This paper introduces and analyzes a class of nonlinear congestion control algorithms called binomial algorithms, motivated in part by the needs of streaming audio and video applications for which a drastic reduction in transmission rate upon congestion is problematic. Binomial algorithms generalize TCP-style additive-increase by increasing inversely proportional to a power k of the current window (for TCP, k=0); they generalize TCP-style multiplicative-decrease by decreasing proportional to a power l of the current window (for TCP, l=1). We show that there are an infinite number of deployable TCP-friendly binomial algorithms, all of which satisfy k+l=1, and that all binomial algorithms converge to fairness under a synchronized-feedback assumption provided k+l > 0; k, l >= 0. Our simulation results show that binomial algorithms interact well with TCP across a RED bottleneck gateway. We focus on two particular algorithms, IIAD (inverse-increase/additive-decrease, k=1, l=0) and SQRT (k=l=0.5), showing that they are well-suited to applications that do not react well to large TCP-style window reductions. We also find that TCP-friendliness in terms of the relationship between throughput and loss rate of an algorithm does not necessarily imply fairness relative to TCP performance, especially for drop-tail bottleneck gateways.
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