Bernoulli控制下的带有负顾客和启动时间的M/M/1休假排队

M/M/1 Queue with Negative Customers and Setup Time and Vacation Policy Under Bernoulli Schedule

研究在Bernoulli控制下的带有负顾客和启动时间的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，服务员以概率α（0≤α≤1）进入普通休假，或以概率β（β=1—α）进入工作休假．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队长的影响．

In this paper, we study an M/M/1 queue with negative customers and setup time and vacation policy under Bernoulli schedule. Negative customer removes posi- tive customer being service at the head of the queue. During a normal period, when the system becomes empty, the server either begins an ordinary vacation with proba- bility α（0≤α≤1）or takes a working vacation with probability β（β=1-α）. Using quasi birth and death（QBD）process and matrix geometric solution method, we obtain the steady-state distribution for the queue length. Finally, some numerical examples are presented to show the effect of some parameters on the expected queue length.