Transient study of a queueing system with one unreliable server, batch arrivals, two types of verification, loss and vacation. Issue 10 (19th May 2019)

• Record Type: Journal Article
• Authors: Terfas, Imane; Saggou, Hafida; Ourbih-Tari, Megdouda
• Is Part Of: Communications in statistics. Volume 48:Issue 10(2019)
• Page Start: 2580
• Page End: 2601
• Publication Date: 2019-05-19
• Subjects: Batch arrivals -- delay time -- geometric loss -- random breakdowns -- supplementary variable method -- vacation time; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2018.1472780
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: 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.