Abstract
This paper develops the first method for the exact simulation of reflected Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The running time of generating exact samples of non-stationary RBM at any time is uniformly bounded by where is the average drift of the process. The method can be used as a guide for planning simulations of complex queueing systems with non-stationary arrival rates and/or service time.
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