具有两类服务中断的离散时间重试排队分析

A Discrete-time Retrial Queue with Two Types of Server Interruptions

本文考虑了具有破坏性和非破坏性服务中断的离散重试排队系统.两类中断都发生在顾客接受服务的过程中,假设服务台在工作时发生破坏性中断,则正在接受服务的顾客中断服务,进入到重试空间中去,重新尝试以接受服务;若服务台在工作时发生非破坏性中断,则正在接受服务的顾客将等待中断结束后再继续完成剩余的服务量.求出了系统存在稳态的充分必要条件.利用补充变量法,求出了系统稳态时系统和重试区域中队长分布的概率母函数,以及其他一些重要的排队指标,并且给出了对应的连续时间下具有两类服务中断的M/G/1排队的队长分布的概率母函数.最后,通过数值算例研究了各种参数对平均队长的影响.

We consider a discrete queueing system with disruptive and non-disruptive server interruptions. Both disruptive and nomdisruptive interruptions may start when there is a customer in service. If a disruptive interruption occur, the customer is obliged to join the orbit; Otherwise, if a non-disruptive interruption occur, the customer waits and continues its service after a non-disruptive interruption. We analyze the equilibrium distribution of the system and obtain the generating functio,ns of the limiting distribution. Moreover, we prover that M/G/1 retrial queue with two types of server interruptions. Finally, some numerical examples are presented.