带有负顾客且具有Bernoulli反馈的M/M/1工作休假排队(英文)

M/M/1 Bernoulli Feedback Queue with Negative Customers and Working Vacations

本文研究带反馈的具有正、负两类顾客的M/M/1工作休假排队模型.工作休假策略为空竭服务多重工作休假.负顾客一对一抵消队尾的正顾客(若有),若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务.完成服务的正顾客以概率p(0<p(?)1)离开系统,以概率1-p反馈到队尾寻求再次服务.使用拟生灭过程和矩阵几何解方法得到了系统队长的稳态分布,证明了系统队长随机分解结果并给出稳态下系统中正顾客的平均队长.本模型是M/M/1工作休假排队模型的推广.

The paper deals with an M/M/1 feedback queue with working vacations in which customers axe either “positive” or “negative”. The working vacation policy is exhaustive service and multiple working vacations. Negative customers remove positive customers only one by one at the tail （if present）. When a negative customer arrives, if the system is empty, it will disappear. Negative customers need no services. Just after completion of his service, a positive customer may leave the system with probability p（0〈P≤1）, or feedback with probabilityl-p. Using QBD （quasi birth and death） process and Matrix-Geometric solution, we derive the steady-state distributions for the number of customers in the system and prove the result of stochastic decomposition of the queue length and gain mean of the system size of positive customers. The model is an extension of M/M/1 queue with working vacations.