假期中顾客以概率θ进人的Geo/G/1(E,SV)排队系统的队长分布  

The Queue Length Distribution for Geo/G/1(E,SV)Queueing System with θ-Entering Discipline During Server Vacation

作　　者：魏宏源[1] 顾建雄[2] 魏瑛源[3] 

机构地区：[1]河西学院土木工程学院,甘肃张掖734000 [2]河西学院物理与机电工程学院,甘肃张掖734000 [3]河西学院数学与统计学院,甘肃张掖734000

出　　处：《数学的实践与认识》2014年第24期197-206,共10页Mathematics in Practice and Theory

基　　金：河西学院科研创新与应用校长基金(XZ2013-06)

摘　　要：考虑单重休假的Geo/G/1离散时间排队系统,其中在服务员休假期间到达的顾客以概率θ(0<θ≤1)进入系统.通过引入"服务员忙期"和使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,导出了在任意时刻n瞬态队长分布的z-变换的递推表达式和稳态队长分布的递推表达式,以及稳态队长的随机分解.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并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有重要的价值.This paper considers a discrete-time Geo/G/1queue with exhaustive service policy and single vacation in which the customs who arrive during server vacation enter the system with probability θ（θ〈θ ≤ 1）.By introducing the server busy period and using the total probability decomposition technique,we study the transient and equilibrium properties of the queue length from the beginning of the any initial state,obtain both the recursion expressions of the z-transformation of the transient queue length distribution at any time n and the recursion expressions of the steady state queue length distribution,and the stochastic decomposition of the queue length at a random point in equilibrium.Finally,by numerical examples,we discuss the sensitivity of the steady state queue length distribution towards system parameters,and illustrate the important value of the expressions of the steady state queue length distribution for calculating conveniently in the system capacity design.

关 键 词：离散时间排队 θ-进入规则 全概率分解技术 队长分布 随机分解 系统容量设计 

分 类 号：O226[理学—运筹学与控制论]