Worst-Case Rate-Based Flow Control with an ARMA Model of the Available Bandwidth

Abstract

A central control problem that arises in high-speed networks is the control of the rate of flow of information into the network. A rate that is too high may result in congestion and hence in the degradation of performance measures: high delays within the network, high loss probabilities of information packets, and large delay variations; a rate that is too low may result in the under-utilization of the network and in low throughput. Most of the existing and future telecommunications networks therefore include dynamic flow control mechanisms, which have often been developed on growing available experience, using ad hoc techniques that did not come as a result of a control-theoretical study. This is due to the high complexity of the controlled systems, that are typically decentralized, have nonlinear dynamics, and may only use partial noisy delayed information. Some attempts have been made in recent years to use control theory to design flow controllers with, however, no explicit objective functions to be minimized; moreover, the class of control policies in existing theoretical work is quite restricted. In this paper we formulate explicitly some cost criteria to be minimized, related to performance measures mentioned above, including delays, throughputs, and loss probabilities. We present an approximating linearized model with quadratic cost, and follow two approaches to model interfering traffic and other unknown data: the H ^∞ approach, and LQG approach. We determine for both cases the optimal controllers, and illustrate the theoretical results using simulation.