A Payne-Whitham model of urban traffic networks in the presence of traffic lights and its application to traffic optimisation

TL;DR

The paper extends the Payne-Whitham macroscopic traffic model to urban networks with intersections and traffic signals (PWTL) and derives coupling conditions that account for turning behavior and speed reductions at intersections. It calibrates and initializes the model using OpenStreetMap data for Warsaw, TomTom flows, and Ljubljana fundamental diagram data, yielding realistic FD parameters and initial states. To tackle the computational burden of optimizing signal timings, the authors deploy surrogate models (LR, SVR, MLP, RF) to predict congestion metrics and apply Differential Evolution to search for configurations that maximize average speed or minimize total queue length, validating the results by re-simulating with the full PWTL. The study finds that surrogate models can substantially accelerate optimization while yielding practical improvements in traffic flow, though simpler models like Linear Regression can perform very well in simulated dynamics; this framework offers a scalable tool for urban traffic management and highlights directions for richer data and model enhancements.

Abstract

Urban road transport is a major civilisational and economic challenge, affecting the quality of life and economic activity. Addressing these challenges requires a multidisciplinary approach and sustainable urban planning strategies to mitigate the negative effects of traffic in cities. In this paper, we introduce an extension of one of the most popular macroscopic traffic simulation models, the Payne-Whitham model. We investigate how this model, originally designed to model highway traffic on straight road segments, can be adapted to more realistic conditions with arbitrary road network graphs and multiple intersections with traffic signals. Furthermore, we showcase the practical application of this extension in experiments aimed at optimising traffic signal settings. For computational reasons, these experiments involve the adoption of surrogate models for approximating our extended Payne-Whitham model, and subsequently, we utilise the Differential Evolution optimization algorithm, resulting in the identification of traffic signal settings that enhance the average speed of cars and decrease the total length of queues, thereby facilitating smoother traffic flow.

Figures (8)

• Figure 1: A sample output of the density of cars that is calculated using the Payne-Whitham macroscopic model.
• Figure 2: The fundamental diagram of traffic flow for $\rho_{cr}=0.05$ cars/m, $v_{max}=16$ m/s and different values of the parameter $a\in\{2,1\}$.
• Figure 3: An intersection with the virtual initial and final densities (blue values are virtual).
• Figure 4: The relation between density and speed obtained by running the algorithm (blue) is consistent with the fundamental diagram (orange) for all four categories of roads.
• Figure 5: An example of a 4 road intersection. In such cases, we assume that the road segments that are opposite to each other share the same traffic light configuration.

Theorems & Definitions (2)

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