The macroscopic fundamental diagram explained by a walking experiment in class

Knoop, Victor L.; Hegyi, Andreas; Duives, Dorine · 2025 · Crossref

DOI: 10.1186/s12544-025-00759-0

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Summary

This paper introduces a pedagogical walking experiment designed to teach the concept of the Macroscopic Fundamental Diagram (MFD) in traffic flow theory. The MFD describes the relationship between the number of vehicles in a defined area (accumulation) and their average speed or exit rate (performance). While this concept is central to modern traffic control strategies like perimeter control, it is often difficult to illustrate in classroom settings due to the impracticality of conducting vehicle-based experiments. The authors propose using students as pedestrians in a confined space to physically demonstrate how increasing density initially increases flow but eventually causes congestion and reduced performance, thereby providing an intuitive understanding of traffic dynamics. The experimental setup involves a rectangular area (2 m × 3 m) containing four stools arranged in the corners. Participants follow randomized routes that require them to visit specific stools, waiting two seconds at each to simulate task completion and increase interaction time. The experiment is conducted in multiple runs, each lasting 2–4 minutes, with a pre-defined target accumulation (number of participants in the area). Inflow is controlled manually using a "bang-bang" algorithm: participants are allowed to enter only when the current accumulation is below the target threshold. Data collection utilizes a custom web-based application that tracks entry and exit times via smartphone buttons, alongside overhead video recording for detailed analysis. The study was conducted with 25–30 participants during a summer school, testing accumulation levels ranging from 3 to 20 pedestrians. The results demonstrate that the experiment successfully generates an MFD with the expected inverted U-shape. As accumulation increased, the exit flow rate (performance) initially rose, reached a maximum, and then declined as congestion hindered movement. The authors note that while the manual counting method was susceptible to minor user errors—particularly at higher densities where rapid exits caused confusion—the resulting data points were sufficient to visualize the theoretical curve. Participants also physically experienced the delays associated with high accumulation, reinforcing the theoretical concepts through direct observation of reduced outflow rates during crowded conditions. The significance of this work lies in its contribution to traffic engineering education. By providing a reproducible, low-cost experimental framework, the paper offers instructors a tool to make abstract traffic flow theories tangible for students. The authors share the software and route-generation tools to facilitate replication. They also discuss potential refinements, such as adding haptic feedback to the counting app to reduce errors and starting experiments with participants already distributed throughout the area to minimize flow fluctuations. This approach bridges the gap between theoretical models and practical understanding, helping students grasp the implications of perimeter control and congestion management without requiring complex infrastructure.

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• traffic density