IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v87y2017i1d10.1007_s11134-017-9536-z.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-017-9536-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11134-017-9536-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    5. 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.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Michael N. Katehakis & Benjamin Melamed & Jim Junmin Shi, 2022. "Optimal replenishment rate for inventory systems with compound Poisson demands and lost sales: a direct treatment of time-average cost," Annals of Operations Research, Springer, vol. 317(2), pages 665-691, October.
    3. 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.
    4. Benjamin Legros, 2021. "Age-based Markovian approximation of the G/M/1 queue," Post-Print hal-03605431, HAL.
    5. Boxma, Onno & Frostig, Esther & Perry, David & Yosef, Rami, 2017. "A state dependent reinsurance model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 170-181.
    6. Esther Frostig & Adva Keren–Pinhasik, 2017. "Parisian ruin in the dual model with applications to the G/M/1 queue," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 261-275, August.
    7. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:queues:v:87:y:2017:i:1:d:10.1007_s11134-017-9536-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.