In this article we focus on the simulation of large Markov chains described as event driven stochastic models. Two kinds of simulations are considered : the simulation of large independent samples of trajectories or steady-state, and the simulation of very long trajectories. For independent samples we duplicate the simulation kernel on several cores and to ensure the reproducibility we control precisely the randomness sources. For very long trajectories, the difficulty is mainly in the control of the output process, as, in our kernels, transition execution time is much smaller than the transfer time of data from the machine. We propose to parallelize the output process and obtain significant execution time reduction. All these parallel kernels had been implemented in the software framework PSI.
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