GI/G/1排队系统的逼近问题

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英文题名：The Approximation of GI/G/1 Queuing System 作者：申培霞 论文级别：硕士 学科专业名称：概率论与数理统计 中文关键词：GI/G/1排队系统 ; 马尔可夫骨架过程 ; Doob骨架过程 ; 转移函数 英文关键词：GI/G/1 queuing system ; Markov skeleton process ; Doob skeleton pro- 英文关键词：cess ; transition function 学位年度：2012 导师：阎国军 学科代码：070103 学位授予单位：郑州大学 论文提交日期：2012-04-01

摘要

GI/G/1排队系统是排队论中非常重要的模型.侯振挺等人证明了GI/G/1排队系统是马尔可夫骨架过程,并运用马尔可夫骨架过程的向后方程理论证明了GI/G/1排队系统的平稳分布和遍历性,给出了队长的转移函数所满足的方程.本文研究了GI/G/1排队系统队长的逼近问题,即：如果一列GI/G/1排队系统{Qum,m∈N}的输入分布{A(m)(x)}和服务时间的分布{B(m)(x)}分别收敛到连续分布A(x)和B(x),其中A(x)和B(x)分别是GI/G/1排队系统Qu的输入分布和服务时间的分布,那么这列排队系统{Qum,m∈N}队长的转移概率也收敛到Qu的队长的转移概率.
GI/G/1 queueing systems are important queue model in queue theory. Hou zhen ting and his colleagues prove that GI/G/1 queueing systems are Markov skeleton pro-cesses, and apply backward equations theory of Markov skeleton process to prove the stationary distributions and ergodic theorem,and give the explicit equation of the tran-sition function of the queue length of GI/G/1 queueing system.This paper investigates the approximation problem of the queue length of GI/G/1 queueing system,i.e.:If the distribution of inpnt{A(m) (x)} and the service time{B(m) (x)}of a list of GI/G/1 queue-ing systems{Qum,m∈N} respectively convergence to A(x)and B(x),here A(x)and B(x) respectively indicates the distribution of input and the service time of GI/G/1 queueing system Qu,then the transition probability of the queue length of{Qum,m∈N}convergence to the transition probability of the queue length of Qu.

引文

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