带RCE抵消策略的负顾客GI／M／1工作休假排队

考虑服务员在休假期间不是完全停止工作,而是以相对于正常服务期的低些的服务率服务顾客的GI/M/1工作休假排队模型.在此模型基础上,针对现实的GI/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 in the end)抵消策略的负顾客GI/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.首先通过引进补充变量得到一个向量马氏过程,然后由矩阵几何解方法成功求得到达时刻和任意时刻系统队长的稳态分布.

GI/M/1 queue with RCE strategy of negative customers and working vacations

Consider a GI/M/1 queue 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 in the GI/M/1 queueing system,the GI/M/1 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 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.By adding supplementary variable,a new vector Markov process is obtained.Using matrix-geometric solution,the steady-state distributions are obtained for the number of customers in the system both at arrival and arbitrary epochs.