IDEAS home Printed from https://ideas.repec.org/a/eee/oprepe/v5y2018icp280-287.html
   My bibliography  Save this article

The number of overtakes in an M/M/2 queue

Author

Listed:
  • Baumann, Hendrik
  • Neumann, Berenice Anne

Abstract

The phenomenon of overtaking in queueing systems and queueing networks has been addressed by several authors with various motivations in the last decades. Nevertheless, up to now, for the relatively simple M/M/2/FCFS queue, the distribution of the number of overtakes a stationary customer suffers from was not known. In this paper, we characterize this distribution by its probability generating function. As a consequence, we derive the expectation (which is well-known) and the variance.

Suggested Citation

  • Baumann, Hendrik & Neumann, Berenice Anne, 2018. "The number of overtakes in an M/M/2 queue," Operations Research Perspectives, Elsevier, vol. 5(C), pages 280-287.
  • Handle: RePEc:eee:oprepe:v:5:y:2018:i:c:p:280-287
    DOI: 10.1016/j.orp.2018.09.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2214716018301593
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.orp.2018.09.001?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. Richard C. Larson, 1987. "OR Forum—Perspectives on Queues: Social Justice and the Psychology of Queueing," Operations Research, INFORMS, vol. 35(6), pages 895-905, December.
    2. Neumann, Berenice Anne & Baumann, Hendrik, 2018. "The expected discrimination frequency for two-server queues," Operations Research Perspectives, Elsevier, vol. 5(C), pages 145-149.
    Full references (including those not matched with items on IDEAS)

    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. Ryan W. Buell, 2017. "Last Place Aversion in Queues," Harvard Business School Working Papers 18-053, Harvard Business School, revised Oct 2019.
    2. Gad Allon & Awi Federgruen, 2007. "Competition in Service Industries," Operations Research, INFORMS, vol. 55(1), pages 37-55, February.
    3. Mirko Kremer & Laurens Debo, 2016. "Inferring Quality from Wait Time," Management Science, INFORMS, vol. 62(10), pages 3023-3038, October.
    4. Rebecca L. C. Taylor, 2020. "A Mixed Bag: The Hidden Time Costs of Regulating Consumer Behavior," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 7(2), pages 345-378.
    5. Opher Baron & Oded Berman & Dmitry Krass & Jianfu Wang, 2014. "Using Strategic Idleness to Improve Customer Service Experience in Service Networks," Operations Research, INFORMS, vol. 62(1), pages 123-140, February.
    6. Niu, Baozhuang & Li, Qiyang & Mu, Zihao & Chen, Lei & Ji, Ping, 2021. "Platform logistics or self-logistics? Restaurants’ cooperation with online food-delivery platform considering profitability and sustainability," International Journal of Production Economics, Elsevier, vol. 234(C).
    7. Sandipan S. Sen & Aliosha Alexandrov & Subhash Jha & William C. McDowell & Emin Babakus, 2023. "Convenient = competitive? How Brick-And-Mortar Retailers can cope with Online Competition," Review of Managerial Science, Springer, vol. 17(5), pages 1615-1643, July.
    8. Richard Charles Larson, 2002. "Public Sector Operations Research: A Personal Journey," Operations Research, INFORMS, vol. 50(1), pages 135-145, February.
    9. Ann Melissa Campbell & Dieter Vandenbussche & William Hermann, 2008. "Routing for Relief Efforts," Transportation Science, INFORMS, vol. 42(2), pages 127-145, May.
    10. Kwangji Kim & Mi-Jung Kim & Jae-Kyoon Jun, 2020. "Small Queuing Restaurant Sustainable Revenue Management," Sustainability, MDPI, vol. 12(8), pages 1-14, April.
    11. Yina Lu & Andrés Musalem & Marcelo Olivares & Ariel Schilkrut, 2013. "Measuring the Effect of Queues on Customer Purchases," Management Science, INFORMS, vol. 59(8), pages 1743-1763, August.
    12. Sezer Ülkü & Chris Hydock & Shiliang Cui, 2020. "Making the Wait Worthwhile: Experiments on the Effect of Queueing on Consumption," Management Science, INFORMS, vol. 66(3), pages 1149-1171, March.
    13. Robert J. Batt & Christian Terwiesch, 2017. "Early Task Initiation and Other Load-Adaptive Mechanisms in the Emergency Department," Management Science, INFORMS, vol. 63(11), pages 3531-3551, November.
    14. Tingliang Huang & Gad Allon & Achal Bassamboo, 2013. "Bounded Rationality in Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 263-279, May.
    15. Simon C. Moore & Thomas E. Woolley & James White, 2022. "An Exploration of the Multiplicative Effect of “Other People” and Other Environmental Effects on Violence in the Night-Time Environment," IJERPH, MDPI, vol. 19(24), pages 1-14, December.
    16. Söderlund, Magnus, 2011. "Other customers in the retail environment and their impact on the customer’s evaluations of the retailer," Journal of Retailing and Consumer Services, Elsevier, vol. 18(3), pages 174-182.
    17. Hideaki Takagi, 2016. "Waiting time in the M/M/ $$ m $$ m LCFS nonpreemptive priority queue with impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 257-289, December.
    18. Opher Baron & Oded Berman & Dmitry Krass & Jianfu Wang, 2017. "Strategic Idleness and Dynamic Scheduling in an Open-Shop Service Network: Case Study and Analysis," Manufacturing & Service Operations Management, INFORMS, vol. 19(1), pages 52-71, February.
    19. Robert J. Batt & Christian Terwiesch, 2015. "Waiting Patiently: An Empirical Study of Queue Abandonment in an Emergency Department," Management Science, INFORMS, vol. 61(1), pages 39-59, January.
    20. Stefanos A. Zenios & Glenn M. Chertow & Lawrence M. Wein, 2000. "Dynamic Allocation of Kidneys to Candidates on the Transplant Waiting List," Operations Research, INFORMS, vol. 48(4), pages 549-569, August.

    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:eee:oprepe:v:5:y:2018:i:c:p:280-287. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/operations-research-perspectives .

    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.