Performance evaluation of timed automata
Résumé
We introduce automata over the (max, +) algebra : this formalism encompasses in particular (max, +) linear systems and a subclass of stochastic timed event graphs. Performance evaluation is considered in the worst,mean, and optical cases. A simple algebraic reduction is provided for the worst case. The later cases are reduced to projective finiteness properties of semigroups of matrices. The mean performance is given by the Kolmogorov equation of a Markov chain in the projective space. The optimal performance is given by an analogous Hamilton-Jacobi-Bellman equation.