The reliability theory of the multi-state system (MSS) has received considerable attention in recent years, as it is able to characterize the multi-state property and complicated deterioration process of systems in a finer way than that of binary-state system. In general, the performance of the task processing type MSS is typically measured by an operation time (processing speed). Whereas, considering the queueing phenomenon caused by the random arrival and processing of tasks, some other criteria should be taken into account to evaluate the quality of service (QoS) and the profit of stakeholders, such as waiting time, service and abandon rate of tasks and consequent profit rate. In this article, we focus on the queueing process of tasks and analyse the performance and reliability of MSS in an M/M/2 queueing model, which is referred to as a multi-state queueing system (MSQS). Two kinds of deterioration are studied including the gradual degradation of servers and the sudden breakdown of the whole system. A performance assessment function is defined to obtain the profit rate of MSQS in different performance states. Based on the proposed performance function, the selective maintenance method is studied to optimize the accumulated profit under the constraint of maintenance resource and time.

多态系统（MSS）的可靠性理论近年来受到广泛关注，因为它能够比二元系统更精细地表征系统的多态特性和复杂的恶化过程。一般而言，任务处理类型MSS的性能通常以操作时间（处理速度）来衡量。而考虑到任务随机到达和处理造成的排队现象，还应考虑其他一些标准来评估服务质量（QoS）和利益相关者的利润，例如等待时间、服务和任务放弃率以及随之而来的利润率。在本文中，我们重点关注任务的排队过程，并在 M/M/2 排队模型中分析 MSS 的性能和可靠性，这被称为多状态排队系统（MSQS）。研究了服务器的逐渐退化和整个系统的突然崩溃两种退化。定义了一个绩效评估函数来获得MSQS在不同绩效状态下的利润率。基于所提出的性能函数，研究了在维修资源和时间约束下优化累积利润的选择性维修方法。