Najla Chamseddine , Marie Duflot , Laurent Fribourg and Claudine Picaronny Determinate Probabilistic Timed Automata as

We consider probabilistic systems modeled under the form of a special class of probabilistic timed automata. Such automata have “no choice”: when the automaton arrives at a node, the time at which it will leave it is determined; when the automaton leaves the node, there is just one distribution of target nodes. In the paper, we give a method for computing the expected time A for the automaton to reach an “absorbing” node. Roughly speaking, the method consists in putting the automaton under the form of a Markov chain with costs (corresponding to durations). Under certain conditions, the method is parametric in the sense that A is computed as a function of the constants appearing in the outgoing conditions and the invariants of nodes, but does not assume known their explicit values. We illustrate the method on the CSMA/CD protocol.