Discrete-Time Analysis of Adaptive Rate Control Mechanisms

We analyze the performance of a generic feedback ow control mechanism which captures the properties of several such mechanisms recently proposed in the literature. These mechanisms dynamically regulate the rate of data ow into a network based on feedback information about the network state. They are used in a variety of networks and they have been advocated for upcoming high-speed networks. However, they are diicult to model realistically. In this paper, we present a stochastic discrete-time approach that yields models which are realistic and yet tractable and computationally easy to solve. For our generic mechanism, the feedback consists of an exponentially averaged estimate of the bottleneck service rate and queue size. We obtain a model described by non-linear stochastic diierence equations. We nd the conditions under which these equations converge to a steady-state and we characterize the speed of convergence to steady-state. We then consider a linearized version of the model for which we can derive closed-form solutions. These solutions bring out a tradeoo between eecient steady-state behavior and rapid adaptability to varying network conditions. We indicate how a dynamic averaging technique of the feedback information can overcome this disadvantage. We also identify the cases when the linear model is a good approximation to the non-linear model.