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Queuing Problems with Heterogeneous Arrivals and Service

Author

Listed:
  • U. Yechiali

    (New York University, New York, New York)

  • P. Naor

    (The Technion, Haifa, Israel)

Abstract

This paper studies a two-level modification of the M / M /1 queuing model where the rate of arrival and the service capacity are subject to Poisson alternations. The ensuing “two-dimensional” problem is analyzed by using partial-generating-function techniques, which appear to be essential in the present context. The steady-state probabilities and the expected queue are evaluated, and numerous special and extreme cases are analyzed in detail.

Suggested Citation

  • U. Yechiali & P. Naor, 1971. "Queuing Problems with Heterogeneous Arrivals and Service," Operations Research, INFORMS, vol. 19(3), pages 722-734, June.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:3:p:722-734
    DOI: 10.1287/opre.19.3.722
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    Cited by:

    1. Nimrod Dvir & Refael Hassin & Uri Yechiali, 2020. "Strategic behaviour in a tandem queue with alternating server," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 205-244, December.
    2. Qiu, Qinjing & Kawai, Reiichiro, 2022. "A decoupling principle for Markov-modulated chains," Statistics & Probability Letters, Elsevier, vol. 182(C).
    3. Refael Hassin & Ran I. Snitkovsky, 2017. "Strategic customer behavior in a queueing system with a loss subsystem," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 361-387, August.
    4. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.

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