Heat-Diffusion: Pareto optimal dynamic routing for time-varying wireless networks

A new routing policy, named Heat-Diffusion (HD), is developed for multihop wireless networks subject to stochastic arrivals, time-varying topology, and inter-channel interference, using only current queue congestion and current channel states, without requiring the knowledge of topology and arrivals. Besides throughput optimality, HD minimizes a quadratic routing cost defined by endowing each channel with a cost-factor. It also minimizes average total queue congestion, and so average network delay, within the class of routing policies that base decision only on current queue lengths and current channel states. Further, within this class, HD provides a Pareto optimal tradeoff between average delay and average routing cost, meaning that no policy can improve either one without detriment to the other. Finally, HD fluid limit follows graph combinatorial heat equation that opens a new way to study wireless networks using heat calculus, a very active area of pure mathematics.