具有耐烦服务员和N-策略的M/G/1可中断休假排队系统

An M/G/1 Vacation Queueing System with Patient Server,N-policy and Vacation Interruption

考虑具有耐烦服务员和N-策略的M/G/1休假排队系统,其中服务员的假期可中断.运用全概率分解技术、更新理论和拉普拉斯变换工具,分析了系统的瞬态队长分布和稳态队长分布,获得了瞬态队长分布的拉普拉斯变换表达式和稳态队长分布的递推表达式,并进一步证明了稳态队长的随机分解性质.最后,通过建立费用结构模型,结合数值实例,讨论了使系统在长期单位时间内的期望费用最小的最优控制策略N*.

This paper considers an M/G/1 vacation queueing system with patient server and N-policy,where the server’s vacation can be interrupted.Applying the total probability decomposition technique,the renewal theory and the Laplace transform tool,the transient and steady-state queue length distributions of the system are analyzed,and the expression of the transient queue length distribution as well as the explicit recursive formulas of the steady-state queue length distribution are derived.Further-more,the stochastic decomposition property of the steady-state queue length is proved.Finally,a cost structure model is formulated and the optimal control policy N∗for minimizing the long-run expected cost per unit time is discussed through a numerical example.