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Fluid and diffusion approximations of probabilistic matching systems

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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