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Stability analysis of parallel server systems under longest queue first

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  • Golshid Baharian

  • Tolga Tezcan

Abstract

We consider the stability of parallel server systems under the longest queue first (LQF) rule. We show that when the underlying graph of a parallel server system is a tree, the standard nominal traffic condition is sufficient for the stability of that system under LQF when interarrival and service times have general distributions. Then we consider a special parallel server system, which is known as the X-model, whose underlying graph is not a tree. We provide additional “drift” conditions for the stability and transience of these queueing systems with exponential interarrival and service times. Drift conditions depend in general on the stationary distribution of an induced Markov chain that is derived from the underlying queueing system. We illustrate our results with examples and simulation experiments. We also demonstrate that the stability of the LQF depends on the tie-breaking rule used and that it can be unstable even under arbitrary low loads. Copyright Springer-Verlag 2011

Suggested Citation

  • Golshid Baharian & Tolga Tezcan, 2011. "Stability analysis of parallel server systems under longest queue first," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 257-279, October.
    • Handle: RePEc:spr:mathme:v:74:y:2011:i:2:p:257-279
    DOI: 10.1007/s00186-011-0362-5
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    References listed on IDEAS

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    1. Tolga Tezcan & J. G. Dai, 2010. "Dynamic Control of N -Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic," Operations Research, INFORMS, vol. 58(1), pages 94-110, February.
    2. Hunt, P. J. & Kurtz, T. G., 1994. "Large loss networks," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 363-378, October.
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    3. Kuang Xu & Yuan Zhong, 2020. "Information and Memory in Dynamic Resource Allocation," Operations Research, INFORMS, vol. 68(6), pages 1698-1715, November.

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