On monotonicity of FIFO-diverging junctions

TL;DR

This paper investigates the monotonicity properties of FIFO-diverging junctions in traffic network models, revealing they are monotone with respect to a specific polyhedral cone, which aids in analyzing traffic dynamics.

Contribution

It shows that FIFO-diverging junctions, previously thought non-monotone, are actually monotone under a certain partial order, enabling better analysis of traffic flow models.

Findings

FIFO-diverging junctions are monotone with respect to a polyhedral cone.

This monotonicity facilitates analysis of traffic network dynamics.

The result applies to compartmental models in traffic networks.

Abstract

This technical note concerns the dynamics of FIFO-diverging junctions in compartmental models for traffic networks. Many strong results on the dynamical behavior of such traffic networks rely on monotonicity of the underlying dynamics. In road traffic modeling, a common model for diverging junctions is based on the First-in, first-out principle. These type of junctions pose a problem in the analysis of traffic dynamics, since their dynamics are not monotone with respect to the positive orthant. However, this technical note demonstrates that they are in fact monotone with respect to the partial order induced by a particular, polyhedral cone.