具有Min(N,D,V)-策略控制的M/G/1排队系统

M/G/1 queueing system with Min(N,D, V)-policy control

研究服务员具有多重休假和系统采取Min(N,D,V)-策略控制的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,研究了系统队长的瞬态分布和稳态分布,得到了队长瞬态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,同时给出了稳态队长的随机分解结果和附加队长分布的显示表达式.进一步讨论了当N→∞,或D→∞,或p{V=∞}=1,或p{V=0}=1的一些特殊情况.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控制策略(N~*,D~*),而且与单一的最优N~*-控制策略和D~*-控制策略进行了比较.

In this paper,we consider the M/G/1 queueing system with multiple server vacations and Min(N,D,V)-policy.By using the total probability decomposition technique and the Laplace transformation tool,the transient queue-length distribution and the steady queue-length distribution are discussed.Both the expressions of the Laplace transformation of the transient queue-length distribution and the recursive expressions of the steady queue-length distribution are obtained.Meanwhile,we present the stochastic decomposition result of the steady queue length and the explicit expression of the additional queue length distribution.Furthermore,some special cases are discussed when N→∞,D→∞,p{V=∞}=1 or p{V=0}=1.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 single optimal N~*-policy and the single optimal D~*-policy.