Asymptotic analysis of adaptive rate control for diverse sources with delayed feedback

This paper analyzes the effectiveness of a class of adaptive algorithms for rate control in a data network with the following two elements: many sources with diverse characteristics (e.g., nonadaptive and adaptive sources with different feedback delays, different constraints on transmission rates) and a switch, based on ATM or cell-relay technology, with finite buffers. Several adaptive sources compete among themselves as well as with other nonadaptive sources for bandwidth at a single queue. We first model random fluctuations in the queue-length process due to the nonadaptive sources as Brownian motion, and we show, for a large class of adaptive strategies, how the amount of bandwidth wasted because of idleness and the amount of offered traffic lost because of overflowing buffers scale with the speed of the network. We then model the arrival process of nonadaptive traffic more realistically as a general stochastic fluid with bounded, positive rates. For a class of adaptive strategies with linear adaptation functions, we prove that the results obtained from the Brownian model of randomness extend to cover the more realistic model. This occurs because the adaptive sources induce heavy-traffic conditions (corresponding to the power-maximizing regime of Mitra (1990)) by accurately estimating and using the residual bandwidth not occupied by the nonadaptive traffic. Our analysis gives new insight about how performance measures scale with the variability of the nonadaptive traffic. We illustrate through simulations that queue fluctuations behave as predicted