  We introduce an algorithm for the uniform generation of infinite runs in
concurrent systems under a partial order probabilistic semantics. We work with
trace monoids as concurrency models. The algorithm outputs on-the-fly
approximations of a theoretical infinite run, the latter being distributed
according to the exact uniform probability measure. The average size of the
approximation grows linearly with the time of execution of the algorithm. The
execution of the algorithm only involves distributed computations, provided
that some - costly - precomputations have been done.
