ANALYSIS OF A RATE-BASED FEEDBACK-CONTROL STRATEGY FOR LONG HAUL DATA TRANSPORT

Digital communication has become fast enough so that the speed of light has become a bottleneck. For example, the round trip transcontinental [USA] delay through a fiber link is approximately 0.04 s; at 150 Megabit/s, a source needs to transmit approximately 8,000,000 bits during one round trip time to utilize the bandwidth fully. As the service rates of queues get large, the time scales of congestion in those queues decrease relative to the round trip time, making the dual goals of keeping buffers small and utilizations high even more difficult to achieve. In this paper we analyze a class of delayed feedback schemes that achieve these goals despite propagation delays and regardless of network rates. We analyze the delayed feedback schemes as a system of delay-differential equations, in which we model the queue-length process and the rate at which a source transmits data as fluids. We assume that a stream of acknowledgements carries information about the state of a bottleneck queue back to the source, which adapts its transmission rate according to any monotone function of that state. We show stability for this class of schemes, in that their rate of transmission and queue length rapidly converge to a small neighborhood of the designed operating point. We identify the appropriate scaling of the model's parameters, as a function of network speed, for the system to perform optimally: with a deterministic service rate of mu at the bottleneck queue, the steady state utilization of the queue is 100 - O(mu - 1/2)% and steady state delay is O(mu - 1/2). We also describe the transient of behavior of the system as another source suddenly starts competing for the bandwidth resources at the bottleneck queue. This work directly applies to the adaptive control of Frame Relay and ATM networks, both of which provide feedback to users on congestion.