Reflected Brownian Motion (RBM), is a multidimensional stochastic process that is defined in terms of a constrained map known as the Skorokhod map. The map involves a multidimensional local‐time‐like process that is implicitly defined in terms of the solution to a certain stochastic differential equation. RBM plays a central role in Operations Research (OR) as it arises as the diffusion limit of a large class of queueing systems. So, designing numerical methods for computing expectation of RBM is of great interest in OR. In this talk we explain how to construct unbiased estimators of expectations of multidimensional RBM (both transient and steady‐state). Some of the basic ideas and techniques actually are useful even beyond RBM. For instance, we shall see how key ideas behind the RBM algorithms can be used to simulate without bias the (measure valued) state descriptor of an infinite server queue in steady state.

Based on joint work with Xinyun Chen and Jing Dong.