  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.
