IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v86y2017i1d10.1007_s11134-017-9516-3.html
   My bibliography  Save this article

Fluid and diffusion approximations of probabilistic matching systems

Author

Listed:
  • Burak Büke

    (The University of Edinburgh)

  • Hanyi Chen

    (The University of Edinburgh)

Abstract

This paper focuses on probabilistic matching systems where two classes of users arrive at the system to match with users from the other class. The users are selective and the matchings occur probabilistically. Recently, Markov chain models were proposed to analyze these systems; however, an exact analysis of these models to completely characterize the performance is not possible due to the probabilistic matching structure. In this work, we propose approximation methods based on fluid and diffusion limits using different scalings. We analyze the basic properties of these approximations and show that some performance measures are insensitive to the matching probability, agreeing with the existing results. We also perform numerical experiments with our approximations to gain insight into probabilistic matching systems.

Suggested Citation

  • Burak Büke & Hanyi Chen, 2017. "Fluid and diffusion approximations of probabilistic matching systems," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 1-33, June.
    • Handle: RePEc:spr:queues:v:86:y:2017:i:1:d:10.1007_s11134-017-9516-3
    DOI: 10.1007/s11134-017-9516-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-017-9516-3
    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/s11134-017-9516-3?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. Avishai Mandelbaum & Petar Momčilović, 2012. "Queues with Many Servers and Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 41-65, February.
    2. Ivo Adan & Gideon Weiss, 2012. "Exact FCFS Matching Rates for Two Infinite Multitype Sequences," Operations Research, INFORMS, vol. 60(2), pages 475-489, April.
    3. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    4. J. G. Dai & Shuangchi He, 2010. "Customer Abandonment in Many-Server Queues," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 347-362, May.
    5. B. R. K. Kashyap, 1966. "The Double-Ended Queue with Bulk Service and Limited Waiting Space," Operations Research, INFORMS, vol. 14(5), pages 822-834, October.
    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. Jose H. Blanchet & Martin I. Reiman & Viragh Shah & Lawrence M. Wein & Linjia Wu, 2020. "Asymptotically Optimal Control of a Centralized Dynamic Matching Market with General Utilities," Papers 2002.03205, arXiv.org, revised Jun 2021.
    2. Antonio Di Crescenzo & Virginia Giorno & Balasubramanian Krishna Kumar & Amelia G. Nobile, 2018. "A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation," Mathematics, MDPI, vol. 6(5), pages 1-23, May.
    3. Jocelyn Begeot & Irène Marcovici & Pascal Moyal, 2023. "Stability regions of systems with compatibilities and ubiquitous measures on graphs," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 275-312, April.

    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. Xin Liu, 2019. "Diffusion approximations for double-ended queues with reneging in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 49-87, February.
    2. Hongyuan Lu & Guodong Pang & Yuhang Zhou, 2016. "$$G/{ GI}/N(+{ GI})$$ G / G I / N ( + G I ) queues with service interruptions in the Halfin–Whitt regime," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 127-160, February.
    3. Lu Wang & Vidyadhar Kulkarni, 2020. "Fluid and diffusion models for a system of taxis and customers with delayed matching," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 101-131, October.
    4. Josh Reed & Tolga Tezcan, 2012. "Hazard Rate Scaling of the Abandonment Distribution for the GI/M/n + GI Queue in Heavy Traffic," Operations Research, INFORMS, vol. 60(4), pages 981-995, August.
    5. Petar Momčilović & Amir Motaei, 2018. "QED limits for many-server systems under a priority policy," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 125-159, October.
    6. Jeunghyun Kim & Ramandeep S. Randhawa & Amy R. Ward, 2018. "Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 285-301, May.
    7. Avishai Mandelbaum & Petar Momčilović, 2017. "Personalized queues: the customer view, via a fluid model of serving least-patient first," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 23-53, October.
    8. Josh Reed & Yair Shaki, 2015. "A Fair Policy for the G / GI / N Queue with Multiple Server Pools," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 558-595, March.
    9. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    10. Max Tschaikowski & Mirco Tribastone, 2017. "A computational approach to steady-state convergence of fluid limits for Coxian queuing networks with abandonment," Annals of Operations Research, Springer, vol. 252(1), pages 101-120, May.
    11. Mohammadreza Nazari & Alexander L. Stolyar, 2019. "Reward maximization in general dynamic matching systems," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 143-170, February.
    12. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    13. Ananda Weerasinghe, 2014. "Diffusion Approximations for G / M / n + GI Queues with State-Dependent Service Rates," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 207-228, February.
    14. A. Korhan Aras & Xinyun Chen & Yunan Liu, 2018. "Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 81-125, June.
    15. Junfei Huang & Hanqin Zhang & Jiheng Zhang, 2016. "A Unified Approach to Diffusion Analysis of Queues with General Patience-Time Distributions," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1135-1160, August.
    16. Hongyuan Lu & Guodong Pang & Yuhang Zhou, 2016. "$$G/{ GI}/N(+{ GI})$$ G / G I / N ( + G I ) queues with service interruptions in the Halfin–Whitt regime," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 127-160, February.
    17. Avishai Mandelbaum & Petar Momčilović, 2012. "Queues with Many Servers and Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 41-65, February.
    18. Bo Zhang & Johan S. H. van Leeuwaarden & Bert Zwart, 2012. "Staffing Call Centers with Impatient Customers: Refinements to Many-Server Asymptotics," Operations Research, INFORMS, vol. 60(2), pages 461-474, April.
    19. Christos Zacharias & Mor Armony, 2017. "Joint Panel Sizing and Appointment Scheduling in Outpatient Care," Management Science, INFORMS, vol. 63(11), pages 3978-3997, November.
    20. Rami Atar & Adam Shwartz, 2008. "Efficient Routing in Heavy Traffic Under Partial Sampling of Service Times," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 899-909, November.

    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:86:y:2017:i:1:d:10.1007_s11134-017-9516-3. 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.