Optimal NT Policies for a Two-Phase Service M/G/1 System with Bernoulli Vacation Schedule

Abstract

This paper studies Optimal NT policies for a two-phase service M/G/1 system with a Bernoulli vacation schedule. This system also covers an unreliable server with a breakdown period and a delaying period. While the server is serving, it may fail and the service channel may be shut for a short intermission. Then the server starts service when the number of the waiting customers approaches threshold value N, or when the waiting time of the leading customers reaches a predetermined time T. If the above policy is utilized, the server resumes its service after a startup time. The server serves the waiting customers in two consecutive phases. After the completion of the two phases of service, the server may take a short vacation or may remain in the system to serve the next unit, which is considered Bernoulli vacation schedule. Moreover, we assume the server fails according to a Poisson process whose repair time follows a general distribution. We obtain the optimal NT threshold to minimize the cost function of the system.

Key Words:

• Bernoulli vacation schedule
• breakdown
• delaying
• NT policies
• repair
• setup
• two-phase service.

Additional information

Notes on contributors

Ching-Chang Kuo

Ching-Chang Kuo is an Assistant Professor in the Department of Applied Statistics at National Taichung University of Science and Technology, Taiwan. He received his Ph.D. degree in Department of Industrial Engineering and Management from National Chiao Tung University, Taiwan. His research interests include queueing theory, reliability, and statistics.

Jau-Chuan Ke

Jau-Chuan Ke is Professor of Statistics at National Taichung University of Science and Technology, Taiwan. He received his Ph.D. degree in Applied Mathematics from National Chung-Hsing University, Taiwan. He is an editorial board member of Applied Mathematical Modelling and Quality Technology & Quantitative Management. His research interests include queueing theory, reliability, statistics, and decision theory.

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