We propose nonstandard simulation estimators of expected
time averages over ¯nite intervals [0; t], seeking to enhance estimation e±ciency. We make three
key assumptions: (i) the underlying stochastic process has regenerative structure, (ii) the time
average approaches a known limit as time t increases and (iii) time 0 is a regeneration time. To
exploit those properties, we propose a residual-cycle estimator, based on data from the regenera-
tive cycle in progress at time t, using only the data after time t. We prove that the residual-cycle
estimator is unbiased and more e±cient than the standard estimator for all su±ciently large t.
Since the relative e±ciency increases in t, the method is ideally suited to use when applying simu-
lation to study the rate of convergence to the known limit. We also consider two other simulation
techniques to be used with the residual-cycle estimator. The ¯rst involves overlapping cycles, par-
alleling the technique of overlapping batch means in steady-state estimation; multiple observations
are taken from each replication, starting a new observation each time the initial regenerative state
is revisited. The other technique is splitting, which involves independent replications of the termi-
nal period after time t, for each simulation up to time t. We demonstrate that these alternative
estimators provide e±ciency improvement by conducting simulations of queueing models.