延迟N-策略Geo/G/1排队系统的队长分布及数值计算  

Queue length distribution and numerical calculation for Geo/G/1 queueing system with delayed N-policy

作　　者：魏瑛源[1] 唐应辉[2] 顾建雄[3] 

机构地区：[1]河西学院数学与统计学院,张掖734000 [2]四川师范大学数学与软件科学学院,成都610066 [3]河西学院物理与机电工程学院,张掖734000

出　　处：《系统工程理论与实践》2011年第11期2151-2160,共10页Systems Engineering-Theory & Practice

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);河西学院科研创新与应用校长基金

摘　　要：考虑延迟N-策略离散时间Geo/G/1排队系统,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 the discrete-time Geo/G/1 queueing system with delayed N-policy. By 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Geo/G/1排队 延迟N-策略 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] O213.2[理学—数学]