Transport on coupled spatial networks

TL;DR

This paper investigates how interdependent spatial networks influence transport efficiency, revealing two distinct regimes where coupling optimizes utility either by minimizing paths or balancing congestion.

Contribution

It introduces a new utility measure for coupled spatial networks and explores their behavior through simulations, highlighting how coupling impacts transport performance.

Findings

Maximum coupling improves utility when flows are concentrated from many sources to few sinks.

Optimal coupling shifts when many sources connect to many sinks, balancing congestion and path length.

Coupled systems exhibit complex behaviors depending on source-sink distribution and randomness.

Abstract

Transport processes on spatial networks are representative of a broad class of real world systems which, rather than being independent, are typically interdependent. We propose a measure of utility to capture key features that arise when such systems are coupled together. The coupling is defined in a way that is not solely topological, relying on both the distribution of sources and sinks, and the method of route assignment. Using a toy model, we explore relevant cases by simulation. For certain parameter values, a picture emerges of two regimes. The first occurs when the flows go from many sources to a small number of sinks. In this case, network utility is largest when the coupling is at its maximum and the average shortest path is minimized. The second regime arises when many sources correspond to many sinks. Here, the optimal coupling no longer corresponds to the minimum average shortest path, as the congestion of traffic must also be taken into account. More generally, results indicate that coupled spatial systems can give rise to behavior that relies subtly on the interplay between the coupling and randomness in the source-sink distribution.