About the reliability analysis of complex dynamical systems via fluidification: numerical approach

The fluidification of stochastic discrete event models is a more interesting method to overcome the problem of combinatorial explosion of states. It allows to relax the conditions of stochastic Petri nets to continuous Petri nets, in order to accelerate the slow convergence of stochastic simulations. In our study, we will study an example of a large manufacturing workshop, in order to give limitations of the direct fluidification which does not always lead to the same behaviour between the two models. Secondly, we propose a numerical approach called adaptive that devotes to the adaptation of the maximum speeds of crossing the transitions that is considered as functions depending on the time. Consequently, this approach shows an excellent convergence of the continuous model to the stochastic one whatever the type of network and whatever the initial marking.