Statistical inference for M-t/G/Infinity queueing systems under incomplete observations

doi:10.1016/j.ejor.2019.06.055

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	Statistical inference for M-t/G/Infinity queueing systems under incomplete observations
	Li, Dongmin 1,2; Hu, Qingpei1,2 ; Wang, Lujia 3; Yu, Dan1,2
	2019-12-16
发表期刊	EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
ISSN	0377-2217
卷号	279 期号:3 页码:882-901
摘要	M-t/G/Infinity queueing systems have been widely used to analyse complex systems, such as telephone call centres, software testing systems, and telecommunication systems. Statistical inferences of performance measures, such as the expected cumulative numbers of arrivals and departures, are indispensable for decision makers in analysing the current scenario, predicting future scenarios, and making cost-effective decisions. In most scenarios, we only obtain interval censored data, namely, counts in fixed time intervals, instead of complete data because we either do not want or are not able to monitor arrivals and departures. We provide a general framework for statistical inference in M-t/G/Infinity queueing systems given interval censored data. A maximum-likelihood estimation (MLE) method is proposed for inferring the arrival rate and service duration. This method is applicable to general forms of the arrival rate functions and general service duration distributions. More importantly, we propose a combination of the bootstrap method and the delta method for inferring the expected cumulative numbers of arrivals and departures. The results of the simulation study demonstrate that the point and interval estimates of the proposed MLE method are satisfactory overall. As the number of intervals increases, the estimates based on the proposed MLE approach the estimates based on MLE with complete data. Our procedure enables estimates to be obtained without the need to keep track of each item, thereby substantially reducing resource consumption for monitoring items and storing data. An application in a software testing system demonstrates that the goodness-of-fit performance of the proposed MLE method is satisfactory. (C) 2019 Elsevier B.V. All rights reserved.
关键词	Queueing Interval censored data Maximum-likelihood estimation (MLE) Parametric bootstrap Delta method
DOI	10.1016/j.ejor.2019.06.055
语种	英语
资助项目	National Key R&D Programs of the Ministry of Science and Technology of China[2018YFB0704304] ; National Center for Mathematics and Interdisciplinary Sciences ; Key Laboratory of Systems and Control (CAS)
WOS研究方向	Business & Economics ; Operations Research & Management Science
WOS类目	Management ; Operations Research & Management Science
WOS记录号	WOS:000481560600015
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35485
专题	系统科学研究所
通讯作者	Hu, Qingpei
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Ctr Qual & Data Sci, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China 3.Arizona State Univ, Sch Comp Informat & Decis Syst Engn, Phoenix, AZ USA
推荐引用方式 GB/T 7714	Li, Dongmin,Hu, Qingpei,Wang, Lujia,et al. Statistical inference for M-t/G/Infinity queueing systems under incomplete observations[J]. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH,2019,279(3):882-901.
APA	Li, Dongmin,Hu, Qingpei,Wang, Lujia,&Yu, Dan.(2019).Statistical inference for M-t/G/Infinity queueing systems under incomplete observations.EUROPEAN JOURNAL OF OPERATIONAL RESEARCH,279(3),882-901.
MLA	Li, Dongmin,et al."Statistical inference for M-t/G/Infinity queueing systems under incomplete observations".EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 279.3(2019):882-901.