A unified algorithm for finite and infinite buffer content distribution of Markov fluid models

Abstract

This paper is interested in the asymptotic distribution of fluid models with finite or infinite buffer capacity. The probability distribution of the buffer content is controlled by a linear differential system with specific boundary conditions. All earlier methods are forced to test the singularity of the drift matrix before starting any computation. Also, the finite and infinite buffer capacity cases are treated differently. Our approach leads to a unified algorithm which is able to compute simultaneously the buffer workload distribution for finite and infinite buffer capacity without looking into the drift matrix singularity. The proposed method is not spectral and it is based on the uniformization technique. An example of a video traffic is firstly modeled by a Markovian fluid and secondly analyzed.