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A dynamic routing policy, referred to as Heat-Diffusion (HD), is developedfor multihop uniclass wireless networks subject to random traffic, time-varyingtopology and inter-channel interference.The policy uses only current conditionof queue occupancies and channel states, with requiring no knowledge of trafficand topology.Besides throughput optimality, HD minimizes an average quadraticrouting cost defined by endowing each channel with a time-varying cost factor.Further, HD minimizes average network delay in the class of routing policiesthat base decisions only on current condition of traffic congestion and channelstates. Further, in this class of routing policies, HD provides a Paretooptimal 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 canopen a new way to study wireless networks using heat calculus, a very activearea of pure mathematics.

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