带启动时间和工作故障的M/M/1/N排队系统性能分析
Performance analysis of M/M/1/N queue with setup time and working breakdown
摘要点击 128  全文点击 267  投稿时间:2018-06-05  修订日期:2018-11-05
查看全文  查看/发表评论  下载PDF阅读器
DOI编号  10.7641/CTA.2018.80415
  2019,36(4):561-569
中文关键词  可修排队模型  工作故障  拟生灭过程  矩阵几何方法  性能分析
英文关键词  repairable queueing system  working breakdown  quasi birth and death process  matrix geometric method  performance analysis
基金项目  国家自然科学基金项目(61663024), 欧盟国际合作项目(573879), 教育部春晖计划合作科研项目(Z2016001),甘肃省重点研发计划项 目(18YF1GD099),甘肃省中小企业创新基金项目(18CX5JA014), 兰州市人才创新创业项目(2017-RC-82), 兰州交通大学青年基金(2015007)
学科分类代码  
作者单位E-mail
杨喜娟 兰州交通大学 yangxj331@163.com 
李忠学 兰州交通大学  
黎锁平 兰州理工大学  
武福 兰州交通大学  
中文摘要
      本文在M/M/1/N可修排队系统中引入了工作故障和启动时间. 服务台在忙期允许出现故障, 且在故障期间不是完全停止服务而是以较低的服务速率为顾客服务. 同时, 从关闭期到正规忙期有服从指数分布的启动时间. 通过分析此模型的二维连续时间Markov过程, 求解出系统平稳方程, 建立此系统的有限状态拟生灭过程(Quasi Birthand Death Process, QBD). 根据系统参数, 求解出水平相依的子率阵, 从而得到系统稳态概率向量的矩阵几何表示形式. 在系统稳态概率向量的基础上, 求解出系统吞吐率、系统稳态可用度、系统稳态队长及系统处于各个状态的概率等性能指标的解析表达式. 文中的敏感性分析体现了这种方法的有效性和可用性, 同时, 对系统各性能受系统参数的影响进行了探索. 实验表明, 文中提出模型的稳定性较好, 且更贴近实际服务过程, 因此这种模型将被广泛应用于各种实际服务中.
英文摘要
      In this paper, the working breakdown and setup time strategies are introduced into the M/M/1/N repairable queueing system. The server is subject to breakdown when it is busy, rather than completely stopping service, it will decrease its service rate. Meanwhile, setup time, following exponential distribution, exists from idle period to regular busy period. The steady state equations are obtained by analyzing the two dimensional continuous time Markov process of the system, and the finite quasi birth and death(QBD) process of the system is established. According to system parameters, the level dependent sub-rate matrices are solved and the matrix geometric representation of the steady state probability vector of the system is obtained. Based on the steady state probability vector, the analytic expression of the performances, such as the throughput of the system, the steady state availability, the steady state queueing length and probability of each states, are obtained. The effectiveness and availability of the approach are fully shown in the sensitivity analysis and the influences of the parameters on the performances of the system are explored preliminarily. Experiments demonstrate that the proposed model is more stable and closer to the actual service process. Therefore, the model will be widely used in various practical services.