Correlated Queues with Inter-Arrival Times Depending on Service Times

被引：3

作者：

Jia, Zhenzhen ^{[1
]}

Dai, Weimin ^{[1
]}

Hu, Jian-Qiang ^{[1
]}

机构：

[1] Fudan Univ, Sch Management, Shanghai 200433, Peoples R China

来源：

ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH | 2024年 / 41卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Correlated queues; waiting time; departure process; MacLaurin series expansion; Pade approximation; DEPARTURE PROCESS; INTERARRIVAL; DEPENDENCY; IMPACT;

D O I：

10.1142/S0217595923500227

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We consider a type of correlated queue in which the inter-arrival time between two consecutive customers linearly depends on the service time of the first customer. We first derive infinite systems of linear equations for the moments of the waiting time in two special cases, based on which we then develop several methods to calculate the moments of the waiting time by using MacLaurin series approximation, Pade approximation and truncation method. In addition, we show how the moments and covariances of the inter-departure times of the correlated queue can be calculated based on the moments of the waiting time. Finally, extensive numerical examples are provided to validate our methods.

引用

页数：23

共 50 条

[1] Correlated queues with service times depending on inter-arrival times
Dai, Weimin
Hu, Jian-Qiang
[J]. QUEUEING SYSTEMS, 2022, 100 (1-2) : 41 - 60
[2] Correlated queues with service times depending on inter-arrival times
Weimin Dai
Jian-Qiang Hu
[J]. Queueing Systems, 2022, 100 : 41 - 60
[3] Queues with correlated inter-arrival and service times
Wang, Qixin
Hu, Jian-Qiang
[J]. QUEUEING SYSTEMS, 2024, 108 (1-2) : 1 - 30
[4] Performance of correlated queues: the impact of correlated service and inter-arrival times
Hwang, GU
Sohraby, K
[J]. PERFORMANCE EVALUATION, 2004, 55 (1-2) : 129 - 145
[5] Queues with correlated service and inter-arrival times and their application to optical buffers
Lambert, J
Van Houdt, B
Blondia, C
[J]. STOCHASTIC MODELS, 2006, 22 (02) : 233 - 251
[6] SINGLE SERVER QUEUES WITH DEPENDENT SERVICE AND INTER-ARRIVAL TIMES
JOHN, FI
[J]. JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1963, 11 (03): : 526 - 534
[7] The Effect of Correlated Service and Inter-arrival Times on System Performance
Hwang, Gang Uk
[J]. PROCEEDINGS OF WORLD ACADEMY OF SCIENCE, ENGINEERING AND TECHNOLOGY, VOL 8, 2005, 8 : 50 - 55
[8] USING INTER-ARRIVAL TIMES FOR SCHEDULING IN NON-OBSERVABLE QUEUES
Konovalov, Mikhail
Razumchik, Rostislav
[J]. PROCEEDINGS - 31ST EUROPEAN CONFERENCE ON MODELLING AND SIMULATION ECMS 2017, 2017, : 667 - 672
[9] PEAK FLOW INTER-ARRIVAL TIMES
ANDERSON, MG
[J]. JOURNAL OF HYDROLOGY, 1976, 30 (1-2) : 105 - 112
[10] STABILITY OF A QUEUE WITH NON-INDEPENDENT INTER-ARRIVAL AND SERVICE TIMES
LOYNES, RM
[J]. PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1962, 58 (JUL): : 497 - &

← 1 2 3 4 5 →