A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks

TL;DR

This paper introduces a new traffic flow model on networks that tracks driver groups by destination, allowing for dynamic route choices and analyzing different driver behaviors to identify multiple Wardrop equilibria.

Contribution

It presents a novel LWR-like model that incorporates destination-based driver groups and dynamic route decision-making, extending traditional traffic flow models.

Findings

Different driver behaviors lead to distinct traffic patterns.

Multiple Wardrop equilibria can exist under the proposed model.

Numerical simulations demonstrate the model's ability to capture complex traffic dynamics.

Abstract

In this paper we propose a LWR-like model for traffic flow on networks which allows one to track several groups of drivers, each of them being characterized only by their destination in the network. The path actually followed to reach the destination is not assigned a priori, and can be chosen by the drivers during the journey, taking decisions at junctions. The model is then used to describe three possible behaviors of drivers, associated to three different ways to solve the route choice problem: 1. Drivers ignore the presence of the other vehicles; 2. Drivers react to the current distribution of traffic, but they do not forecast what will happen at later times; 3. Drivers take into account the current and future distribution of vehicles. Notice that, in the latter case, we enter the field of differential games, and, if a solution exists, it likely represents a global equilibrium among drivers. Numerical simulations highlight the differences between the three behaviors and suggest the existence of multiple Wardrop equilibria.