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Correlated queues with service times depending on inter-arrival times

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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.

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Notes

  1. The verification of (13) is beyond the scope of this paper; however, it is an interesting future research topic.

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Funding

This work is supported in part by the National Natural Science Foundation of China (NSFC) under Grants 71720107003 and 72033003.

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  1. School of Management, Fudan University, 670 Guoshun Road, Shanghai, 200433, China

    Weimin Dai & Jian-Qiang Hu

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  1. Weimin Dai
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  2. Jian-Qiang Hu
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This work is supported in part by the National Natural Science Foundation of China (NSFC) under Grants 71720107003 and 72033003.

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Dai, W., Hu, JQ. Correlated queues with service times depending on inter-arrival times. Queueing Syst 100, 41–60 (2022). https://doi.org/10.1007/s11134-021-09718-7

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