| We introduce a model for probabilistic systems with concurrency. The system is distributed over two local sites. Global trajectories of the system are composed of local trajectories glued along synchronizing points. Global trajectories are thus given as partial orders of events, and not as paths. As a consequence, time appears as a dynamic partial order, contrasting with the universal chain of integers we are used to. It is surprising to see how natural it is to adapt mathematical techniques for processes to this new conception of time. The probabilistic model has two features: first, it is Markov, in a sense convenient for concurrent systems; and second, the local components have maximal independence, beside their synchronization constraints. We construct such systems and characterize them by finitely many real parameters, that are the analogous to the transition matrix for discrete Markov chains. This construction appears as a generalization of the "synchronization of Markov chains" developed in an earlier collaboration. |
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