Nonlinear Analysis: Hybrid Systems

We consider resource contention games in a stochastic hybrid system setting using Stochastic Flow Models (SFM) with multiple classes and class-dependent objectives. We present a general modeling framework for such games, where Infinitesimal Perturbation Analysis (IPA) estimators are derived for the derivatives of various class-dependent objectives. This allows us to study these games from the point of view of system-centric optimization of a performance metric and compare it to the user-centric approach where each user optimizes its own performance metric. We derive explicit solutions for a specific model in which the competing user classes employ threshold control policies and service is provided on a First Come First Serve (FCFS) basis. The unbiasedness of the IPA estimators is established in this case and it is shown that under certain conditions the system-centric and user-centric optimization solutions coincide. © 2010 Elsevier Ltd. All rights reserved.