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

doi:10.7641/CTA.2018.80415

CORC > 兰州理工大学 > 兰州理工大学

	Performance analysis of M/M/1/N queue with setup time and working breakdown
	Yang, Xi-Juan 1,3; Li, Zhong-Xue 2; Li, Suo-Ping 3; Wu, Fu 2
刊名	Kongzhi Lilun Yu Yingyong/Control Theory and Applications
	2019-04-01
卷号	36 期号:4 页码:561-569
关键词	Continuous time systems Markov processes Queueing networks Queueing theory Sensitivity analysis Matrix geometric methods Performance analysis Quasi-birth and death process Queueing system Working breakdown
ISSN号	10008152
DOI	10.7641/CTA.2018.80415
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. © 2019, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.
语种	中文
出版者	South China University of Technology
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/114351]
专题	兰州理工大学
作者单位	1.School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou; Gansu; 730070, China; 2.School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou; Gansu; 730070, China; 3.School of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou; Gansu; 730050, China
推荐引用方式 GB/T 7714	Yang, Xi-Juan,Li, Zhong-Xue,Li, Suo-Ping,et al. Performance analysis of M/M/1/N queue with setup time and working breakdown[J]. Kongzhi Lilun Yu Yingyong/Control Theory and Applications,2019,36(4):561-569.
APA	Yang, Xi-Juan,Li, Zhong-Xue,Li, Suo-Ping,&Wu, Fu.(2019).Performance analysis of M/M/1/N queue with setup time and working breakdown.Kongzhi Lilun Yu Yingyong/Control Theory and Applications,36(4),561-569.
MLA	Yang, Xi-Juan,et al."Performance analysis of M/M/1/N queue with setup time and working breakdown".Kongzhi Lilun Yu Yingyong/Control Theory and Applications 36.4(2019):561-569.