Engineering Physics and Mathematics
Analysis of an unreliable retrial G-queue with working vacations and vacation interruption under Bernoulli schedule

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Abstract

In this paper, we consider a single server retrial queueing system with working vacations. Further vacation interruption is considering with the regular busy server is subjected to breakdown due to the arrival of negative customers. When the orbit becomes empty at the time of service completion for a positive customer, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. If there are customers in the system at the end of each vacation, the server becomes idle and ready for serving new arrivals with probability p (single WV) or it remains on vacation with probability q (multiple WVs). By using the supplementary variable technique, we found out the steady state probability generating function for the system and its orbit. System performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented.

Keywords

Retrial queue
G-queue
Working vacations
Vacation interruption
Supplementary variable technique

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P. Rajadurai holds his Master of Science degree in Mathematics from Anna University, Chennai. He has completed his Master of Philosophy in VIT University. At present, he is doing his Ph.D. research program under the guidance of Dr. V.M. Chandrasekaran and Dr. M.C. Saravanarajan in School of Advanced Sciences at VIT University. He has published more than 25 research papers in international journals and international conferences. His area of specialization is Stochastic processes and its applications, in particular Queueing theory.

V.M. Chandrasekaran is working as Senior Professor in Department of Mathematics, School of Advanced Sciences, VIT University. He was awarded Ph.D. degree by Madras University in the year 1997. He has 20 years of teaching and research experience. His area of research is algebra and queueing theory. He has published more than 60 research articles in reputed national and international journals. He has guided four Ph.D. and five M.Phil. scholars. At present, He is guiding six Ph.D scholars.

M.C. Saravanarajan is working as an Assistant Professor (Senior) in Department of Mathematics, School of Advanced Sciences, VIT University. He has 14 years of teaching experience. He has completed his Ph.D. degree in VIT University under the guidance of Dr. V.M. Chandrasekaran in queueing theory. He has published more than 30 research papers in international journals and international conferences. He is currently guiding four Ph.D scholars. His area of specialization is Stochastic processes and its applications, in particular Queueing theory.

Peer review under responsibility of Ain Shams University.

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