On the role of spatial dynamics and topology on network flows

TL;DR

This paper investigates how spatial dynamics and network topology influence congestion in spatial networks, revealing that these factors significantly alter the critical loading rate and the nature of phase transitions to congestion.

Contribution

It introduces an analytical framework and demonstrates how spatial dynamics change congestion onset, with implications for real-world road networks like San Francisco.

Findings

Spatial dynamics lower the critical loading rate for congestion.

Transition to congestion shifts from continuous to discontinuous with spatial effects.

Identifies roads that trigger congestion, differing from betweenness-based predictions.

Abstract

Particle flows in spatial networks are susceptible to congestion. In this paper, we analyze the phase transitions of these networks to a state of congested transport and the influence of both topology and spatial dynamics on its emergence. We systematically show that the value of the critical loading rate at which congestion emerges is affected by the addition of spatial dynamics, changing the nature of this transition from a continuous to a discontinuous one. Our numerical results are confirmed by introducing an analytical solvable framework. As a case of study, we explore the implications of our findings in the San Francisco road network where we can locate the roads that originate the congested phase. These roads are the spatially constrained, and not necessarily those with high betweenness as predicted by models without spatial dynamics.