First-principles modeling of wireless networks for rate control

Achieving fair and optimal data rates in wireless networks is an area of continued research. Distributed algorithms have been developed directly from mathematical optimization problems that guarantee fair and optimal rates. However, the algorithms developed thus far are based on simplified models of wireless networks. This research presents a first-principles model of wireless networks that reduces to the classical models under certain limiting conditions. The model uses random sets to represent the times during which a channel is perceived to be utilized. Although the resulting optimization problem is non-convex, its solution can be derived offline to offer insight into situations where the classical models succeed or fail. We provide the framework for a branch and bound solution to this offline problem.