We discuss a way of simulating M replications of a uniformizable Markov chain simultaneously and in parallel (the so-called parallel replication approach). Simulation is performed to estimate the expectation of some cumulative reward over a finite deterministic time horizon. Distributed implementation on a number of processors and parallel SIMD implementation on massively parallel computers are described. We investigate the adaptation of Fishman's rotation sampling approach (Fishman 1983a and 1983b) to our setting in order to reduce the variance of the estimators. It is pointed out that the algorithms can be used in conjunction with the Standard Clock simulation of uniformized chains at distinct parameters (Vakili 1992) to increase the effectiveness of the Standard Clock simulation.
['Simon Streltsov', 'Pirooz Vakili']
Parallel replicated simulation of Markov chains: implementation and variance reduction