Exploiting multiple regeneration sequences in simulation output analysis

The 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 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. In a previous paper we introduced an efficiency-improvement technique for regenerative simulation of processes having two sequences of regeneration times based on permuting regeneration cycles associated with the second sequence of regeneration points. In this paper we show how the same basic idea can be extended 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.