Traffic Analysis in Random Delaunay Tessellations and Other Graphs

TL;DR

This paper analyzes traffic flow and degree distribution in various random graph models, revealing how different structures affect routing efficiency and how adding matchings can reduce maximum flow congestion.

Contribution

It provides a comparative study of traffic flow in Delaunay triangulations, Erd"os-Renyi, geometric, expanders, and regular graphs, introducing methods to reduce flow congestion.

Findings

Maximum vertex and edge flow depend on graph type and routing method.

Adding a random matching significantly reduces maximum vertex flow.

Flow characteristics vary notably across different random graph models.

Abstract

In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erd\"os-Renyi random graphs, geometric random graphs, expanders and random $k$-regular graphs. Moreover we show that adding a random matching to the original graph can considerably reduced the maximum vertex flow.