On the Catalyzing Effect of Randomness on the Per-Flow Throughput in Wireless Networks

TL;DR

This paper explores how randomness in node distribution and network topology can enhance per-flow throughput in multi-hop wireless networks, revealing that certain types of randomness can significantly improve capacity.

Contribution

It demonstrates how the distribution of nodes, hops, and spatial correlations influence throughput, showing that randomness can lead to larger throughput scalings than deterministic models.

Findings

Randomness in node density and hop count can increase throughput scaling.

Per-flow capacity may improve with randomness, opposite to network capacity.

Spatial correlations negatively impact throughput by a logarithmic factor.

Abstract

This paper investigates the throughput capacity of a flow crossing a multi-hop wireless network, whose geometry is characterized by general randomness laws including Uniform, Poisson, Heavy-Tailed distributions for both the nodes' densities and the number of hops. The key contribution is to demonstrate \textit{how} the \textit{per-flow throughput} depends on the distribution of 1) the number of nodes $N_j$ inside hops' interference sets, 2) the number of hops $K$, and 3) the degree of spatial correlations. The randomness in both $N_j$'s and $K$ is advantageous, i.e., it can yield larger scalings (as large as $\Theta(n)$) than in non-random settings. An interesting consequence is that the per-flow capacity can exhibit the opposite behavior to the network capacity, which was shown to suffer from a logarithmic decrease in the presence of randomness. In turn, spatial correlations along the end-to-end path are detrimental by a logarithmic term.