Opti{c,m}al: Optical/Optimal Routing in Massively Dense Wireless Networks

摘要

We study routing for massively dense wireless networks, i.e., wirelessnetworks that contain so many nodes that, in addition to their usualmicroscopic description, a novel macroscopic description becomes possible. Themacroscopic description is not detailed, but nevertheless contains enoughinformation to permit a meaningful study and performance optimization of thenetwork. Within this context, we continue and significantly expand previouswork on the analogy between optimal routing and the propagation of lightaccording to the laws of Geometrical Optics. Firstly, we pose the analogy in amore general framework than previously, notably showing how the eikonalequation, which is the central equation of Geometrical Optics, also appears inthe networking context. Secondly, we develop a methodology for calculating thecost function, which is the function describing the network at the macroscopiclevel. We apply this methodology for two important types of networks: bandwidthlimited and energy limited.