一般限量服务M／G／1型单重休假排队系统的随机分解

Stochastic Decomposition of an M/G/1 Type Queue with Single-vacation and General-limited Service

本文研究了M／G／1型一般限量服务单重休假排队系统,根据稳态下M／G／1型非空竭服务休假排队系统的队长的随机分解的一般结构,提出简便算法一结构分析法,并且在先到先服务规则下(FCFS)求得稳态下队长的随机分解的概率母函数(GFP)和服务时间的随机分解的Laplace变换(LST),还充分地讨论了系统平稳的条件及其概率含义。

An M/G/1 type queue with a single vacation and generally limited services is studied. According to the general structure in steady state of the queue length of a M/G/1 type queueing system with single or mutiple vacations and nonexhaustive services, under the service rule that custmors who first come would first get the service, an simplified algorithm called the structure-analysis method is offered to get the stochastic decomposition of the queue length with the generating function of probability （GFP） and the waiting time with Laplace-Stieltjes transforms （LST）. At the same time, the condition that the system is going to a steady state with its probability meaning is also sufficiently discussed.