The paper "performability analysis: a new algorithmrdquo describes an algorithm for computing the complementary distribution of the accumulated reward over an interval of time in a homogeneous Markov process. In this comment, we show that in two particular cases, one of which is quite frequent, small modifications of the algorithm may reduce significantly its storage complexity.

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.

We propose, in this paper, a new algorithm to compute the performability distribution. Its computational complexity is polynomial and it deals only with nonnegative numbers bounded by one. This important property allows us to determine truncation steps and so to improve the execution time of the algorithm.