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 where Pn is an estimate of, the loss-event ratio. Function f (the target loss-throughput function) defines the objective of the control method: we would like that the throughput 3, attained by the source, satisfies the equation _). If so, we say that the control is conservative. In the Internet, function f is obtained by analyzing the dependency of throughput versus the loss-event ratio 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. Our main finding is a set of two conditions whose conjunction is sufficient for the control to be conservative. Suppose that 1/15n is an unbiased estimator of 1/i. Then, it is sufficient that (1) f(p) is a concave function with l/p, and (2) the expected time between two consecutive loss-events, given the current rate x, is non-increasing with x. To verify our finding, we formulate a model of the control and study numerical and simulation results for some special cases. We show there exists statistics of the loss-event inter-arrival times such that the control is non-conservative, even if f(p) is a concave function of l/p, which should necessarily imply that our second sufficient condition does not hold in those cases. As a by-product, our theory explains why the control is overly conservative when the loss-event ratio is high. 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.

In  Proc. of the 17th International Teletraffic Congress (ITC-17)


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