Guaranteed performance regions for multi-user Markov models

Abstract

A user facing a multi-user resource-sharing system considers a vector of performance measures (e.g. response times to various tasks). Acceptable performance is defined through a set in the space of performance vectors. Can the user obtain a (time-average) performance vector which approaches this desired set? We consider the worst-case scenario, where other users may, for selfish reasons, try to exclude his vector from the desired set. For a controlled Markov model of the system, we give a sufficient condition for approachability, and construct appropriate policies. Under certain recurrence conditions, a complete characterization of approachability is then provided for convex sets. The mathematical formulation leads to a theory of approachability for stochastic games. A simple queueing example is analyzed to illustrate the applicability of this approach.