串联排队系统平均等待时间的近似分析  

MeanWaiting Time Approximation of Tandem Queueing Systems

作　　者：侯佳辰 赵宁 刘文奇 侍颖 HOU Jiachen;ZHAO Ning;LIUWenqi;SHI Ying(Faculty of Science,Kunming University of Science and Technology,Kunming 650500,China;Center of Data Science,Kunming University of Science and Technology,Kunming 650500,China;School of International Business,Guangdong University of Finance and Economics,Guangzhou 510320,China)

机构地区：[1]昆明理工大学理学院,云南昆明650500 [2]昆明理工大学数据科学研究中心,云南昆明650500 [3]广东财经大学国际商学院,广东广州510320

出　　处：《山西大学学报（自然科学版）》2022年第1期41-49,共9页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(71701182)。

摘　　要：文章研究GI/G/1→/G/1串联排队系统,该系统由两个单一服务器串联而成,系统的到达过程是更新过程,两个站的服务时间服从一般分布。由于系统的到达时间间隔和服务时间服从一般分布,导致很难用解析的方法进行分析。根据系统的到达时间间隔和服务时间的三阶矩,文章分别将两个站的到达过程近似为MAP,服务时间近似为PH分布,从而将GI/G/1→/G/1排队系统近似为MAP/PH/1→/PH/1排队系统,构建相应的马尔可夫过程,采用矩阵几何解的方法求解系统的平均排队时间等数量指标。通过数值实验,验证了文章提出的近似方法的有效性。The GI/G/1→/G/1 tandem queuing system with two stations was studied.The system consists of two single servers in series,and the arrival process is a renewal process and the service times at the two stations follow the general distributions.Due to the general distributed arrival intervals and service times,it is difficult to analyze the system analytically.This paper proposes to approximate the arrival processes of the two stations by MAPs and approximate the service time by a phase type distribution by the first three moments of arrival intervals and service times.The GI/G/1→/G/1 queueing system is approximated by a MAP/PH/1→/PH/1 system.By constructing a Markovian process,the mean waiting time and the other performance measures are computed by matrix geometric method.Through the numerical experiments,the effectiveness of the method proposed in this paper is verified.

关 键 词：串联排队系统 平均等待时间 离去过程 近似分析 

分 类 号：O226[理学—运筹学与控制论]