具有延迟休假和Min(N,V)-策略控制的M/G/1排队系统容量的优化设计与最优控制策略N^*

System Capacity Optimization Design and Optimal Control threshold N^*for M/G/1 Queueing System with Delayed Vacation and Min(N,V)-policy

把“休假延迟”引进到具有多重休假和Min(N,V)-策略控制的M/G/1排队系统中,研究了系统的稳态队长分布和队长的随机分解,获得了系统稳态队长分布的递推表达式和附加队长分布的显示表达式,同时讨论了一些特殊情形.进一步,通过数值计算实例,讨论了系统有关参数对附加平均队长的敏感性以及系统容量的优化设计问题.最后,在建立费用模型下,应用更新报酬过程我们推导出了长期单位时间内平均费用的显示表达式,并用数值计算实例确定了使其最小的最优控制策略N^*.

In this paper the "delayed vacation" is introduced in the M/G/1 queueing system with Min(N,V)-policy control,in which N is a predefined threshold that the server immediately interrupts his(her) vacation based on multiple server vacation.We investigate the distribution and stochastic decomposition of the queue length in equilibrium,and then obtain both the recursion expression of the steady state queue length distribution and the explicit expression of the additional queue length distribution.Meanwhile,some special cases are discussed.Furthermore,by numerical examples we discuss the sensitivity of the expected additional queue length towards system parameters and system capacity optimum design.Finally,employing the renewal reward process,the explicit expression of the long-run average cost function per unit time is derived under a given cost structure.The optimal control policy value N*for economizing the cost is also numerically determined.