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Stochastic networks and semimartingale reflecting Brownian motions in piecewise smooth domains

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Semimartingale Reflecting Brownian Motions (SRBMs) living in the closures of domains with piecewise smooth boundaries are of interest in applied probability because of their role as heavy traffic approximations for stochastic networks. Modern applications such as bandwidth sharing and packet switches can yield stochastic network models and SRBM approximations that are more general than those associated with conventional multiclass queueing networks. In justifying the approximation of a stochastic network by an SRBM , a crucial step is the use of a perturbation result or invariance principle. In essence this implies that a process satisfying the definition of an SRBM , except for small random perturbations in the defining conditions, is close in distribution to an SRBM . Here we describe sufficient conditions for an invariance principle to hold for SRB Ms in piecewise smooth domains. A crucial ingredient in the proof of this result is an oscillation inequality for solutions of a perturbed Skorokhod problem. Some applications of our results and open problems will be discussed.

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