performance performance NOUN cana-3613 150 2 evalutation evalutation NOUN cana-3613 150 3 63 63 NUM cana-3613 150 4 , , PUNCT cana-3613 150 5 pp pp ADJ cana-3613 150 6 . . PUNCT cana-3613 151 1 654–81 654–81 NUM cana-3613 151 2 . . PUNCT