Fluid limits of string valued Markov processes

Abstract

The stability properties of the bandwidth allocation algorithm first fit are analyzed for the distributions concentrated on three sizes for the requests. We give the explicit expression of the ergodicity condition of this model; it involves a quadratic functional of the input parameters. The stochastic processes describing these systems are string valued Markov processes. The notion of a smooth random state is introduced. Starting from a smooth random state the fluid limits of the process can be investigated. The fluid limits of interest are random dynamical systems in $\mathbb{R}^2$ which are products of random $2\times2$ matrices.