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This paper presents a theoretical study on distributed contention window control algorithms for achieving arbitrary bandwidth allocation policies and efficient channel utilization. By modeling different bandwidth allocation policies as an optimal contention window assignment problem, we design a general and fully distributed contention window control algorithm, called GCA (general contention window adaptation), and prove that it converges to the solution of the contention window assignment problem. By examining the stability of GCA, we identify the optimal stable point that maximizes channel utilization and provide solutions to control the stable point of GCA near the optimal point. Due to the generality of GCA, our work provides a theoretical foundation to analyze existing and design new contention window control algorithms.