# Car Path Tracking in Traffic Flow Networks with Bounded Buffers at Junctions

## TL;DR

This paper models individual car trajectories in traffic networks with bounded buffers at junctions using coupled PDE-ODE systems, enabling traffic flow analysis and navigation applications.

## Contribution

It introduces a novel macroscopic traffic model incorporating bounded buffers at junctions and develops numerical algorithms for tracking individual vehicle paths.

## Key findings

- Effective modeling of car trajectories in complex networks.
- Numerical algorithms enable trajectory tracking.
- Potential use as navigation tools.

## Abstract

This article deals with the modeling for an individual car path through a road network, where the dynamics is driven by a coupled system of ordinary and partial differential equations. The network is characterized by bounded buffers at junctions that allow for the interpretation of roundabouts or on-ramps while the traffic dynamics is based on first-order macroscopic equations of Lighthill-Whitham-Richards (LWR) type. Trajectories for single drivers are then influenced by the surrounding traffic and can be tracked by appropriate numerical algorithms. The computational experiments show how the modeling framework can be used as navigation device.