Section: New Results
Fundamentals and algorithms: probabilistic models
Participants : Albert Benveniste, Anne Bouillard, Sidney Rosario.
Our work on true concurrency probabilistic models is joint work with our former PhD student Samy Abbes, now Maître de Conférences in Mathematics at Paris VI, PPS Laboratory. We have established the foundations for probabilistic models of distributed and concurrent systems, in which traces, not interleaving sequences, are randomized. We have been able to extend our Markov net model beyond nets with finite confusion (those which yield locally finite event structures). Markov nets are now defined in most general cases. Extensions required a fine understanding of probabilistic fairness. This result was published in FOSSACS'2009 [17] . Regarding true concurency compositional probabilistic models, we are currently working at extending our previous results concerning the fully probabilistic synchronous product of two Markov chains—this differs from products of Probabilistic Automata, which yield mixed probabilistic/nondeterministic models.
On another direction, we have studied probabilistic path criticality for stochastic Petri nets. Targeted applications are workflow nets such as used in the modeling of orchestrations. In concurrent real-time processes, the speed of individual components has a double impact: on the one hand, the overall latency of a compound process is affected by the latency of its components. But, if the composition has race conditions, the very outcome of the process will also depend on the latency of component processes. Using stochastic Petri nets, we investigate the probability of a transition occurrence being critical for the entire process, i.e. such that a small increase or decrease of the duration of the occurrence entails an increase or decrease of the total duration of the process. The first stage of the analysis focuses on occurrence nets, as obtained by partial order unfoldings, to determine criticality of events; we then lift to workflow nets to investigate criticality of transitions inside a workflow. This is joint work with Stefan Haar. It has been published in [20] .
