带援助和伪障碍的Geom／Geom／1休假排队模型

摘要

Takeassistance and false malfunction into discrete time queue with vacation interrup‐tionstrategy .T hiscombinationenrich know n queuing model .T he assistance offset the positive customers w ho are being served from the head of the queue one by one .If thesystem suddenly stopped working ,thissystem failure .There are true and false failure .This paperuse quasi‐birth‐and‐death process and matrix‐geometric solution method ,thesteady‐state distributions for queue length and the probability generating function are given .Then the stochastic decom‐position structure of queue length and sojourn time in the stationary state is gained and ob‐tained the distributionsfor additional queue length and additional waiting timeby this paper .%在离散时间Geom／Geom／1工作休假排队系统中，同时考虑外来支援与伪障碍两个因素，这个组合丰富了原有的排队论模型。外来援助帮助系统减少顾客，一对一抵销队尾顾客。若系统突然停止工作，则称系统有障碍出现，障碍分为真障碍和伪障碍两类。本文应用拟生灭链和矩阵几何解的方法，得到了模型各状态的稳态分布，队长和等待时间在稳态条件下的随机分解。