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

作　　者：唐应辉[1] 黄蜀娟[2] 余玅妙[3] 云曦[2] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610066 [2]电子科技大学应用数学学院,成都610054 [3]四川理工学院数学系,自贡643000

出　　处：《工程数学学报》2009年第2期251-259,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(70871084);教育部高校博士点专项研究基金(200806360001)

摘　　要：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.

关 键 词：M/G/1排队 队长 瞬态分布 稳态分布 最优策略 

分 类 号：O213.2[理学—概率论与数理统计]