Abstract — While packet capture has been observed in real implementations of wireless devices randomly accessing shared channels, fair rate control algorithms based on accurate channel models that describe the phenomenon have not been developed. In this paper, using a general physical channel model, we develop the equation for the optimal attemp rate to maximize the aggregate log utility. We use the least squares method to approximate the equation to a linear function of the attempt rate. Our analysis on the approximation error shows that the linear function obtained is close enough to the original with the square of the residuals more than 0.9
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