Correlated queues with service times depending on inter-arrival times

We consider a type of correlated queue in which the service time of a customer depends on the inter-arrival time between him and the previous customer. We first derive an infinite system of linear equations for the moments of the system time, based on which we then develop several methods to calcula...

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Bibliographic Details
Published inQueueing systems Vol. 100; no. 1-2; pp. 41 - 60
Main Authors Dai, Weimin, Hu, Jian-Qiang
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2022
Springer Nature B.V
Subjects
Approximation
Business and Management
Computer Communication Networks
Control
Correlation
Customer services
Customers
Linear equations
MacLaurin series
Mathematical analysis
Methods
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Queues
Random variables
Series expansion
Supply Chain Management
Systems Theory
90B22
Departure process
68M20
MacLaurin series expansion
60K25
Correlated queues
Waiting time
Padé approximation
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Summary:We consider a type of correlated queue in which the service time of a customer depends on the inter-arrival time between him and the previous customer. We first derive an infinite system of linear equations for the moments of the system time, based on which we then develop several methods to calculate the moments of the system time by using MacLaurin series expansion and Padé approximation. 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 system time. Finally, numerical examples are provided to validate our methods.
ISSN:0257-0130
1572-9443
DOI:10.1007/s11134-021-09718-7