Exact Simulation of Non-stationary Reflected Brownian Motion

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 t is uniformly bounded by O(1/γ̄2) where γ̄ 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. ∗Corresponding author. Department of Management Science & Engineering, Stanford University, email: [email protected], web: www.stanford.edu/∼mousavi. †Department of Management Science & Engineering, Stanford University, email: [email protected], web: www.stanford.edu/∼glynn. 1 ar X iv :1 31 2. 64 56 v1 [ m at h. PR ] 2 3 D ec 2 01 3