Abstract

In this article, we propose a finite buffer impatient customer queue with second optional service (SOS) and working vacations. When the server is busy, an arriving customer either joins the queue or balks on the basis of state-dependent joining/balking probabilities. For each customer, the server provides two phases of service, namely, first essential service (FES) and SOS. All the customers demand FES, whereas only few customers opt for SOS after the completion of FES. At a service completion instant, if the system is empty, the server leaves for working vacation. During working vacations, the waiting customers activate an impatient timer which is exponentially distributed. It is assumed that the interarrival times, vacation times, service times during FES, SOS and during working vacations follow exponential distribution. The steady-state probabilities of the model and various performance measures are derived. In order to optimize the total expected cost of the system, particle swarm optimization technique has been adopted for finding the optimum service rates of the server. Numerical results are sketched out to demonstrate the impact of the system and cost parameters.

摘要

在本文中，我们提出了一个有限缓冲区的急客户队列，该队列具有第二可选服务（SOS）和工作假期。当服务器忙时，到达的客户要么加入队列，要么根据状态相关的加入/拒绝概率拒绝。服务器为每个客户提供两个阶段的服务，即第一基本服务（FES）和SOS。所有客户都要求 FES，而只有少数客户在 FES 完成后选择 SOS。在服务完成瞬间，如果系统为空，则服务器离开工作假期。在工作假期期间，等待的顾客会激活一个不耐烦的计时器，该计时器呈指数分布。假设在 FES、SOS 和工作假期期间的到达间隔时间、休假时间、服务时间服从指数分布。推导出模型的稳态概率和各种性能指标。为了优化系统的总预期成本，采用粒子群优化技术来寻找服务器的最佳服务率。勾勒出数值结果以证明系统和成本参数的影响。