Section: New Results

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

With C. Singh (IIT), F. Baccelli and B. Blaszczyszyn worked on combining adaptive protocol design, utility maximization and stochastic geometry. The focus was on a spatial adaptation of Aloha within the framework of ad hoc networks. Quasi-static networks are considered, in which mobiles learn the local topology and incorporate this information to adapt their medium access probability (MAP) selection to their local environment. The cases where nodes cooperate in a distributed way to maximize the global throughput or to achieve either proportional fair or max-min fair medium access were considered. The proportionally fair sharing case leads to closed-form performance expressions in two extreme cases: (1) the case without topology information, where the analysis boils down to a parametric optimization problem leveraging stochastic geometry; (2) the case with full network topology information, which was recently solved using shot-noise techniques. It was shown that there exists a continuum of adaptive controls between these two extremes, based on local stopping sets, which can also be analyzed in closed form. These control schemes are implementable, in contrast to the full information case which is not. As local information increases, the performance levels of these schemes are shown to get arbitrarily close to those of the full information scheme. The analytical results are combined with discrete event simulation to provide a detailed evaluation of the performance of this class of medium access controls.

These results were published in [16] .