Some Observations on Equation-Based Rate Control

We consider one aspect of the general problem of unicast equation based rate control in the Internet, which we formulate as follows. When a so called “loss-event” occurs, a data source updates its sending rate by setting it to f(p̂n), where p̂n is an estimate of p, the rate of loss-events. Function f (the target loss-throughput function) defines the objective of the control method: we would like that the throughput x, attained by the source, satisfies the equation x f(p). If so, we say that the control is conservative. In the Internet, function f is obtained by analyzing the dependency of throughput versus the rate of loss-events for a real TCP source. A non-TCP source which implements a control system as we describe is said to be TCP-friendly if the control is conservative. In this paper, we examine whether such a control system is conservative. We first consider a simple stochastic model which assumes that the intensity of the loss-events is proportional to the current sending rate. We show that, for this model, the control is always conservative if f(p) is a concave function of 1=p; otherwise this may not be true. Then we consider a second model where the loss-event inter-arrival times is an exogeneous stationary random process. We show that, for this second model, there exist statistics of the loss-event inter-arrival times such that the control is non-conservative, even if f(p) is a concave function of 1=p. We validate our analytical results with simulations. Another aspect of unicast equation-based rate control in the Internet is the influence of the variability of round-trip times, which is not analyzed in this paper.