In pricing-based congestion control protocols it is common to assume that the rate of congestion feedback from the network is limited to a single bit per packet. To obtain a precise estimate of available bandwidth (as summarized by the congestion price) under the single-bit constraint, a session must consider feedback contained in a number of recently received packets. As more packets are considered, however, the estimate includes increasingly older information about the network state. We study this tradeoff between the quality and timeliness of feedback using control-theoretic approach, modeling the 'memory' incorporated into the price estimate as additional feedback delay. We show through analysis that obtaining arbitrary precision in the estimated price causes control instability, making it more difficult for a session to track its targeted optimal rate. Through continuous-time simulation of our model and packet-level simulations, we find that crude estimates of congestion price based on very few packets can yield good performance while allowing the session to operate far away from the boundary of instability. We also investigate the impact of estimation bias on protocol performance, showing that protocols use a form of integral control can compensate for biased price estimates.
['Jonathan K. Shapiro', 'C. V. Hollot', 'Donald F. Towsley']
Trading precision for stability in congestion control with probabilistic packet marking