TRANSIENT ANALYSIS OF A MARKOV MODULATED FLUID QUEUE WITH LINEAR SERVICE RATE

摘要

We consider an infinite capacity fluid queue governed by a continuous time Markov chain and with linear service rate. The transient behavior of this fluid flow model is described by a linear differential equation. We study the transient distribution of the fluid level in the queue and we derive a partial differential equation satisfied by the cumulative distribution function of the fluid level. Using this partial differential equation, we obtain a simple expression of the moments of this transient distribution, as well as its Laplace transform.