An Unreliable Server Retrial Queue with Two Phases of Service and General Retrial Times Under Bernoulli Vacation Schedule

Abstract

This paper deals with the steady state behavior of an M/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with the FCFS (first come, first served) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability p or serves the next unit, if any, with probability (1 – p). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property. We also provide a reliability analysis of this model, which is one of the chief objectives of the paper. Finally, numerical illustrations show how the performance measures obtained are used to manage the system.

Key Words:

• Random breakdown
• reliability function
• repair time
• stationary queue size distribution
• second phase of service.

Additional information

Notes on contributors

Gautam Choudhury

Gautam Choudhury holds his M.Sc and Ph.D. in Statistics from Gauhati University, Guwahati, Assam, India. Presently, he is working as an Associate Professor in Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Paschim Boragoan, Guwahati, Assam, India. His areas of interest are queueing theory, stochastic models in communication systems and statistical inference in stochastic processes. He has numerous publications in journals of mathematics, statistics, and operations research.

Lotfi Tadj

Lotfi Tadj is an Assistant Professor in the Department of Information Systems and Decision Sciences at Fairleigh Dickinson University (Canada). He holds an MSc in Applied Mathematics from Carnegie-Mellon University (USA) and a Ph.D. in Operations Research from the Florida Institute of Technology (USA). His research interests include the optimal control of queueing and inventory systems. He has numerous publications in journals of mathematics, statistics, and operations research.

Mitali Deka

Mitali Deka holds her M.Sc. in Statistics from Gauhati University, Guwahati, Assam, India. Presently, she is working as a Guest Faculty in Assam Institute of Management, Guwahati, Assam. Her research interest includes stochastic processes and queueing theory.