  We propose two algorithms for simulating continuous time Markov chains in the
presence of metastability. We show that the algorithms correctly estimate,
under the ergodicity assumption, stationary averages of the process. Both
algorithms, based on the idea of the parallel replica method, use parallel
computing in order to explore metastable sets more efficiently. The algorithms
require no assumptions on the Markov chains beyond ergodicity and the presence
of identifiable metastability.
  In particular, there is no assumption on reversibility. For simpler
illustration of the algorithms, we assume that a synchronous architecture is
used throughout of the paper. We present error analyses, as well as numerical
simulations on multi-scale stochastic reaction network models in order to
demonstrate consistency of the method and its efficiency.
