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We deal with the characterization and computation of the p value, say p/sub opt/, corresponding to the maximum protocol capacity in p-persistent carrier-sense multiaccess (CSMA) protocols. The contribution of this paper is twofold. First, we give an analytical justification, and a numerical validation of a heuristic formula widely used in the literature to characterize the p/sub opt/. Second, we provide closed formulas for the p/sub opt/, and we show that the optimal capacity state, given the message length distribution, is characterized by an invariant figure: the Mp/sub opt/ product.