带有负顾客的M/M/c多重工作休假排队

M/M/c Queue With Negative Customers and Multiple Working Vacations

考虑服务台在休假期间不是完全停止工作,而是以相对于正常服务期低些的服务率服务顾客的M/M/c工作休假排队模型.在此模型基础上,针对现实的M/M/c排队模型中可能出现的外来干扰因素,提出了带有负顾客的M/M/c工作休假排队这一新的模型.服务规则为先到先服务.工作休假策略为空竭服务异步多重工作休假.抵消原则为负顾客一对一抵消处于正常服务期的正顾客,若系统中无处于正常服务期的正顾客时,到达的负顾客自动消失,负顾客不接受服务.首先,由该多重休假模型得到其拟生灭过程及生成元矩阵,然后运用矩阵几何方法给出系统队长的稳态分布表达式和若干系统指标.

Consider an M/M/c queue with vacations such that the servers work with different rates rather than completely terminate service during a vacation period. In order to solve the interfering factors in the M/M/c queueing system, the M/M/c queueing system with negative customers and working vacations is studied. The serve rule is first come first served. The working vacation policy is exhaustive service and asynchronous multiple working vacations. Negative customers remove positive customers who are in normal service period only one by one（if present）. When a negative customer arrives, if the system is empty or only the customers in the vacation period exist, it will disappear. Negative customers need no services. A quasi-birth-and-death process and infinitesimal generator for the process are obtained from the model that has been described. Matrix-geometric approach is utilized to obtain the steadystate distributions of queue length and some system characteristics.