On the role of spatial dynamics and topology on network flows

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 spatially constrained, and not necessarily those with high betweenness as predicted by models without spatial dynamics.