A Theory of Routing for Large-Scale Wireless Ad-Hoc Networks

TL;DR

This paper develops a theoretical framework using path integrals to analyze routing strategies in large-scale wireless ad-hoc networks, deriving path length distributions and capacity scaling laws.

Contribution

It introduces the effective radius as a key parameter to evaluate routing strategies and demonstrates their asymptotic behavior and capacity scaling in large networks.

Findings

Distribution of path lengths for various routing strategies

Identification of 'good' routing strategies based on effective radius

Finite effective radius strategies have capacity scaling as Θ(√N)

Abstract

In this work we develop a new theory to analyse the process of routing in large-scale ad-hoc wireless networks. We use a path integral formulation to examine the properties of the paths generated by different routing strategies in these kinds of networks. Using this theoretical framework, we calculate the statistical distribution of the distances between any source to any destination in the network, hence we are able to deduce a length parameter that is unique for each routing strategy. This parameter, defined as the {\it effective radius}, effectively encodes the routing information required by a node. Analysing the aforementioned statistical distribution for different routing strategies, we obtain a threefold result for practical Large-Scale Wireless Ad-Hoc Networks: 1) We obtain the distribution of the lengths of all the paths in a network for any given routing strategy, 2) We are able to identify "good" routing strategies depending on the evolution of its effective radius as the number of nodes, $N$, increases to infinity, 3) For any routing strategy with finite effective radius, we demonstrate that, in a large-scale network, is equivalent to a random routing strategy and that its transport capacity scales as $\Theta(\sqrt{N})$ bit-meters per second, thus retrieving the scaling law that Gupta and Kumar (2000) obtained as the limit for single-route large-scale wireless networks.