Title: Analysis of bulk retrial queue using maximum entropy principle

Authors: Madhu Jain; Amita Bhagat

Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, India

Abstract: In the present investigation, we study the maximum entropy principle (MEP) for the M^x/G/1 retrial queue with general retrial times and unreliable server. The customers arrive in bulk in Poisson fashion and are served if they find the server idle otherwise join the virtual pool of customers called orbit. By using maximum entropy principle, approximate results for the queue length as well as waiting time are obtained. We construct the maximum entropy function by using several known constraints so as to determine the probability distributions. Moreover, a comparative study has been done between the exact analytic expressions obtained by the supplementary variable technique and approximate results obtained by MEP.

Keywords: bulk retrial queues; maximum entropy principle; MEP; queue length; bulk arrivals; second optional services; balking; reneging; setup times; unreliable servers.

DOI: 10.1504/IJOR.2015.070146

International Journal of Operational Research, 2015 Vol.23 No.4, pp.477 - 496

Received: 09 Feb 2013
Accepted: 16 Jul 2013
Published online: 28 Jun 2015 *

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