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A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule
Jinbiao Wu1; Zhaotong Lian2
2012-10-01
Source PublicationComputers and Industrial Engineering
ABS Journal Level2
ISSN0360-8352
Volume64Issue:1Pages:84-93
Abstract

We consider an M/G/1 retrial queue with negative customers and priority under Bernoulli vacation schedule subject to the server breakdowns and repairs. Arrivals of both positive customers and negative customers are two independent Poisson processes. Positive customers receive service immediately if the server is idle upon their arrivals. Otherwise, they may either with probability p join the priority queue or with complementary probability-p enter a retrial orbit. A breakdown at the busy server is represented by the arrival of a negative customer which causes the the customer being in service to be lost. The server takes Bernoulli vacation after a service or a repair completion. It is assumed that the server has arbitrary repair time and vacation time distributions. With the help of Lyapunov functions we have obtained the necessary and sufficient condition for ergodicity of embedded Markov chain. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law. Besides, some special cases of interest are discussed. Finally, the effects of various parameters on the system performance are analyzed numerically.

KeywordEmbedded Markov Chain G-queues Reliability Retrial Queues Stochastic Decomposition
DOI10.1016/j.cie.2012.08.015
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Interdisciplinary Applications ; Engineering, Industrial
WOS IDWOS:000315309300008
PublisherPERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
The Source to ArticleScopus
Scopus ID2-s2.0-84869128774
Fulltext Access
Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF ACCOUNTING AND INFORMATION MANAGEMENT
University of Macau
Corresponding AuthorJinbiao Wu
Affiliation1.School of Mathematics and Statistics, Central South University, Changsha 410075, Hunan, PR China
2.Faculty of Business Administration, University of Macau, Macau SAR, PR China
Recommended Citation
GB/T 7714
Jinbiao Wu,Zhaotong Lian. A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule[J]. Computers and Industrial Engineering, 2012, 64(1), 84-93.
APA Jinbiao Wu., & Zhaotong Lian (2012). A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule. Computers and Industrial Engineering, 64(1), 84-93.
MLA Jinbiao Wu,et al."A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule".Computers and Industrial Engineering 64.1(2012):84-93.
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