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This work presents a comprehensive theoretical framework for memoryless window-based congestion control protocols that are designed to converge to fairness and efficiency. We first derive a necessary and sufficient condition for stepwise convergence to fairness. Using this, we show how fair window increase/decrease policies can be constructed from suitable pairs of monotonically nondecreasing functions. We generalize this to smooth protocols that converge over each congestion epoch. The framework also includes a simple method for incorporating TCP-friendliness. Well-studied congestion control protocols such as TCP, GAIMD, and Binomial congestion control can be constructed using this method. Thus, we provide a common framework for the analysis of such window-based protocols. We also present two new congestion control protocols for streaming media-like applications as examples of protocol design in this framework: The first protocol, LOG, has the objective of reconciling the smoothness requirement of an application with the need for a fast dynamic response to congestion. The second protocol, SIGMOID, guarantees a minimum bandwidth for an application but behaves exactly like TCP for large windows.