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.
Pages
2689-2751
Volume
347
Issue
8
Recommended Citation
DUPUIS, P and Ellis, RS, "THE LARGE DEVIATION PRINCIPLE FOR A GENERAL-CLASS OF QUEUING-SYSTEMS .1." (1995). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 343.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/343
Comments
The published version is located at http://www.jstor.org/stable/info/2154753