Distributed semi-Markov processes in stochastic T-timed Petri nets

The heaps of pieces modelling approach (see Gaubert/Mairesse, PNPM'99) admits a (max,+)-linear model for the time consumption, under earliest firing and a given trace, of safe T-timed nets. The present paper shows that this type of model can be extended, using an appropriate partial order semantics under cluster view, to include stochastic choice and timing; we give the algorithmic construction of that semantics and obtain a semi-Markov property in multi-dimensional real time.