Title: Steady state analysis of a bulk arrival general bulk service queueing system with modified M-vacation policy and variant arrival rate

Authors: M. Balasubramanian, R. Arumuganathan

Addresses: Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore 641 004, Tamil Nadu, India. ' Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore 641 004, Tamil Nadu, India

Abstract: In this paper, a M[X]/G (a, b)/1 queueing system with modified M-vacation policy and variant arrival rate is considered. After a service completion, if the number of waiting customers is less than a, then the server avails of multiple vacations till the queue length reaches a or consecutively avail of M number of vacations, whichever occurs first. After completing the Mth vacation, if the queue length is still less than a then the server remains in the system till it reaches a. The server starts the service only if the queue length ξ≥a, with a batch of min (ξ,b) customers, where b≥a. It is considered that the arrival rate is dependent on the state of the server. The steady state queue size distribution at an arbitrary time is obtained. The expected queue length, waiting time, length of busy and idle periods are derived. Numerical illustration is also presented.

Keywords: bulk queues; multiple vacations; busy periods; M-vacation policy; steady state solution; bulk service queueing; queue size distribution; queue length; waiting times; idle periods.

DOI: 10.1504/IJOR.2011.041799

International Journal of Operational Research, 2011 Vol.11 No.4, pp.383 - 407

Published online: 14 Feb 2015 *

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