Title: M^X/G/1 queuing model with state dependent arrival and Second Optional 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: This investigation deals with single server state dependent queuing systems, wherein the arrivals of units are in batches and follow the Poisson process with state dependent arrival rates. After availing of the First Regular Vacation (FRV) in a case when there is no customer in the system, the server may also take a Second Optional Vacation (SOV). By using supplementary variable techniques, the probability generating function of the queue length distribution is established to study various performance measures. The maximum entropy approach is also used to find queue length distribution for evaluation of steady state probabilities in all different states. Numerical illustrations are provided to verify the tractability of performance measures obtained analytically.

Keywords: M^X/G/1; bulk arrivals; queue length; state dependent rate; optional vacations; supplementary variables; maximum entropy; queuing models; modelling.

DOI: 10.1504/IJMOR.2012.044474

International Journal of Mathematics in Operational Research, 2012 Vol.4 No.1, pp.78 - 96

Published online: 23 Dec 2014 *

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