Queues with correlated inter-arrival and service times

Qixin Wang and Jian-Qiang Hu ()
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Qixin Wang: Fudan University
Jian-Qiang Hu: Fudan University

Queueing Systems: Theory and Applications, 2024, vol. 108, issue 1, No 1, 30 pages

Abstract: Abstract We study a type of correlated queue in which its inter-arrival and service times are correlated, with their joint distribution being characterized by a copula function. This characterization allows for very generally correlated inter-arrival and service times. For such a queue, we first derive an infinite system of linear equations for the moments of the waiting time, based on which we design an algorithm to calculate the moments of the waiting time. In contrast with traditional methods, our algorithm incorporates a recursive procedure which is computationally much more efficient. Furthermore, we show how the moments and covariances of the inter-departure times of the queue can be obtained based on the moments of the waiting time. Numerical experiments are provided to validate our method.

Keywords: Correlated queues; Waiting time; Departure process; MacLaurin series expansion; Padé approximation; 60K25; 68M20; 90B22 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11134-024-09913-2

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