On a congestion management scheme for high speed networks using aggregated large deviations principle

We consider a stochastic server fed by a set of parallel buffers offering dynamics evolving in discrete-time and following a service called ''on demand processor sharing'' (ODPS). This environment can be encountered in several situations in telecommunications including multi-class communication switches. In this paper, an analytic study of the multiclass model is proposed by using the concept of virtual queue that we have presented [Comput. Commun., 23 (2000) 912] and a multi level aggregation technique. The arrival process in each buffer is assumed to be arbitrary, and possibly auto-correlated, stochastic process. By using the large deviation principle to study the buffers' congestion, we provide a lower upper bound on the buffers overflow probabilities. We also consider the problem of finding a most likely sample path that leads to an overflow control problem, and give some applications of these results in the traffic engineering of high-speed networks.