The classical regenerative method of simulation
output analysis exploits the regenerative structure of
a stochastic process to break up a path into independent
and identically distributed cycles based on a single sequence
of regeneration times. If a process is regenerative with
respect to more than one sequence of regeneration times,
the classical regenerative method does not exploit the
additional structure, and the variance of the resulting
estimator for certain performance measures (e.g., the time-average
variance constant) can vary greatly, depending on the particular
regeneration sequence chosen. In a previous article, we
introduced an efficiency-improvement technique for regenerative
simulation of processes having two sequences of regeneration
times based on permuting regenerative cycles associated
with the second sequence of regeneration points. In this
article, we show how to exploit more than two regeneration
sequences. In particular, for birth–death Markov
chains, the regenerations associated with hitting times
to each state can all be exploited. We present empirical
results that show significant variance reductions in some
cases, and the results seem to indicate that the permuted
estimator for the time-average variance constant can have
a variance that is independent of the primary regeneration
sequence used to run the simulation.