On the long-run behavior of equation-based rate control

We consider unicast equation-based rate control, where, at some points in time, a source adjusts its rate to f(p,r). Here p is an on-line estimate of the loss-event rate, r, of the mean round-trip time, both as observed by this source, and f is a TCP throughput formula. It was generally believed that such a source would be TCP-friendly, that is, under the same operating conditions, its long-run time-average send rate (throughput) would not be larger than that of a TCP source. Our goal is to identify whether, and how far, this is true. First, we identify factors that play a role in TCP friendliness and find that it is important to study them separately. Then we analyze the importance of individual factors. A first factor is conservativeness (= throughput not larger than f(p,r)). We show that conservativeness is influenced by some convexity properties of f(p,r) with respect to p, and the covariance of the loss process. We show that in many real life cases these conditions result in conservativeness and, sometimes, excessive conservativeness. This explains the previously observed phenomena of throughput-drop when losses are high and f is the so-called PFTK formula. The second factor is that the source may experience considerably different loss-event rate than a TCP source. We identify and analyze two limit cases where this may lead to either TCP-friendliness or, in contrast, non-TCP-friendliness. Other factors such as round trip time and obedience of TCP to its own formula are found to be less significant. Our claims are obtained by analysis, and verified by numerical examples, simulations, laboratory and Internet experiments. Our results suggest that TCP-friendliness is difficult to verify in practice, whereas conservativeness is easier.