THE LARGE DEVIATION PRINCIPLE FOR A GENERAL-CLASS OF QUEUING-SYSTEMS .1.

Publication Date

1995

Journal or Book Title

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Abstract

We prove the existence of a rate function and the validity of the large deviation principle for a general class of jump Markov processes that model queueing systems. A key step in the proof is a local large deviation principle for tubes centered at a class of piecewise linear, continuous paths mapping [ 0, 1] into Rd. In order to prove certain large deviation limits, we represent the large deviation probabilities as the minimal cost functions of associated stochastic optimal control problems and use a subadditivity-type argument. We give a characterization of the rate function that can be used either to evaluate it explicitly in the cases where this is possible or to compute it numerically in the cases where an explicit evaluation is not possible.

Comments

The published version is located at http://www.jstor.org/stable/info/2154753

Pages

2689-2751

Volume

347

Issue

8

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