Fluid queue driven by an M/E2/1 queueing mode

Abstract

This paper deals with the stationary analysis of a fluid queue driven by an M/E2/1 queueing model. The underlying system of differential difference equations that governs the process are solved using generating function methodology. Explicit expressions for the joint steady state probabilities of the state of the background queueing model and the content of the buffer are obtained in terms of a new generalisation of the modified Bessel function of the second kind. Numerical illustrations are added to depict the convergence of the joint probabilities with the steady state solutions of the underlying queueing models.