Analysis of G-Queue with Pseudo-Fault and Multiple Working Vacations
Analysis of G-Queue with Pseudo-Fault and Multiple Working Vacations
复制标题
具有伪故障和多重工作假期的G队列分析
DOI：
10.1007/s11424-020-8117-0
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发表时间：
2020-04-29
影响因子：
2.1
通讯作者：
Wang, Pengcheng
中科院分区：
文献类型：
--
作者：
Ma, Zhanyou;Chen, Li;Wang, Pengcheng
本文提出了一种具有伪故障、负客户和多个工作假期的离散时间Geo/Geo/1可修复排队系统新模型。作者假设系统服务可能因故障或伪故障而中断，该系统只有在正常繁忙时段才可能被禁用，负面客户采用两种典型的查杀策略。在本文中，作者知道系统的演化可以用二维马尔可夫链来描述，并且二维马尔可夫链满足准生死链的条件。基于矩阵几何求解的方法，作者分别得到了RCH和RCE策略中平稳队列长度的分布。并对系统的可靠性进行了分析，得到了系统稳定状态下的客户数量和客户等待时间。作者比较分析了两种查杀策略对系统的影响。本文研究了积极顾客的个体和社会最优行为，并提出了积极顾客的定价策略，因此，作者获得了社会最优到达率。提供了各种数值结果来显示性能指标的变化。
This paper presents a new model of discrete time Geo/Geo/1 repairable queueing system with pseudo-fault, negative customers and multiple working vacations. The authors assume that system service may be interrupted by breakdown or pseudo-fault, this system may become disabled only when it is in a regular busy period, and negative customers adopt two types of typical killing strategies. In this paper, the authors know that the evolution of the system can be described by a two-dimensional Markov chain, and the two-dimensional Markov chain satisfies the condition of quasi birth and death chains. Based on the method of matrix-geometric solution, the authors obtain distributions for the stationary queue length in RCH and RCE strategy, respectively. Moreover, the reliability of the system is analyzed and the number of customers and waiting time of a customer in the system in steady state are obtained. The authors analyze the impact of two killing strategies on the system comparatively. This paper studies the individually and socially optimal behaviors of positive customers, and presents a pricing policy for positive customers, therefore, the authors obtain the socially optimal arrival rate. Various numerical results are provided to show the change of performance measures.