带备用服务员及启动期和负顾客的Geo/Geo/1休假排队

摘要

The Geom/Geom/1 vacation queueing system with set-up time and a spare server was analyzed, inrnwhich customers were either ' positive' or ' negative' . Negative customers take the place of positive customersrnwho are served one by one in the front ( if present). When a negative customer arrives, and there isn ' t arnpositive customer in the system,the negative customer will disappear. Negative customers don't accept service.rnIn the system, there are two servers, the one is a main server, the other is a spareserver. When the system isrnempty, it turns off. Using QBD ( quasi-birth-and death) process and matrix-geometric solution method, thernsteady-state distribution for queue length is obtained. Besides,the conditional stochastic decomposition of queuernlength in the stationary state and the distributions for additional queue length are proved. Finally,the model isrnimitated reasonably well by using numerical examples.%分析了一类带备用服务员、启动期和负顾客的Geom/Geom/1休假排队系统.负顾客一对一抵消队首正在服务的正顾客(若有),如果系统中无正顾客,到达的负顾客自动离去,负顾客不接受服务.系统中有两个服务员,其中一个是主服务员,一个是备用服务员.当系统变空时,系统关闭.运用拟生灭过程和矩阵几何解的方法,得到了稳态队长的分布,证明了稳态存在的条件下队长的随机分解,从而得到附加队长的分布以及平均附加队长和平均队长.最后给出数值例子.