Perturbation analysis of stochastic hybrid systems and applications to resource contention games

Abstract

We provide an overview of the recently developed general infinitesimal perturbation analysis (IPA) framework for stochastic hybrid systems (SHSs), and establish some conditions under which this framework can be used to obtain unbiased performance gradient estimates in a particularly simple and efficient manner. We also propose a general scheme for systematically deriving an abstraction of a discrete event system (DES) in the form of an SHS. Then, as an application of the general IPA framework, we study a class of stochastic non-cooperative games termed “resource contention games” modeled through stochastic flow models (SFMs), where two or more players (users) compete for the use of a sharable resource. Simulation results are provided for a simple version of such games to illustrate and contrast system-centric and user-centric optimization.

Keywords

stochastic flow model (SFM) / perturbation analysis / stochastic hybrid system (SHS) / resource contention games / cyber-physical systems

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg