Title: Transient analysis of a fluid queue driven by a chain sequenced birth and death process with catastrophes

Authors: T. Vijayalakshmi; V. Thangaraj

Addresses: Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai – 600 005, India ' School of Mathematics, Vel Tech Technical University, Avadi, Chennai – 600 062, India

Abstract: In this paper, we analyse the transient behaviour of a fluid queue modulated by a birth and death processes (BDPs) whose birth and death rates are suggested by a chain sequence and catastrophes. We derive a system of differential equations satisfied by this fluid model. We employ the Laplace transform technique and continued fraction methodology to obtain a simple closed form transient state probability distribution. Also we find the distribution of busy period and analyse the system when there are no catastrophes.

Keywords: fluid queues; chain sequence; catastrophes; continued fractions; Laplace transform; busy periods; birth and death processes; differential equations; probability distribution; stochastic modelling; queueing theory.

DOI: 10.1504/IJMOR.2016.074853

International Journal of Mathematics in Operational Research, 2016 Vol.8 No.2, pp.164 - 184

Received: 30 Dec 2013
Accepted: 30 Jun 2014

Published online: 21 Feb 2016 *

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