An invariance principle for semimartingale reflecting Brownian motions in an orthant

Authors:
R. J. Williams
Affiliations:
Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA
Venue:
Queueing Systems: Theory and Applications
Year:
1998

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Abstract

Semimartingale reflecting Brownian motions in an orthant (SRBMs) are of interest in applied probability because of their role as heavy traffic approximations for open queueing networks. It is shown in this paper that a process which satisfies the definition of an SRBM, except that small random perturbations in the defining conditions are allowed, is close in distribution to an SRBM. This perturbation result is called an invariance principle by analogy with the invariance principle of Stroock and Varadhan for diffusions with boundary conditions. A crucial ingredient in the proof of this result is an oscillation inequality for solutions of a perturbed Skorokhod problem. In a subsequent paper, the invariance principle is used to give general conditions under which a heavy traffic limit theorem holds for open multiclass queueing networks.