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Analysis of the M1, M2/G/1 G-queueing system with retrial customers
Jinbiao Wu1,2,3; Zhaotong Lian2
2013-02
Source PublicationNonlinear analysis: real world applications
ISSN1468-1218
Volume14Issue:1Pages:365-382
Abstract

We consider a single server retrial queue with waiting places in service area and three classes of customers subject to the server breakdowns and repairs. When the server is unavailable, the arriving class-1 customer is queued in the priority queue with infinite capacity whereas class-2 customer enters the retrial group. The class-3 customers which are also called negative customers do not receive service. If the server is found serving a customer, the arriving class-3 customer breaks the server down and simultaneously deletes the customer under service. The failed server is sent to repair immediately and after repair it is assumed as good as new. We study the ergodicity of the embedded Markov chains and their stationary distributions. We obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law, the busy period of the system and the virtual waiting times. Finally, an application to cellular mobile networks is provided and the effects of various parameters on the system performance are analyzed numerically.

KeywordNonlinear System Retrial Queues Negative Customers Embedded Markov Chain Reliability
DOI10.1016/j.nonrwa.2012.06.009
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000309784600026
PublisherPERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
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Citation statistics
Cited Times [WOS]:5   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Business Administration
DEPARTMENT OF ACCOUNTING AND INFORMATION MANAGEMENT
Corresponding AuthorJinbiao Wu; Zhaotong Lian
Affiliation1.School of Mathematics and Statistics, Central South University
2.Faculty of Business Administration, University of Macau
3.Department of Information Science, Central South University
First Author AffilicationFaculty of Business Administration
Corresponding Author AffilicationFaculty of Business Administration
Recommended Citation
GB/T 7714
Jinbiao Wu,Zhaotong Lian. Analysis of the M1, M2/G/1 G-queueing system with retrial customers[J]. Nonlinear analysis: real world applications,2013,14(1):365-382.
APA Jinbiao Wu,&Zhaotong Lian.(2013).Analysis of the M1, M2/G/1 G-queueing system with retrial customers.Nonlinear analysis: real world applications,14(1),365-382.
MLA Jinbiao Wu,et al."Analysis of the M1, M2/G/1 G-queueing system with retrial customers".Nonlinear analysis: real world applications 14.1(2013):365-382.
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