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

TL;DR

This paper develops a macroscopic framework for routing in massively dense wireless networks, drawing an analogy with geometrical optics, and introduces a methodology to compute cost functions for bandwidth and energy constraints.

Contribution

It generalizes the optical analogy to network routing, derives the eikonal equation in this context, and provides a method to calculate network cost functions for different limitations.

Findings

Established the eikonal equation as a model for network routing.

Developed a methodology for computing cost functions in dense networks.

Applied the framework to bandwidth and energy limited scenarios.

Abstract

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.