  The standard interference functions introduced by Yates have been very
influential on the analysis and design of distributed power control laws. While
powerful and versatile, the framework has some drawbacks: the existence of
fixed-points has to be established separately, and no guarantees are given on
the rate of convergence of the iterates. This paper introduces contractive
interference functions, a slight reformulation of the standard interference
functions that guarantees the existence and uniqueness of fixed-points along
with linear convergence of iterates. We show that many power control laws from
the literature are contractive and derive, sometimes for the first time,
analytical convergence rate estimates for these algorithms. We also prove that
contractive interference functions converge when executed totally
asynchronously and, under the assumption that the communication delay is
bounded, derive an explicit bound on the convergence time penalty due to
increased delay. Finally, we demonstrate that although standard interference
functions are, in general, not contractive, they are all para-contractions with
respect to a certain metric. Similar results for two-sided scalable
interference functions are also derived.
