推广的(t，T)策略下M/G/1排队系统队长分布的递推解及最优策略

The Optimum Policy T~* and Recursion Solution of the Queue-length Distribution in M/G/1 Queue System with Generalized (t,T) Policy

本文考虑当系统变空后的延迟关闭时间为一般概率分布的(t,T)策略下的M/G/1/排队系统。通过引进"服务员忙期"和使用全概率分解技术,首次研究了系统在任意时刻队长的瞬态性质,导出了队长瞬态分布的L变换的递推表达式和稳态分布的递推表达式,进一步得出了系统稳态队长的随机分解结果。最后,建立系统的费用结构模型,讨论了系统变空后的最优关闭时间,并给出了具体数值计算例子。

This paper considers the generalized （t, T） policy M/G/1 queue under the delayed closetime which has a general probability distribution function when the system becomes empty. By introducing the ＂server busy period＂ and using the total probability decomposition technique, we study the transient and equilibrium properties of the queue-length, and obtain the recursion expression of the L-transformation of the transient queue-length distribution and the recursion expression of the equilibrium queue-length distribution. Furthermore, we also obtain the stochastic decomposition of the queue length at a random point in equilibrium. Finally, we discuss the optimum policy and give an example for obtaining the optimum policy under the assumed cost structure model.