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

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.