GI/G/1排队系统的近似分析  

Approximate analysis method of the GI/G/1 queuing system

作　　者：赵宁 黄小峰 刘文奇 Zhao Ning;Huang Xiaofeng;Liu Wenqi(Data Science Research Center,Kunming University of Science and Technology,Kunming 650500,China;Faculty of Science,Kunming University of Science and Technology,Kunming 650500,China)

机构地区：[1]昆明理工大学数据科学研究中心,云南昆明650500 [2]昆明理工大学理学院,云南昆明650500

出　　处：《南京理工大学学报》2022年第2期211-218,共8页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(71501086)。

摘　　要：为了更准确地分析GI/G/1排队系统的性能指标,该文提出根据随机变量前三阶矩将一般到达过程近似为马尔可夫到达过程,将服务时间分布近似为相位分布,从而将GI/G/1排队系统构建为MAP/PH/1排队系统。采用矩阵几何解的方法分析相应的MAP/PH/1排队系统,得到GI/G/1排队系统的近似性能指标。通过大量的数值试验,对该文提出的方法与现有的近似方法进行误差分析,比较各种参数下GI/G/1排队系统平均等待时间的模拟值与近似值,验证了该文提出的方法的有效性和可行性。To accurately analyze the performance index of the GI/G/1 queuing system,this paper proposes to construct the GI/G/1 queue as a MAP/PH/1 queue approximately.This paper approximates the general arrival process as a Markovian arrival process and approximates the general service time distribution as a phase type distribution according to the first three moments of variables.By analyzing the corresponding MAP/PH/1 queuing system with matrix geometric methods,and the approximate performance index of the GI/G/1 queuing system is obtained.The proposed method is compared with the existing approximation methods by analyzing the mean relative error of the mean waiting times for GI/G/1 queuing system with various parameters.It is shown that the proposed method is effective and feasible.

关 键 词：排队系统 GI/G/1 MAP/PH/1 马尔可夫过程 平均等待时间 

分 类 号：O226[理学—运筹学与控制论]