Title: Steady state analysis of a non-Markovian bulk queue with restricted vacations

Authors: S. Jeyakumar, R. Arumuganathan

Addresses: Department of Mathematics, Chikkanna Government Arts College, Tirupur 641602, India. ' Department of Mathematics and Computer Applications, PSG College of Technology Coimbatore 641 004, India

Abstract: A M^X/G(a, b)/1 queueing system with restricted number of vacations is considered here. After completing a bulk service, if the queue size is less than |a| then the server leaves for a vacation of random length. When he returns from a vacation, if queue length is still less than |a|, he avails another vacation and so on until he completes M number of vacations in successions or he finds at least |a| customers wait for service. After M vacations, if the queue size is less than |a| then the server will remain in the system until he finds |a| customers in the queue. After a vacation or service completion if the server finds at least |a| customers waiting for service then the server serves according to Neut|s bulk service rule. The probability generating function of queue size at an arbitrary time and some important system performance measures are obtained. Cost model is discussed with numerical illustration.

Keywords: bulk service; restricted vacations; supplementary variables; vacations; dormant period; bulk queues; cost modelling.

DOI: 10.1504/IJOR.2011.038904

International Journal of Operational Research, 2011 Vol.10 No.3, pp.307 - 332

Published online: 14 Feb 2015 *

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