Title: Maximum Entropy Approach for discrete-time unreliable server Geo^X/Geo/1 queue with working vacation

Authors: Madhu Jain; G.C. Sharma; Richa Sharma

Addresses: Department of Mathematics, IIT, Roorkee 247667, India. ' Department of Mathematics, I.B.S., Khandari, Agra 282002, India. ' Department of Mathematics, St. Johns College, Agra 282002, India

Abstract: This paper analyses a discrete-time Geo^X/Geo/1 queue with unreliable server and working vacation. During the vacation period, the server renders service to the primary job at lower rate rather than completely stopping service; this type of vacation is considered as working vacation. For modelling the queueing problem, the inter-arrival time, service time and repair time are treated as discrete random variables. The customers are assumed to arrive at the system in batches according to a geometric process during the consecutive slots. Using the probability generating function method, we obtain the steady-state distribution of the number of the customers in the system. Furthermore, Maximum Entropy Approach (MEA) is employed to obtain the approximate formulae for the probability distributions of the number of customers and the expected waiting time in the system in terms of several well-known results. Finally, the sensitivity analysis is also carried out to illustrate the effect of different parameters on several performance characteristics.

Keywords: discrete-time queues; unreliable servers; working vacations; geometric batch arrivals; generating functions; maximum entropy; queue size; waiting times; modelling.

DOI: 10.1504/IJMOR.2012.044473

International Journal of Mathematics in Operational Research, 2012 Vol.4 No.1, pp.56 - 77

Published online: 23 Dec 2014 *

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