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

We study routing for massively dense wireless networks, i.e., wireless networks that contain so many nodes that, in addition to their usual microscopic description, a novel macroscopic description becomes possible. The macroscopic description is not detailed, but nevertheless contains enough information to permit a meaningful study and performance optimization of the network. Within this context, we continue and significantly expand previous work on the analogy between optimal routing and the propagation of light according to the laws of Geometrical Optics. Firstly, we pose the analogy in a more general framework than previously, notably showing how the eikonal equation, which is the central equation of Geometrical Optics, also appears in the networking context. Secondly, we develop a methodology for calculating the cost function, which is the function describing the network at the macroscopic level. We apply this methodology for two important types of networks: bandwidth limited and energy limited.