A Two-Phase Service System with Bernoulli Vacation Schedule, Setup Time and N-policy for an Unreliable Server with Delaying Repair

Abstract

This paper deals with an M/G/1 queueing system with two phases of service and Bernoulli vacation schedule for an unreliable server, which consist of a breakdown period and a delay period, under N-policy and a random setup time. While the server is working with any phase of service, it may break down at any instant and the service channel will fail for a short interval of time. Further, concept of the delay time is also introduced. If no customer arrives during the breakdown period, the server becomes idle in the system until the queue size builds up to a threshold value (N > 1). As soon as the queue size becomes at least N, the server immediately begins to serve the waiting customers in two successive phases of service. The first phase of service is followed by a second phase of service, after the completion of which, the server may take a vacation or may remain in the system to serve the next unit, if any. We derive the queue size distribution at different points of time, delay busy period distribution and optimal N-policy.

Key Words:

• Bernoulli vacation and N-policy
• delay time
• queue size distribution
• random breakdown
• repair time

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 published more than 65 research papers in various journals of Statistics, Mathematics and Operations Research. He is an Associate Editor of Far East Journal of Theoretical Statistics.

Lotfi Tadj

Lotfi Tadj earned the B.S. degree in mathematics at Houari Boumediene University, Algiers, Algeria, in 1983; the M.S. degree in applied mathematics at Carnegie-Mellon University, Pittsburgh, PA, in 1986; and the Ph.D. degree in operations research at Florida Institute of Technology, Melbourne, FL, in 1993. He is currently a Professor of Operations Research in the Department of Statistics and Operations Research, King Saud University, Riyadh, Saudi Arabia. His research interests include the optimal control of queueing and inventory systems. He is an editorial board member of the Journal of Probability and Statistical Science. He has numerous publications in journals of mathematics, statistics, and operations research.

Jau-Chuan Ke

Jau-Chuan Ke is Professor of Statistics at National Taichung Institute of Technology, Taiwan. He received his Ph.D. degree in Applied Mathematics from National Chung-Hsing University, Taiwan. His research interests include queueing theory, reliability, statistics, and decision theory.