Comparison of computation methods for the steady-state markov modulated fluid queues

The Markov-modulated fluid models are mathematical tools widely used in telecommunication networks modeling. These models represent the discrete entities of the network traffic as a continuous fluid whose rates depend on a Markov process. The study of the fluid models shows that they are governed by a linear differential system. Many techniques are used to solve these equations such as spectral analysis, Laplace transforms, orthogonal polynomials and recurrence relations. The purpose of this work is to study mathematically the resolution techniques and to compare them in term of computational complexity, accuracy and stability.