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Analyse quantitative paramétrée d'automates temporisés probabilistes

Abstract : We focus here on a special class of probabilistic timed automata (PTA), called "Determinate Probabilistic Timed Automata" (DPTA. Such automata are fully probabilistic (no non-determism) : There is a single distribution of outgoing actions per node (no non-determinism of actions). One stays at each location during a specific amount of time (no non-determinism of duration) : for each node s, the guard of the (unique) outgoing action is of the form x=a, where x is a clock variable and a nonnegative constant ; furthermore, node s has x<=a as an invariant. (This means that the outgoing action is always taken when x reaches a). We claim that , often in practice, the worst behavior of a PTA (modeling, e.g., for IEEE-1394 root contention, CSMA-CD and Philips BRP protocols. We give a method for computing the expected time A for a DPTA to reach the absorbing point. Roughly speaking, the method consists in putting the automaton under the form of a Markov chain with costs (corresponding to durations). The method is parametric in the sense that A is computed as a function of the timing constants, but does not assume known their explicit values. In particular, the complexity of the computation of the expected time is independent from the (maximal) constant(s) bounding the values of the clocks. Another advantage of the method is that the comlexity of the computation is only polynomial in the number of clocks, locations and edges of the original PTA.
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Najla Chamseddine. Analyse quantitative paramétrée d'automates temporisés probabilistes. Informatique [cs]. École normale supérieure de Cachan - ENS Cachan, 2009. Français. ⟨NNT : 2009DENS0041⟩. ⟨tel-00626062⟩

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