Uniformization and Hybrid Simulation/Analytic Models of Renewal Processes

In this paper we demonstrate the use of uniformization in the simulation of renewal processes. Using uniformization, we represent the continuous random variable of interest as the first passage time of a continuous-time stochastic process associated with a Poisson process. We then use this result to develop a hybrid simulation/analytic method to model renewal processes. The estimators obtained from the hybrid simulation/analytic models have lower variance than the variance of the estimators of the traditional simulation models. We also discuss the possible impact of this method on the future of simulation methodology.