具有延迟休假和Min(N,D,V)-策略的M/G/1排队的最优控制策略

The Optimal Control Policy for M/G/1 Queue with Delayed Vacations and Min(N,D,V)-Policy

本文研究具有延迟多重休假和系统采取Min(N,D,V)-策略的M/G/1排队系统.运用全概率分解技术和拉普拉斯变换工具讨论了系统从任意初始状态出发,在任意时刻t的瞬态队长分布和稳态队长分布,得到了瞬态队长分布的拉普拉斯变换的表达式和稳态队长分布的递推表达式,进一步也得到稳态队长的随机分解结果和附加队长分布的显示表达式.最后,在建立系统费用结构模型的基础上,导出了系统长期单位时间内的期望费用的显示表达式,并通过数值实例不但确定了使得系统在长期单位时间内的期望费用最小的联合最优控制策略(N^*,D^*),而且与无延迟休假的系统最优控制策略做了比较.

This paper is concerned with a M/G/1 queueing system with delayed multiple vacations and Min(N,D,V)-policy.Applying the total probability decomposition technique and the Laplace transform,we discuss the transient queue-length distribution and the steady queue-length distribution at any time t of the system,which started from an arbitrary initial state.Both the expression of the Laplace transform of the transient queue-length distribution and the recursive expressions of the steady-state queue length distribution are explicitly derived.Moreover,the stochastic decomposition result of the steady-state queue length and the explicit expressions for the probability distribution of the additional queue length are also given.Finally,the explicit expression of the long-run expected cost rate is derived under a given cost structure.And by through numerical calculation,we determine the optimal control policy(N^*,D^*)for minimizing the long-run expected cost per unit time as well as compare with the optimal control policy of the system without delayed vacations.