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The proportionally fair sharing of the capacity of a Poisson network usingSpatial-Aloha leads to closed-form performance expressions in two extremecases: (1) the case without topology information, where the analysis boils downto a parametric optimization problem leveraging stochastic geometry; (2) thecase with full network topology information, which was recently solved usingshot-noise techniques. We show that there exists a continuum of adaptivecontrols between these two extremes, based on local stopping sets, which canalso be analyzed in closed form. We also show that these control schemes areimplementable, in contrast to the full information case which is not. As localinformation increases, the performance levels of these schemes are shown to getarbitrarily close to those of the full information scheme. The analyticalresults are combined with discrete event simulation to provide a detailedevaluation of the performance of this class of medium access controls.

Analysis of a Proportionally Fair and Locally Adaptive spatial Aloha in Poisson Networks