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<p>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.</p>

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Insensitivity for Matching Systems

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年6月2日

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  • Runhan Xie,
  • Elene Anton,
  • Kristen Gardner,
  • Rhonda Righter

摘要

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.