基于多重休假的min(N,V)-策略M/G/1排队系统的队长分布  

Queue length distribution of M/G/1 queueing system with min(N,V)-policy based on multiple server vacations

作　　者：唐应辉[1,2] 吴文青[1] 刘云颇[3] 刘晓云[4] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610068 [2]四川师范大学基础教学学院,成都610068 [3]成都大学信息科学与技术学院,成都610031 [4]电子科技大学自动化工程学院,成都610054

出　　处：《系统工程理论与实践》2014年第6期1533-1546,共14页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71171138;70871084)

摘　　要：运用全概率分解技术和拉普拉斯变换工具,研究了基于服务员多重休假的min(N,V)-策略M/G/1排队系统,其中N是预设的休假终止的门限值.讨论了从任意初始状态出发队长的瞬态分布,获得了队长瞬态分布的拉普拉斯变换的递推表达式和稳态队长分布的递推表达式,同时求出了附加队长分布的显示表达式.进一步讨论了当休假时间V分别服从负指数分布和定长分布P{V=T}=1,以及当N=1,N→∞,P{V=0}=1与P{V=∞}=1时的特殊情形.最后,通过数值实例阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中的重要价值.Applying the method of the total probability decomposition technique and the Laplace transform tool, the M/G/1 queueing system with min（N, V）-policy based on multiple server vacations which N is a predefined threshold that the server immediately interrupts his vacation is studied, and the transient queue length distribution from the beginning of the any initial state is discussed. We obtain both the recursion expressions of the Laplace-transformation of the transient queue length distribution and the recursion expressions of the steady state queue length distribution. Meanwhile, we present the explicit expression of the additional queue length distribution. Furthermore, we discuss some special cases, such as the vacation time has an exponential distribution or P{V = T} = 1, and N = 1 or N → ∞, and P{V = O} = 1 or P{V = ∞} = 1, respectively. Finally, by numerical examples, we illustrate the important value of the expression of the steady state queue length distribution for calculating conveniently in the system capacity design.

关 键 词：多重休假 min(N V)-策略 队长分布 全概率分解技术 系统容量设计 

分 类 号：O213.2[理学—概率论与数理统计] O226[理学—数学]