To batch or not to batch

When designing steady-state computer simulation experiments, one is often faced with the choice of batching observations in one long run or replicating a number of smaller runs. Both methods are potentially useful in simulation output analysis. We give results and examples to lend insight as to when one method might be preferred over the other. In the steady-state case, batching and replication perform about the same in terms of estimating the mean and variance parameter, though replication tends to do better than batching when it comes to the performance of confidence intervals for the mean. On the other hand, batching can often do better than replication when it comes to point and confidence-interval estimation of the steady-state mean in the presence of an initial transient. This is not particularly surprising, and is a common rule of thumb in the folklore.