Correlated queues with service times depending on inter-arrival times

Weimin Dai and Jian-Qiang Hu ()
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Weimin Dai: Fudan University
Jian-Qiang Hu: Fudan University

Queueing Systems: Theory and Applications, 2022, vol. 100, issue 1, No 4, 60 pages

Abstract: Abstract 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.

Keywords: Correlated queues; Waiting time; Departure process; MacLaurin series expansion; Padé approximation; 60K25; 68M20; 90B22 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11134-021-09718-7

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