  We analyze the convergence to equilibrium of one-dimensional reflected
Brownian motion (RBM) and compute a number of related initial transient
formulae. These formulae are of interest as approximations to the initial
transient for queueing systems in heavy traffic, and help us to identify
settings in which initialization bias is significant. We conclude with a
discussion of mean square error for RBM. Our analysis supports the view that
initial transient effects for RBM and related models are typically of modest
size relative to the intrinsic stochastic variability, unless one chooses an
especially poor initialization.
