Title: Analysis of single server finite queueing model with reneging

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: The present investigation deals with the analysis of Markovian queueing model with finite capacity and finite population wherein the server works in fast and slow random environments, depending on the status of service system, with exponential distributed time parameters. On arrival of the customer in slow mode, the exponential distributed time may be fixed. Due to the impatient behaviour (reneging), the customer may leave the queue after some time of joining the system if the server does not change its state before expiry of the timer. To discuss the behaviour of the queue length distribution and to obtain the transient solution, Runge-Kutta method of the fourth order is used. Various performance measures are determined in terms of transient probabilities of the system states. The numerical illustrations are facilitated to validate the tractability of performance measures as far as computational aspect is concerned.

Keywords: Markovian modelling; finite queues; reneging; Runge-Kutta; transient probability; random environment; single server queueing; finite capacity; finite population; impatient behaviour; queue length.

DOI: 10.1504/IJMOR.2016.077558

International Journal of Mathematics in Operational Research, 2016 Vol.9 No.1, pp.15 - 38

Received: 25 Aug 2014
Accepted: 11 Oct 2014
Published online: 06 Jul 2016 *

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