This paper considers the customers’ equilibrium and socially optimal joining–balking behavior in a single-server Markovian queue with a single working vacation and Bernoulli interruptions. The model is motivated by practical service systems where the service rate can be adjusted according to whether or not the system is empty. Specifically, we focus on a single-server queue in which the server's service rate is reduced from a regular to a lower one when the system becomes empty. This lower rate period is called a working vacation for the server which may represent that part of the service facility is under a maintenance process or works on other non-queueing job, or simply for saving the energy (for a machine server case). In this paper, we assume that the working vacation period is terminated after a random period or with probability p after serving a customer in a non-empty system. Such a system is called a queue with single working vacation and Bernoulli interruptions. Customers are strategic and can make choice of joining or balking based on different levels of system information. We consider four scenarios: fully observable, almost observable, almost unobservable, and fully unobservable queue cases. Under a reward-cost structure, we analyze the customer's equilibrium and social-optimal strategies. In addition, the effects of system parameters on optimal strategies are illustrated by numerical examples.

本文考虑了单服务器马尔可夫队列中的客户均衡和社会最优加入-阻止行为，其中有一个工作假期和伯努利中断。该模型以实际服务系统为灵感，可以根据系统是否为空来调整服务费率。具体来说，我们关注一个单服务器队列，在该队列中，当系统为空时，服务器的服务率从正常降低到较低。这个较低的费率时期称为服务器的工作假期，这可能表示服务设施的一部分正在维护过程中或从事其他非排队工作，或者只是为了节省能源（对于机器服务器情况）。在本文中，我们假设工作假期在一个随机周期之后或有概率终止p在非空系统中为客户服务后。这样的系统被称为单工作假期和伯努利中断的队列。客户具有战略意义，可以根据不同级别的系统信息来选择加入或拒绝。我们考虑四种场景：完全可观察、几乎可观察、几乎不可观察和完全不可观察的队列情况。在奖励成本结构下，我们分析了客户的均衡策略和社会最优策略。此外，通过数值例子说明了系统参数对最优策略的影响。