带有工作故障的M/M/1重试排队系统的性能分析  

Performance analysis of M/M/1 retrial queuing system with working breakdowns

作　　者：叶晴晴 陈钰 Ye Qingqing;Chen Yu(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044

出　　处：《河南师范大学学报（自然科学版）》2023年第3期82-89,共8页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11901307);江苏省自然科学基金(BK20180783).

摘　　要：研究了带有工作故障的M/M/1重试排队系统.基于广义特征值法,根据平衡方程得到了重试空间中顾客数与服务台状态的稳态联合概率分布的显示解,推导出排队系统的重要性能指标,并对任意客户逗留时间分布函数进行Laplace-Stieltjes变换,以此获得任意顾客的平均逗留时间.最后,通过数值例子来分析系统的参数变化对系统性能指标的影响,此外,还将广义特征值法与矩阵几何解法进行了比较.This paper studies the M/M/1 retrial queueing system with working breakdowns.Basing on the spectral expansion method,we solve the balance equations to obtain the explicit solution of the steady-state joint probability distribution of the number of customers in the orbit and the server state.Further,some important performance measures of queuing system are derived.Particularly,the expected sojourn time of the cuseomers is obtained by Laplace-Stieltjes transformation.Finally,we provide numerical examples to illustrate the effects of various system parameters on performance measures.In addition,we compare the spectral expansion method with the matrix geometric solution method in the analysis of retrial queue with working breakdowns.

关 键 词：重试排队 工作故障策略 广义特征值法 逗留时间 

分 类 号：O226[理学—运筹学与控制论]