On the Long-Run Behavior of Equation-Based Rate Control

We consider unicast equation-based rate control, where, at some points in time, a sender adjusts its rate to f(p,r), where p is an on-line estimate of the loss-event rate observed by this source, r of the average round-trip time, and f is a TCP throughput formula. Conventional wisdom holds that such a source would be TCP-friendly, that is, it would not attain a larger long-run average send rate than a TCP source under the same operating conditions. Our goal is to identify the key factors that determine whether, and how far, this is true. We point out that it is important to breakdown the TCP-friendliness condition into sub-conditions and study them separately. One sub-condition is conservativeness (throughput not larger than f(p,r)). The conservativeness is primarily influenced by some convexity properties of the function f, and a covariance property of the loss process. In many cases, these conditions result in conservativeness, in some cases, excessive conservativeness. Another sub-condition is that the source experiences a loss-event rate that is not smaller than that of TCP. We show two limit cases for which the last sub-condition, respectively, does and does not hold. We show that in the latter situation, the outcome can be a significant non-TCP-friendliness. The claims suggested by our analysis are verified by numerical examples, simulations, Internet and lab experiments. Our findings should help us better understand when to expect the source to be TCP-friendly, or in contrast, non-TCP-friendly. On the basis of our analysis and empirical evaluations we observe that TCP-friendliness is difficult to verify, whereas conservativeness is easier.