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Statistical inference for M-t/G/Infinity queueing systems under incomplete observations
Li, Dongmin1,2; Hu, Qingpei1,2; Wang, Lujia3; Yu, Dan1,2
2019-12-16
Source PublicationEUROPEAN JOURNAL OF OPERATIONAL RESEARCH
ISSN0377-2217
Volume279Issue:3Pages:882-901
AbstractM-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.
KeywordQueueing Interval censored data Maximum-likelihood estimation (MLE) Parametric bootstrap Delta method
DOI10.1016/j.ejor.2019.06.055
Language英语
Funding ProjectNational 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 Research AreaBusiness & Economics ; Operations Research & Management Science
WOS SubjectManagement ; Operations Research & Management Science
WOS IDWOS:000481560600015
PublisherELSEVIER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35485
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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