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In complex stochastic systems, Monte-Carlo simulation is often the only way to estimate equilibrium expectations. The question then arises what is better: a single run of length T, or n runs, each of length T/n. In this paper, it is argued that if there is a good state to start the simulation in, multiple runs may be advantageous. To illustrate this, we use numerical examples. These examples are obtained by using deterministic methods, that is, methods based on probability theory not using Monte-Carlo methods. The results of our numerical calculations forced us to make a sharp distinction between the time to reach equilibrium and the appropriate length of the warm-up period, and this distinguishes our study from earlier investigations.

Using Multiple Runs in the Simulation of Stochastic Systems for Estimating Equilibrium Expectations