We consider the simulation of transient performance measures of high reliable fault-tolerant computer systems. The most widely used mathematical tools to model the behavior of these systems are Markov processes. Here, we deal basically with the simulation of the mean time to failure (MTTF) and the reliability, R(t), of the system at time t. Some variance reduction techniques are used to reduce the simulation time. We will combine two of these techniques: Importance Sampling and Conditioning Technique. The resulting hybrid algorithm performs significant reduction of simulation time and gives stables estimations.

A second order optimality condition for multiobjective optimization with a set constraint is developed; this condition is expressed as the impossibility of nonhomogeneous linear systems. When the constraint is given in terms of inequalities and equalities, it can be turned into a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced.

We study networks with positive and negative customers (or Generalized networks of queues and signals) in a random environment. This environment may change the arrival rates, the routing probabilities, the service rates and also the effect of signals. We prove that the steady-state distribution has a product form. This property is obtained as a corollary of a much more general result on multidimensional Markov chains.

In this work we propose a ranking procedure. This procedure uses an ordinal information about the criterion weights and a non-cardinal or mixed information for the potential actions evaluation. The advantage of this procedure is that it uses the linear programming software packages to compute the intervals of relative proximities from where the rankings are obtained.

This paper deals with the problem of scheduling n tasks on m identical processors in the presence of communication delays. A new approach of modelisation by a decision graph and a resolution by a tabu search method is proposed. Initial solutions are constructed by list algorithms, and then improved by a tabu algorithm operating in two phases. The experiments carried on arbitrary graphs show the efficiency of our method and that it outperformed the principle existent heuristics.