Résumé : 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 process. To analyze these processes we introduce the notion of a smooth initial state. Starting from a smooth initial state the fluid limits of this systems can be investigated. The fluid limits of interest are random dynamical systems in $\R^2$ which are products of random $2\times2$ matrices.