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Controlling an oscillating Jackson-type network having state-dependent service rates

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  • Arnon Arazi
  • Eshel Ben-Jacob
  • Uri Yechiali

Abstract

We consider a Jackson-type network comprised of two queues having state-dependent service rates, in which the queue lengths evolve periodically, exhibiting noisy cycles. To reduce this noise a certain heuristic, utilizing regions in the phase space in which the system behaves almost deterministically, is applied. Using this heuristic, we show that in order to decrease the probability of a customers overflow in one of the queues in the network, the server in that same queue – contrary to intuition – should be shut down for a short period of time. Further noise reduction is obtained if the server in the second queue is briefly shut down as well, when certain conditions hold. Copyright Springer-Verlag 2005

Suggested Citation

  • Arnon Arazi & Eshel Ben-Jacob & Uri Yechiali, 2005. "Controlling an oscillating Jackson-type network having state-dependent service rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 453-466, December.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:3:p:453-466
    DOI: 10.1007/s00186-005-0041-5
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    References listed on IDEAS

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    1. Arazi, Arnon & Ben-Jacob, Eshel & Yechiali, Uri, 2004. "Bridging genetic networks and queueing theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 585-616.
    2. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
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    Cited by:

    1. Kostia Avrachenkov & Efrat Perel & Uri Yechiali, 2016. "Finite-buffer polling systems with threshold-based switching policy," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 541-571, October.
    2. Leite, Saul C. & Fragoso, Marcelo D., 2013. "Diffusion approximation for signaling stochastic networks," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2957-2982.

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