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<p>We consider a system with two servers, each with its own queue: one observable and the other unobservable. Upon arrival, customers choose which queue to join. It is known that a unique threshold-type equilibrium strategy exists when the service rates of the two servers are equal. Dvir, Hassin, and Haviv (2022) demonstrated that such a strategy does not always exist when the service rates differ. However, through extensive numerical experiments, they observed that a unique threshold-type equilibrium strategy exists whenever the service rate of the unobservable queue is greater than or equal to that of the observable queue. In this paper, we rigorously prove this observation.</p>

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Equilibrium in a customer choice between observable and unobservable queues with heterogeneous servers

  • 期刊论文

  • 发表日期：

    2025年10月22日

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  • Bara Kim,
  • Jeongsim Kim,
  • Chia-Li Wang

摘要

We consider a system with two servers, each with its own queue: one observable and the other unobservable. Upon arrival, customers choose which queue to join. It is known that a unique threshold-type equilibrium strategy exists when the service rates of the two servers are equal. Dvir, Hassin, and Haviv (2022) demonstrated that such a strategy does not always exist when the service rates differ. However, through extensive numerical experiments, they observed that a unique threshold-type equilibrium strategy exists whenever the service rate of the unobservable queue is greater than or equal to that of the observable queue. In this paper, we rigorously prove this observation.