具有工作休假和休假中断的M/M/1重试排队系统策略分析
Equilibrium of M/M/1 Retrail Queue System with Working Vacations and Vacation Interruption
摘要: 本文对具有工作休假和休假中断的M/M/1重试排队进行了研究。在队列中，顾客根据服务台是否被占用，服务台是否休假的情况，选择是否进入重试空间。通过对重试系统进行拟生灭过程研究并利用矩阵几何解法求出系统的性能指标，给出了顾客均衡和最优进队策，并给出均衡策略和最优策略下的社会均衡收益和社会最优收益。通过数值算例，比较了不同信息水平下的策略和收益。
Abstract: This paper studies M/M/1 retrail queue with working vacations and vacation interruption. In the queue, customers choose whether to enter the retrial orbit according to whether the server is oc-cupied and whether the server is on vacation. By studying the quasi-birth-death process of the retrail system and using the matrix geometric solution to obtain the performance index of the system, the customer equilibrium and the optimal queue strategy are given, and the social equi-librium income and social optimal income under the equilibrium strategy and optimal strategy are given. Through numerical examples, strategies and benefits under different information levels are compared.
文章引用：张晨希. 具有工作休假和休假中断的M/M/1重试排队系统策略分析[J]. 应用数学进展, 2022, 11(3): 1140-1149. https://doi.org/10.12677/AAM.2022.113123

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