Comparing Markov Chains Simulated in Parallel

Abstract

We investigate the dependence induced among multiple Markov chains when they are simulated in parallel using a shared Poisson stream of potential event occurrences. One expects this dependence to facilitate comparisons among systems; our results support this intuition. We give conditions on the transition structure of the individual chains implying that the coupled process is an associated Markov chain. Association implies that variance is reduced in comparing increasing functions of the chains, relative to independent simulations, through a routine argument. We also give an apparently new application of association to the problem of selecting the better of two systems from limited data. Under conditions, the probability of incorrect selection is asymptotically smaller when the systems compared are associated than when they are independent. This suggests a further advantage to linking multiple systems through parallel simulation.