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The authors propose a new scheduling and routing approach, the Heat Diffusion (HD) protocol, using combinatorial analogue of the heat equation in mathematical physics. The algorithm holds for systems subject to time-varying network conditions with general packet arrivals and random topology states, including ad-hoc networks with mobility. Compared to the well-known backpressure policy, the HD protocol is generalized in form and optimized in performance, which considers link penalties and node capacities in the routing. It mitigates the packet looping behavior of backpressure and attempts to communicate less over links of higher costs and with the nodes of lower capacities.
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