带有启动时间和单重工作休假的GI/M/1排队系统分析  

Analysis of GI/M/1 with Single Working Vacation and Setup Time

作　　者：颜娜[1] 吴云江[1] 

机构地区：[1]西安交通大学数学与统计学院,西安710049

出　　处：《工程数学学报》2014年第4期529-538,共10页Chinese Journal of Engineering Mathematics

摘　　要：在过去的二十年里,休假排队系统已经得到了广泛的研究.在各种休假排队模型中,在休假期内服务台是完全停止为顾客服务的.为了更客观地反映现实情况,本文在单重休假GI/M/1排队系统的基础上引入了在休假时服务台仍可低速服务而不是完全停止服务的工作休假策略和启动时间策略.对此模型的分析,我们重点关注顾客到达前夕时刻系统的状态,运用矩阵几何解方法得到了该系统的状态转移概率矩阵,并以概率矩阵为基础求出了系统的稳态平均队长和顾客的平均等待时间.In the past two decades, the queue with vacations has been extensively studied. Generally, the server stops totally and does not serve the customers in various queue models. In order to reflect the real world system more objectively, we introduce two strategies to the GI/M/1 queue system. One is the working vacation during that the server works at a lower rate rather than completely stops serving during a vacation and the other one is setup time. In the analysis of this model, the system state at the eve of the arrival time is focused and the transition probability matrix is obtained via using the geometric matrix method. Based on this matrix, we get the system’s stationary expected queue length and expected waiting time.

关 键 词：运筹学 排队论 MARKOV链 矩阵几何解 

分 类 号：O226[理学—运筹学与控制论]