具有多重休假和两阶段服务的M^x/G/1重试排队系统  

M^X/G/1 Retrial Queue System with Multiple Vacations and Two-phase Service

作　　者：程慧慧 田中连 CHENG Hui-hui;TIAN Zhong-lian(North China University of Water Resources and Electric Power, Zhengzhou 450045, China)

机构地区：[1]华北水利水电大学数学与统计学院,郑州450045

出　　处：《科学技术与工程》2020年第32期13091-13098,共8页Science Technology and Engineering

基　　金：国家自然科学基金(11201145,11501531)。

摘　　要：研究具有多重休假和两阶段服务的重试排队系统,其中休假结束后需要重新启动。批次到达的顾客形成参数为λ的Poisson过程,顾客进行两阶段的服务:必选服务和可选服务,其中第二阶段有多种服务可供选择。首先证明了不等式ρ<1是系统稳定状态存在的充要条件,然后通过引入补充变量求出系统稳定状态分布及相关指标,最后在广义服务时间的定义下,推导出该系统满足随机分解性。A retrial queue with multiple vacations and two-phase service was studied,in which the server was restarted after vacations.Customers arriving in batches formed a generalized Poisson process with the parameterλ.Two-phase service of the essential service and the optional service was provided,and multiple services were available in the optional phase service.Firstly,it was proved that the inequalityρ<1 was a necessary and sufficient condition for the system stable.Then,the steady-state distribution and related indicators of the system were obtained by introducing supplementary variables.Finally,under the definition of generalized vacation,the stochastic decomposition of the system was derived.

关 键 词：多重休假 启动时间 两阶段服务 稳定状态 随机分解 

分 类 号：O226[理学—运筹学与控制论]