具有第二次可选服务的带反馈的N—策略M^x/G/1(E,MV)排队系统分析

On the M^x/G/1(E,SV) with Feedback and Optional Service Based on Multiple Vacation under N—Plicy

研究N策略下的批量到达的具有第二次可选择服务且两次服务均可反馈的多重休假排队系统。建立了休假、反馈、可选服务多类型相结合的排队模型。本文采用补充变量法,首先建立了系统稳态下的状态转移方程,通过求解得到了稳态下系统队长的概率母函数,进而计算出稳态下系统的平均队长。对稳态队长进行分析之后,我们又给出了稳态队长的随机分解定理,其中给出了附加队长的明确概率解释。

we discuss a single server queue with batch arrivals and second optional general service time distribution under N-policy. We provide a multi-type queueing system, including vacation, feedback and optional services. A supplementary variable technique is used to obtain the steady - state function and the steady-state probability generation function of the number of customer in the system., then the mean number of customers and Stochastic decomposition of the number of customer in the system are obtained.