Title: Queueing model with state-dependent bulk arrival and second optional service

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, Roorkee – 247667, India. ' Department of Mathematics, M.L.U. DAV College, Phagwara – 144402, India

Abstract: This paper investigates a single server bulk queueing system with state-dependent rates and second optional service. The service time of the essential service is general-distributed whereas that of optional service follows the exponential distribution. By using supplementary variable technique, the probability-generating functions of the queue length distribution have been obtained. Further, the queue length distribution is established by using maximum entropy approach. The numerical illustrations are provided to verify the tractability of performance measures. The sensitivity analysis is also carried out to examine the effect of system descriptors.

Keywords: Mx/G/1 queues; queue length; state-dependent rate; essential services; optional services; supplementary variables; maximum entropy; queueing models; bulk arrivals; bulk queueing.

DOI: 10.1504/IJMOR.2011.040029

International Journal of Mathematics in Operational Research, 2011 Vol.3 No.3, pp.322 - 340

Published online: 12 Feb 2015 *

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