Traffic flow modeling began in the 1950s to estimate road capacity and safety. Early approaches included the LWR model (1955) by Lighthill, Whitham, and Richards, which treated traffic as a continuous fluid. It used density and intensity variables to calculate shock waves and rarefaction waves, though it assumed an idealized one-dimensional road.
In 1981, Peter Gipps introduced a microscopic model focusing on individual vehicle behavior. It incorporated driver reaction time, desired speed, and safe braking distances. This model demonstrated how individual maneuvers, such as lane changes or braking, create 'phantom traffic jams' and gridlock, and it remains in use in software like Aimsun Next.
The Intelligent Driver Model (IDM), developed in 2000 by Treiber, Hennecke, and Helbing, uses differential equations to show how traffic instability arises from system dynamics. It estimates that road bottlenecks reduce capacity by 5–20%. Meanwhile, the Wiedemann model (1974) introduced human perception thresholds, accounting for cases where drivers do not react to minor changes.
Modern traffic simulation software, such as PTV Vissim and VISUM, continues to utilize these historical mathematical frameworks. While machine learning now allows for data-driven analysis, these foundational models established the basis for understanding traffic flow, bottleneck formation, and the impact of human behavior on road congestion.
