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In studies on conditions guaranteeing variance reduction for common random numbers (CRN), there is often the implicit assumption that the timing inputs, i.e., the random variables of clock samples, are generated via the inverse transform method. Some recommend using only inverse transform method when using CRN, suggesting that this strategy yields the best result, i.e., the highest degree of variance reduction. In this paper, we derive conditions guaranteeing variance reduction for a special class of systems-generalized semi-Markov processes (GSMP) with exponential clock samples-when using CRN and when the clock samples are generated via a version of the acceptance-rejection method. Our preliminary experimental results show that the variance reduction under this construction may be higher, sometimes significantly, than when inverse transform method is used.

Variance reduction for discrete event systems driven by Poisson processes