基于单重休假的Min(N,V)-策略M/G/1排队系统分析

Analysis of M/G/1 Queueing System with Min(N,V)-policy Based on Single Server Vacation

运用全概率分解技术和拉普拉斯变换工具,研究了基于眼务员单重休假的Min(N,V)-策略M/G/1排队系统,讨论了从任意初始状态出发队长的瞬态分布,获得了队长瞬态分布的拉普拉斯变换的递推表达式,并获得了稳态队长分布的递推表达式,同时,给出了稳态队长和稳态等待时间的随机分解结构,求出了附加队长分布的显示表达式,并分别讨论了当N=1,N→o。,P{V=0}=1,与P{V=o。}=1时的特殊情形.最后,通过数值实例研究了休假策略参数(N,V)对系统中附加平均队长和附加平均等待时间的影响.

Applying the method of the total probability decomposition technique and the Laplace transform tool, the M/G/1 queueing system with Min （N, V）-policy based on single server vacation is studied, and the transient queue length distribution from the beginning of the any initial state is discussed. We obtain both the recursive expressions of the Laplacetransformation of the transient queue length distribution and the recursive expressions of the steady state queue length distribution. Meanwhile, we demonstrate stochastic decomposition structures of the steady state queue length and waiting time. Furthermore, we obtain the explicit expression for the probability distribution of the additional queue length and discuss some special cases when N = 1, N→∞, P{V = 0} = 1, and P{V =∞}=1, respectively. Finally, by numerical examples, we study the influence of the vacation policy parameters （N, V） on the expected additional queue length and the expected additional waiting time in this system.