具有不耐烦顾客的MAP/PH/1排队系统的性能分析  

Performance Analysis of an MAP/PH/1 Queueing System with Impatient Customers

作　　者：刘恒丽 李泉林 LIU Hengli;LI Quanlin(School of Economics and Management,Yanshan University,Qinhuangdao 066004;School of Economics and Management,Beijing University of Technology,Beijing 100124)

机构地区：[1]燕山大学经济管理学院,秦皇岛066004 [2]北京工业大学经济与管理学院,北京100124

出　　处：《系统科学与数学》2023年第7期1819-1836,共18页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金重点项目(71932002);国家自然科学基金面上项目(71671158)资助课题。

摘　　要：文章研究了具有不耐烦顾客的MAP/PH/1排队系统,其中顾客的到达过程是马尔可夫到达过程,顾客的服务时间服从位相型分布,顾客的不耐烦时间服从指数分布.针对这个排队系统,文章构建了一个水平相依的拟生灭过程.首先,文章利用平均漂移技术给出了排队系统的稳定性条件.其次,文章借助于马氏过程的RG-分解方法,提供了拟生灭过程的平稳概率向量,并得到排队系统稳态队长的概率分布和平均稳态队长.再次,为了分析任意一个到达顾客在系统中的逗留时间,文章建立了一个具有吸收状态的马氏过程,给出这个逗留时间的概率分布和平均逗留时间.最后,文章使用数值算例分析了一些关键参数对系统性能指标的影响.This paper considers an MAP/PH/1 queueing system with impatient customers.Customers arrive at the queueing system according to a Markovian arrival process,each of the customers requiring a service that is of phase type,and the impatient time of customers is assumed to be exponentially distributed.For analyzing the queueing system,a level dependent quasi-birth-and-death process is constructed.Firstly,the stability condition of the system is obtained by using the mean drift technique.Then the stationary probability vector of the quasi-birth-and-death process is given by using the RG-factorization of Markov process.Based on the stationary probability vector,the probability distribution of the stationary queue length and the average stationary queue length are obtained.Moreover,a Markov process with an absorption state is built for analyzing the sojourn time of any arriving customer in the system,and the probability distribution of the sojourn time and the average sojourn time are given.Finally,the effect of some crucial parameters on the performance measures of the system is analyzed by means of numerical examples.

关 键 词：排队系统 不耐烦顾客 马尔可夫到达过程 位相型分布 RG-分解 

分 类 号：O226[理学—运筹学与控制论]