  Skorokhod problem arises in studying Reflected Brownian Motion (RBM) on an
non-negative orthant, specifically in the context of queueing networks in the
heavy traffic regime. One of the key problems is identifying conditions for
stability of a Skorokhod problem, defined as the property that trajectories are
attracted to the origin. The stability conditions are known in dimension up to
three, but not for general dimensions.
  In this paper we explain the fundamental difficulties encountered in trying
to establish stability conditions for general dimensions. We prove that
stability of Skorokhod problem is an undecidable property when the starting
state is a part of the input. Namely, there does not exist an algorithm (a
constructive procedure) for identifying stable Skorokhod problem in general
dimensions.
