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Insensitivity for Matching Systems

Author

Listed:
  • Runhan Xie

    (University of California)

  • Elene Anton

    (LIUPPA, Université de Pau et des Pays de l’Adour)

  • Kristen Gardner

    (Amherst College)

  • Rhonda Righter

    (University of California)

Abstract

We study matching queues motivated by applications in ride-sharing platforms, where items (e.g., drivers and riders) arrive over time and are matched based on a compatibility graph. Our model generalizes classical compatibility queueing models and queue-based ride-sharing models by allowing exogenous driver arrivals, queues for both drivers and riders, and arbitrary bipartite compatibility structures. We provide sufficient conditions under which the stationary distribution exhibits insensitivity to 1) service-time (drive-time) distributions and 2) the matching policies of drivers and riders, respectively. Using tools from Kelly networks and order-independent queues, we provide simple and unified proofs of insensitivity to service-time distributions and to matching policies for a broad class of models. Our policy insensitivity result requires a finite buffer; we demonstrate through counterexamples that such insensitivity may fail when the buffer is infinite. Our results also shed light on insensitivity in related redundancy systems, offering new insights into their stationary behavior.

Suggested Citation

  • Runhan Xie & Elene Anton & Kristen Gardner & Rhonda Righter, 2025. "Insensitivity for Matching Systems," Queueing Systems: Theory and Applications, Springer, vol. 109(2), pages 1-20, June.
    • Handle: RePEc:spr:queues:v:109:y:2025:i:2:d:10.1007_s11134-025-09943-4
    DOI: 10.1007/s11134-025-09943-4
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    References listed on IDEAS

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    1. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    2. Ragavendran Gopalakrishnan & Sherwin Doroudi & Amy R. Ward & Adam Wierman, 2016. "Routing and Staffing When Servers Are Strategic," Operations Research, INFORMS, vol. 64(4), pages 1033-1050, August.
    3. Kristen Gardner & Rhonda Righter, 2020. "Product forms for FCFS queueing models with arbitrary server-job compatibilities: an overview," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 3-51, October.
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    Keywords

    Matching Queues; Insensitivity;

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