将带RCH抵消策略的负顾客、启动期和$N$策略引入离散时间排队.休假策略为空竭服务多重工作休假.负顾客一对一抵消队首正在接受服务的正顾客, 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.利用拟生灭过程和矩阵几何解方法, 给出了稳态队长分布及其随机分解.通过数值例子表现了启动率和负顾客到达率对稳态队长的影响.

The paper deals with a Geom/Geom/1 queue with set-up time and N-policy and working vacation in which customers are either “positive” or “negative”. The vacation policy is exhaustive service and multiple working vacation. The server works at a lower rate during the working vacation rather than stop working. Negative customers remove positive customers only one by one at the head (if present). When a negative customer arrives, if the system is empty, it will disappear. Negative customers need no services. Using QBD (quasi birth and death) process and matrix-geometric solution, we obtain the steady state distributions for the number of customers in the system and prove the result of stochastic decomposition of the queue length. Furthermore, we gain the mean of the system size of positive customers. Finally, we provide some numerical examples to illustrate the effect of the parameters such as starting rate and negative customer arrival rate on steady-state queue length.