Performance analysis of M/M/1/N queue with setup time and working breakdown

被引：0
|
作者：
Yang X.-J. [1 ,3 ]
Li Z.-X. [2 ]
Li S.-P. [3 ]
Wu F. [2 ]
机构：
[1] School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu
[2] School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu
[3] School of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, 730050, Gansu
来源：
Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2019年 / 36卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Matrix geometric method; Performance analysis; Quasi birth and death process; Repairable queueing system; Working breakdown;
D O I：
10.7641/CTA.2018.80415
中图分类号：
学科分类号：
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. © 2019, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.
引用
收藏
页码：561 / 569
页数：8
相关论文
共 23 条
  • [21] Neuts M.F., Matrix-Geometric Solution in Stochastic Model: an Algorithmic Application, (1981)
  • [22] Tian N., Yue D., Quasi-Birth and Death Process and Matrix Geometric Solution, (2002)
  • [23] Elhafs E.H., Molle M., On the solution to QBD processes with finite state space, Stochastic Analysis and Applications, 25, 4, pp. 763-779, (2007)
123