In the area of distributed systems and networking, performance, reliability or dependability studies have to deal with the complexity of the systems (whose main metrics is the size of the state space et transitions) but also to the precise evaluation of probabilities of rare events. For such cases, the exhaustive analysis is impossible and classical simulation is not precise enough. Algorithmic tools for probabilistic evaluation relying on stationary or transient probabilities are rare compared to similar tools under deterministic assumptions. The research teams involved in this proposal have an internationally recognized expertise in mathematical tools, techniques, algorithms and software packages, which have been applied in other areas : modular decomposition and tensor calculus, trajectories coupling for the computation of bounds, quick convergence of Monte Carlo algorithms, perfect simulation guaranteeing an exact measure, parallel and distributed implementation of the algorithms, links with specification languages and formalisms, collaborations which groups in the area of model checking. The objective of this project is to investigate the applicability of these methodologies to the area of reliability from a quantitative point of view. Indeed, for a large number of applications (real-time, multimedia,etc), correctness formal proof has to go along with performance evaluation. Precisely, results are expected in :

• Algorithms to compute transient probabilities in reliability and dependability using tensor structure.
• Algorithms to compute bounds on trajectories using tensor and sparse format.
• Transformation of SAN (in French RAS) to specify bounds.
• Proofs for bounds based on (Max, +) or Courtois theory.
• Perfect simulation of SAN with or without model transformation.
• Tools to determine the optimal parameters in the case of preferential sampling.
• Development of tools based on the entropia method of Rubinstein.
• These algorithms will be implemented in tools or libraries that will be made available in a common web site.

The merit of this proposal is to put together different techniques and tools for the performability of systems. The capabilities of each tool or library will be enhance and cross utilization will be investigated.