An algebraic approach for modeling and simulation of road traffic networks

TL;DR

This paper introduces an algebraic framework for modeling and simulating large road traffic networks, enabling efficient analysis of traffic flow and control strategies using matrix-based representations.

Contribution

It develops a novel algebraic approach to model complex traffic networks with elementary systems and concatenation operators, incorporating traffic control at intersections.

Findings

Successfully models large regular networks algebraically.

Derives macroscopic traffic diagrams for different intersection controls.

Demonstrates simulation of traffic flow on closed networks.

Abstract

We present in this article an algebraic approach to model and simulate road traffic networks. By defining a set of road traffic systems and adequate concatenating operators in that set, we show that large regular road networks can be easily modeled and simulated. We define elementary road traffic systems which we then connect to each other and obtain larger systems. For the traffic modeling, we base on the LWR first order traffic model with piecewise-linear fundamental traffic diagrams. This choice permits to represent any traffic system with a number of matrices in specific algebraic structures. For the traffic control on intersections, we consider two cases: intersections controlled with a priority rule, and intersections controlled with traffic lights. Finally, we simulate the traffic on closed regular networks, and derive the macroscopic fundamental traffic diagram under the two cases of intersection control.