推广的M^x/G(M/G)/1(M/G)可修排队系统(I)── 一些排队指标

THE GENERALIZED Mx/G(M/G)/1(M/G) REPAIRABLE QUEUING SYSTEM (I) ──SOME QUEUING INDICES

考虑Ｍｘ／Ｇ（Ｍ／Ｇ）／１（Ｍ／Ｇ）可修排队系统，且把该系统推广到休假时间、服务时间、修理时间和延误休假时间都为任意分布（不一定连续），利用服务员忙期和拉普拉斯交换，我们直接获得队长瞬态分布的Ｌ变换递推式和稳态分布的递推式，以及队长的概率母函数，同时指出了１９９４年史定华文中存在的错误．

We consider a kind of the generalized Mx / G (M/ G ) / 1 (M/ G ) repairable queuing system in which the vacation time, service time, repair time and the delay vacation time are all arbitrary distributions. By using the server busy period and Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at time t, the recursion formula of the equilibrium distribution, and also obtain the probability generating function of the queue length, while simultaneously pointing out the errors in the paper of Shi Dinghua in 1994.