Cost Analysis of MAP/G(a, b)/1/N Queue with Multiple Vacations and Closedown Times

Abstract

This paper gives the cost analysis of a finite capacity single server bulk queueing model with closedown times. The server serves the customers in batches of maximum size ‘b’ with a minimum threshold value ‘a’. Customers arrive according to a Markovian Arrival Process (MAP). On completion of a service, if the queue length is less than ‘a’, then the server performs a closedown work and then leaves for a vacation of random length. When the server returns from vacation and if the queue length is still less than ‘a’ he avails another vacation and so on until the server finds ‘a’ customers waiting in the queue. After the completion of a service, if the number of customers in the queue is greater than a specified value ‘a’ then the server will continue the batch service with general bulk service rule. On the other hand, if the server finds at least ‘a’ customers during closedown period, he immediately starts serving the batch of ‘a’ customers. Using supplementary variable and imbedded Markov chain technique, queue length distribution at arbitrary epoch is obtained. Some key performance measures are also obtained. Cost model is discussed with Numerical illustration.

Key Words:

• Closedown times
• cost analysis
• MAP
• multiple vacation.

Additional information

Notes on contributors

A. Senthil Vadivu

A. Senthil Vadivu is currently Assistant Professor in the Department of Mathematics, PSG Institute of Technology and Applied Research, Coimbatore, India. She received his M.Sc. and M. Phil. degrees in Mathematics from Bharathiar University, Coimbatore, India in 2002 and 2005 respectively and Ph.D. degree in Mathematics from Anna University, Coimbatore, India. Her field of interest includes Queuing theory.

R. Arumuganathan

R. Arumuganathan is currently Professor and Head in the Department of Mathematics, PSG College of Technology, Coimbatore, India. He received M. Sc. and M. Phil degrees in Mathematics from Madurai Kamarajar University, Madurai, India in 1985 and 1986 respectively and Ph.D degree in Mathematics from Bharathiar University, Coimbatore, India. His fields of interest include queueing theory, reliability theory and wavelet transforms. He has publications in international journals like Computers and Operations Research, Applied Mathematical Modelling, Asia Pacific Journal of Operational Research, OPSEARCH and Int. J. Information and Management Sciences, etc. He has given invited talks in several international conferences.