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M/G/1 queue with event-dependent arrival rates

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  • Benjamin Legros

    (Université Paris-Saclay)

Abstract

Motivated by experiments on customers’ behavior in service systems, we consider a queueing model with event-dependent arrival rates. Customers’ arrival rates depend on the last event, which may either be a service departure or an arrival. We derive explicitly the performance measures and analyze the impact of the event-dependency. In particular, we show that this queueing model, in which a service completion generates a higher arrival rate than an arrival, performs better than a system in which customers are insensitive to the last event. Moreover, contrary to the M/G/1 queue, we show that the coefficient of variation of the service does not necessarily deteriorate the system performance. Next, we show that this queueing model may be the result of customers’ strategic behavior when only the last event is known. Finally, we investigate the historical admission control problem. We show that, under certain conditions, a deterministic policy with two thresholds may be optimal. This new policy is easy to implement and provides an improvement compared to the classical one-threshold policy.

Suggested Citation

  • Benjamin Legros, 2018. "M/G/1 queue with event-dependent arrival rates," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 269-301, August.
    • Handle: RePEc:spr:queues:v:89:y:2018:i:3:d:10.1007_s11134-017-9557-7
    DOI: 10.1007/s11134-017-9557-7
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    References listed on IDEAS

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    1. Boxma, O. J., 1984. "Joint distribution of sojourn time and queue length in the M/G/1 queue with (in) finite capacity," European Journal of Operational Research, Elsevier, vol. 16(2), pages 246-256, May.
    2. J. Michael Harrison & Sidney I. Resnick, 1976. "The Stationary Distribution and First Exit Probabilities of a Storage Process with General Release Rule," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 347-358, November.
    3. Hsing Paul Luh & Ioannis Viniotis, 2002. "Threshold control policies for heterogeneous server systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 121-142, March.
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