单重延误休假的M^x/G(M/G)/1可修排队系统分析(Ⅰ)—— 一些排队指标

Analysis of the M^x/G(M/G)/1 Repairable Queueing System with Single Delay Vacation (Ⅰ) ——Some Queueing Indices

考虑具有单重延误休假的MxG(MG)1可修排队系统,其中休假时间、服务时间、修理时间和延误休假时间都为任意分布(不一定是连续型),采用一种较简洁的方法,我们获得队长的瞬态解、平稳解和队长的随机分解表达式。

In this paper we consider a kind of M x /G(M/G)/1 repairable queueing system with single delay vacation in which the vacation time, service time, repairing time and the delay vacation time are all arbitrary distributions.By using a concise method, we obtain the transient solution, stationary solution and stochastic decomposition of the queue length. Simultaneously we also give out the stochastic decompositions of the queue lengths in some special cases.