带RCE抵消策略的负顾客M/M/1工作休假排队系统

考虑服务员在休假期间不是完全停止工作,而是以相对于正常工作时低些的速率服务顾客的M/M/1工作休假排队模型.在此模型基础上,笔者针对现实的M/M/1排队模型中可能出现的外来干扰因素,提出了带RCE(Removal of Customers at the End)抵消策略的负顾客M/M/1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多重工作休假.抵消原则为负顾客一对一抵消队尾的正顾客,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.使用拟生灭过程和矩阵几何解方法给出了系统队长的稳态分布,证明了系统队长和等待时间的随机分解结果并给出稳态下系统中正顾客的平均队长和顾客在系统中的平均等待时间.

M/M/1 Queuing System with RCE Strategy of Negative Customers and Working Vacation

Consider an M/M/1queue with vacations such that the server works with different rates rather than completely stops during a vacation period.In order to solve the interfering factors take place in the M/M/1 queuing system,the M/M/1queuing system with negative customers and working vacations is studied.The serve rules are First Come First Served.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.Using QBD(quasi birth and death) process and Matrix-Geometric solution,we gain the steady-state distributions for the number of customers in the system,point out the result of stochastic decomposition of the queue length and obtain mean of the system size of positive customers and waiting time.