Traffic flow densities in large transport networks

TL;DR

This paper derives an asymptotic formula for local traffic flow density in large, randomly scattered transport networks, linking it to network node intensity, traffic generation rates, and navigation structure.

Contribution

It introduces a general asymptotic formula for traffic flow density in large networks, applicable under broad navigation conditions, and verifies it for specific Poisson point process models.

Findings

Derived an asymptotic formula for traffic density in large networks.

Validated the formula for navigation schemes based on directed spanning trees.

Applicable to networks with inhomogeneous node distributions.

Abstract

We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing according to some navigation scheme in a given direction. In the thermodynamic limit of a growing domain, we present an asymptotic formula expressing the local traffic flow density at any given location in the domain in terms of three fundamental characteristics of the underlying network: the spatial intensity of the nodes together with their traffic generation rates, and of the links induced by the navigation. This formula holds for a general class of navigations satisfying a link-density and a sub-ballisticity condition. As a specific example, we verify these conditions for navigations arising from a directed spanning tree on a Poisson point process with inhomogeneous intensity function.