ABSTRACT

This paper studies the equilibrium balking strategies in the single-server Markovian queues with partial breakdowns and interruptible/setup closedown policy. That means the server may fail at any point in time, no matter the server is idle or busy and the service continues at a slower rate instead of stopping service totally. When the system becomes empty, the server ceases to operate by a closedown time. If a customer arrives during the closedown period, the system starts the service immediately without a setup time. After the closedown period, the server needs a setup time before providing the service upon arrival. We presume that the customers decide whether to join or balk immediately after their arrival based on the reward-cost structure of the system. The fully observable case is discussed and the equilibrium threshold strategies and the equilibrium social benefits for all customers are derived. A numerical example and a case study for a bank system are investigated in this regard. Eventually, the effects of several parameters on the equilibrium thresholds, social benefits, balking probability, probability of empty system and stationary distribution are expressed.

摘要

本文研究了具有部分故障和可中断/设置关闭策略的单服务器马尔可夫队列中的平衡抑制策略。这意味着无论服务器空闲还是繁忙，服务器都可能在任何时间发生故障，并且服务以较低的速率继续运行，而不是完全停止服务。当系统变空时，服务器将在关闭时间内停止运行。如果客户在关闭期间到达，则系统将立即启动服务，而无需设置时间。在关闭期之后，服务器需要设置时间才能在到达时提供服务。我们假设客户根据系统的奖励成本结构决定是否在加入后立即加入或退出。讨论了完全可观察的情况，并得出了所有客户的均衡阈值策略和均衡社会效益。在这方面，研究了一个银行系统的数值示例和案例研究。最终，表达了几个参数对均衡阈值，社会收益，阻止概率，空系统的概率和平稳分布的影响。