Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations

TL;DR

This study investigates microscopic traffic fluctuations and their impact on global network properties in scale-free cyclic graphs, revealing how super-structure influences traffic behavior and the transition to jamming.

Contribution

It introduces an analysis of microscopic density fluctuations and their relation to global traffic properties, highlighting the role of super-structure in complex network traffic dynamics.

Findings

Traffic exhibits anti-persistence due to super-structure effects.

Correlation decreases with increasing traffic density and vanishes at jamming.

Global load distributions and queuing times change qualitatively near jamming.

Abstract

We study the microscopic time fluctuations of traffic-load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates $R$ the traffic is stationary and the load timeseries exhibit anti-persistence due to the regulatory role of the super-structure associated with two hub nodes in the network. We discuss how the super-structure effects the functioning of the network at high traffic density and at the jamming threshold. The degree of correlations systematically decreases with increasing traffic density and eventually disappears when approaching a jamming density $R_c$. Already before jamming we observe qualitative changes in the global network-load distributions and the particle queuing-times. These changes are related to the occurrence of temporary crises in which the network-load increases dramatically, and then slowly falls back to a value characterizing free-flow.