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Tandem Brownian queues

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  • P. Lieshout
  • M. Mandjes

Abstract

We analyze a two-node tandem queue with Brownian input. We first derive an explicit expression for the joint distribution function of the workloads of the first and second queue, which also allows us to calculate their exact large-buffer asymptotics. The nature of these asymptotics depends on the model parameters, i.e., there are different regimes. By using sample-path large-deviations (Schilder’s theorem) these regimes can be interpreted: we explicitly characterize the most likely way the buffers fill. Copyright Springer-Verlag 2007

Suggested Citation

  • P. Lieshout & M. Mandjes, 2007. "Tandem Brownian queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 275-298, October.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:2:p:275-298
    DOI: 10.1007/s00186-007-0149-x
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    Cited by:

    1. Masakiyo Miyazawa, 2011. "Light tail asymptotics in multidimensional reflecting processes for queueing networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 233-299, December.
    2. Zbigniew Michna, 2018. "Ruin probabilities for two collaborating insurance companies," Papers 1804.06598, arXiv.org, revised Dec 2018.
    3. Zbigniew Palmowski, 2022. "First exit time for a discrete-time parallel queue," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 329-331, April.
    4. Ernst, Philip A. & Franceschi, Sandro & Huang, Dongzhou, 2021. "Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 634-670.
    5. Krzysztof Dȩbicki, 2022. "Exact asymptotics of Gaussian-driven tandem queues," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 285-287, April.

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