Transient study of a queueing system with one unreliable server, batch arrivals, two types of verification, loss and vacation

This paper studies a transient regime for an unreliable queue with repairs, two delays, geometric loss and Bernoulli schedule server vacations. The server takes always a vacation when during the service, no customer arrives and the queue is empty. The customer whose service is interrupted stays in t...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 48; no. 10; pp. 2580 - 2601
Main Authors Terfas, Imane, Saggou, Hafida, Ourbih-Tari, Megdouda
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 19.05.2019
Taylor & Francis Ltd
Subjects
Batch arrivals
Customer services
Customers
Delay
delay time
geometric loss
Maintenance
Queues
Queuing theory
random breakdowns
Schedules
supplementary variable method
vacation time
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ISSN0361-0926
1532-415X
DOI10.1080/03610926.2018.1472780

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Summary:This paper studies a transient regime for an unreliable queue with repairs, two delays, geometric loss and Bernoulli schedule server vacations. The server takes always a vacation when during the service, no customer arrives and the queue is empty. The customer whose service is interrupted stays in the service, waiting for delay, repair and second delay (verification), after that, he completes his service. Using a supplementary variable method, transient solutions, performance and reliability measures and stochastic decomposition of the system are determined. Numerical results are sketched out to illustrate the effect of the system parameters on the main performances.
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ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2018.1472780