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A rate balance principle and its application to queueing models

Author

Listed:
  • Binyamin Oz

    (University of Auckland)

  • Ivo Adan

    (Technische Universiteit Eindhoven)

  • Moshe Haviv

    (The Hebrew University of Jerusalem)

Abstract

We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth-and-death-like transitions, for which it is shown that for any state n, the rate of two consecutive transitions from $$n-1$$ n - 1 to $$n+1$$ n + 1 coincides with the corresponding rate from $$n+1$$ n + 1 to $$n-1$$ n - 1 . We demonstrate how useful this observation is by deriving well-known, as well as new, results for non-memoryless queues with state-dependent arrival and service processes. We also use the rate balance principle to derive new results for a state-dependent queue with batch arrivals, which is a model with non-birth-and-death-like transitions.

Suggested Citation

  • Binyamin Oz & Ivo Adan & Moshe Haviv, 2017. "A rate balance principle and its application to queueing models," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 95-111, October.
    • Handle: RePEc:spr:queues:v:87:y:2017:i:1:d:10.1007_s11134-017-9536-z
    DOI: 10.1007/s11134-017-9536-z
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    References listed on IDEAS

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    1. Moshe Haviv & Yoav Kerner, 2011. "The age of the arrival process in the G/M/1 and M/G/1 queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 139-152, February.
    2. Ivo Adan & Onno Boxma & David Perry, 2005. "The G/M/1 queue revisited," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 437-452, December.
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    Citations

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    Cited by:

    1. Legros, Benjamin, 2022. "The principal-agent problem for service rate event-dependency," European Journal of Operational Research, Elsevier, vol. 297(3), pages 949-963.
    2. Oz, Binyamin & Adan, Ivo & Haviv, Moshe, 2019. "The Mn/Gn/1 queue with vacations and exhaustive service," European Journal of Operational Research, Elsevier, vol. 277(3), pages 945-952.
    3. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    4. Opher Baron & Antonis Economou & Athanasia Manou, 2022. "Increasing social welfare with delays: Strategic customers in the M/G/1 orbit queue," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2907-2924, July.
    5. Opher Baron & Antonis Economou & Athanasia Manou, 2018. "The state-dependent M / G / 1 queue with orbit," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 89-123, October.
    6. Binyamin Oz, 2022. "Optimal admission policy to an observable M/G/1 queue," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 477-479, April.

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