Mixed Monotonicity of Partial First-In-First-Out Traffic Flow Models

TL;DR

This paper investigates traffic flow models with partial FIFO properties, demonstrating that mixed monotonicity applies to these models and providing conditions for their convergence to equilibrium.

Contribution

It extends the concept of mixed monotonicity to traffic models with partial FIFO behavior, offering new analysis tools for such systems.

Findings

Mixed monotonicity applies to partial FIFO traffic models.

Conditions for convergence to equilibrium are established.

Analysis techniques for traffic flow are enhanced.

Abstract

In vehicle traffic networks, congestion on one outgoing link of a diverging junction often impedes flow to other outgoing links, a phenomenon known as the first-in-first-out (FIFO) property. Simplified traffic models that do not account for the FIFO property result in monotone dynamics for which powerful analysis techniques exist. FIFO models are in general not monotone, but have been shown to be mixed monotone - a generalization of monotonicity that enables similarly powerful analysis techniques. In this paper, we study traffic flow models for which the FIFO property is only partial, that is, flows at diverging junctions exhibit a combination of FIFO and non-FIFO phenomena. We show that mixed monotonicity extends to this wider class of models and establish conditions that guarantee convergence to an equilibrium.