Bernoulli机制下的带有负顾客、反馈和N策略的M/M/1休假排队

M/M/1 Queue with Negative Customers

本文研究在Bernoulli机制下的带有负顾客、反馈和N策略的M/M/1休假排队系统,负顾客抵消队首正在接受服务的正顾客。在正规期,若系统中没有正顾客,服务台以概率α(0≤α ≤1)进入普通休假,或以概率β(β=1-α)进入工作休假。顾客在服务完成后以概率p(0≤p≤1)永远离开系统,或者以概率p(p=1-p)反馈到队尾继续等待服务。在休假期间,当顾客数大于等于N时,休假期结束。反之,则服务台继续休假。利用拟生灭过程和矩阵几何解的方法,得到了系统的稳态队长。最后,通过数值例子来说明一些参数对系统的影响。

In this paper, we study an M/M/1queue with negative customers and feedback and N-policy under Bernoulli schedule.Negative customer removes positive customer being service at the head of thequeue. During a normal period, when the system becomes empty, the server eitherbegins an ordinary vacation with probability α(0≤α≤1) or takes a working vacationwith probability β(β=1-α). When a positive customer completes his/herservice, s/he may leave the system with probability p(0≤p≤1) or return to the back of the queue waiting for another service withprobability p(p=1-p). When a vacation ends, if there are at least Ncustomers in the system, the server switches to the normal working level. Otherwise,the server begins another vacation. Using quasi birth and death (QBD) processand matrix geometric solution method, we obtain the steady-state distributionfor the queue length. Finally, some numerical examples are presented to showthe effect of some parameters on the expected queue length.