基于GI/M/1型Markov过程的Geo/Geo/1多重工作休假排队系统分析  

An Analysis for Geo/Geo/1 Queue with Multiple Working Vacations Based on GI/M/1 Type Markov Process

作　　者：张宏波 彭培让 ZHANG Hong-bo;PENG Pei-rang(School of Statistics and Mathematics,Henan Finance University,Zhengzhou 450046)

机构地区：[1]河南财政金融学院统计与数学学院,郑州450046

出　　处：《工程数学学报》2021年第3期353-361,共9页Chinese Journal of Engineering Mathematics

基　　金：河南省科技攻关计划项目(172102210242).

摘　　要：本文研究Geo/Geo/1多重工作休假排队系统.首先,应用GI/M/1型Markov链给出了该排队问题的一个新数学模型.其次,应用矩阵解析方法对模型求解,不但得到了排队模型平稳队长分布的具体形式,还给出了平稳状态时服务台具体处于第几次工作休假的概率.这些关于服务台状态更为精确的描述是该模型的新结果.最后用数值例子说明了分析方法的有效性.In this paper,the classical Geo/Geo/1 queueing system is investigated.First of all,a new GI/M/1 type Markov Chain model for the queue is proposed.Moreover,by using the matrix analytic method,the joint stationary distribution for the Markov chain is given,the results enable us not only obtain an explicit expression for the stationary queue length distribution of the queueing system,but also give the probability of the exact number of vacations that the sever has taken.Such accurate descriptions for the status of the server are new results for the queueing model.Finally,numerical examples are demonstrated to illustrate the effectiveness of the results.

关 键 词：Geo/Geo/1排队 工作休假 GI/M/1型Markov过程 矩阵几何解 差分方程 

分 类 号：O226[理学—运筹学与控制论]