Title: Analysis of M^X / G / 1 queueing model with balking and vacation

Authors: Charan Jeet Singh; Madhu Jain; Binay Kumar

Addresses: Department of Mathematics, Guru Nanak Dev University, Amritsar-143005, India ' Department of Mathematics, Indian Institute of Technology, Roorkee-247667, India ' Department of Mathematics, M.L.U. DAV College, Phagwara-144402, India

Abstract: In this paper, a single server queueing model, wherein the units arrive in bulk with varying arrival rates in Poisson process, is considered. It is assumed that the service time of units is arbitrarily distributed. Also, we incorporate the optional deterministic vacations for the server. The server may take a vacation of a fixed duration at the completion of each service or may continue to be available in the system for the next service. At busy and vacation states, the customers may balk from the system with different balking probabilities. By using the basic assumptions of probability reasoning and supplementary variable technique, the steady state behaviour of the system is studied and various performance measures are obtained. In order to obtain the approximate values of the system state probabilities, the principle of maximum entropy is also employed. To verify the tractability of the performance measures obtained, the numerical illustrations are provided. Further, the sensitivity analysis is carried out to examine the system performance with respect to different parameters.

Keywords: balking probabilities; arbitrary service time; deterministic vacations; supplementary variables; maximum entropy; bulk queues; queueing models; sensitivity analysis.

DOI: 10.1504/IJOR.2014.058952

International Journal of Operational Research, 2014 Vol.19 No.2, pp.154 - 173

Received: 26 Mar 2012
Accepted: 14 Aug 2012
Published online: 17 Jun 2014 *

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