带有延迟启动时间和部分故障的M/M/1/N排队系统的性能分析
Performance Analysis of M/M/1/N Queue System with Delayed Startup Time and Partial Failure
摘要: 本文研究的是一个带有延迟启动时间和部分故障的M/M/1/N排队系统。在此排队系统中，服务台从关闭期到正常工作期间，需要经过一段随机时长服从指数分布的启动期。本文中所研究的部分故障指的是，系统发生故障后并不会立即停止服务，而是以一个较低的速率服务系统中现存的顾客，同时拒绝新到达的顾客进入系统中，当所有现存顾客服务完成并离开后系统立即进入修复期。易知本文中的二维连续马尔可夫过程为拟生灭过程(QBD)，利用删失技巧及矩阵分析方法便可得到该系统的平稳分布，如此，赋予各参数不同的值，便可进一步分析系统对各参数的敏感度。
Abstract: This paper focuses on an M/M/1/N queuing system with delayed startup time and partial failure. In such a queuing system, the server needs to experience a random time of start-up from the shut-down period to the normal working period which follows an exponential distribution. Partial failure is not to immediately stop service for repair. It means that the system no longer admits any customer from outside, while it conducts service for the existing customers in the system with a lower rate. After all customers finishing the service and leaving, the system enters into the repair period immediately. By analyzing the two dimensional continuous-time Markov chain in this paper, the Quasi Birth and Death (QBD) process for the system is established. By using the censoring technique, the stable distribution of the system is obtained according to the matrix geometric solution method. Therefore, the sensitivity of the system to parameters is further analyzed by assigning different values to the single parameter.
文章引用：卢会军, 宋旸. 带有延迟启动时间和部分故障的M/M/1/N排队系统的性能分析[J]. 运筹与模糊学, 2020, 10(3): 239-248. https://doi.org/10.12677/ORF.2020.103025

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