  This paper develops the first class of algorithms that enable unbiased
estimation of steady-state expectations for multidimensional reflected Brownian
motion. In order to explain our ideas, we first consider the case of compound
Poisson (possibly Markov modulated) input. In this case, we analyze the
complexity of our procedure as the dimension of the network increases and show
that, under certain assumptions, the algorithm has polynomial-expected
termination time. Our methodology includes procedures that are of interest
beyond steady-state simulation and reflected processes. For instance, we use
wavelets to construct a piecewise linear function that can be guaranteed to be
within $\varepsilon$ distance (deterministic) in the uniform norm to Brownian
motion in any compact time interval.
