Heat-Diffusion: Pareto Optimal Dynamic Routing for Time-Varying Wireless Networks

A dynamic routing policy, referred to as Heat-Diffusion (HD), is developed for multihop uniclass wireless networks subject to random traffic, time-varying topology and inter-channel interference. The policy uses only current condition of queue occupancies and channel states, with requiring no knowledge of traffic and topology. Besides throughput optimality, HD minimizes an average quadratic routing cost defined by endowing each channel with a time-varying cost factor. Further, HD minimizes average network delay in the class of routing policies that base decisions only on current condition of traffic congestion and channel states. Further, in this class of routing policies, HD provides a Pareto optimal tradeoff between average routing cost and average network delay, meaning that no policy can improve either one without detriment to the other. Finally, HD fluid limit follows graph combinatorial heat equation, which can open a new way to study wireless networks using heat calculus, a very active area of pure mathematics.