Traffic flow

In transportation engineering, traffic flow is the study of interactions between travellers (including pedestrians, cyclists, drivers, and their vehicles) and infrastructure (including highways, signage, and traffic control devices), with the aim of understanding and developing an optimal transport network with efficient movement of traffic and minimal traffic congestion problems. The foundation for modern traffic flow analysis dates back to the 1920s with Frank Knight's analysis of traffic equilibrium, further developed by Wardrop in 1952. Despite advances in computing, a universally satisfactory theory applicable to real-world conditions remains elusive. Current models blend empirical and theoretical techniques to forecast traffic and identify congestion areas, considering variables like vehicle use and land changes. Traffic flow is influenced by the complex interactions of vehicles, displaying behaviors such as cluster formation and shock wave propagation. Key traffic stream variables include speed, flow, and density, which are interconnected. Free-flowing traffic is characterized by fewer than 12 vehicles per mile per lane, whereas higher densities can lead to unstable conditions and persistent stop-and-go traffic. Models and diagrams, such as time-space diagrams, help visualize and analyze these dynamics. Traffic flow analysis can be approached at different scales: microscopic (individual vehicle behavior), macroscopic (fluid dynamics-like models), and mesoscopic (probability functions for vehicle distributions). Empirical approaches, such as those outlined in the Highway Capacity Manual, are commonly used by engineers to model and forecast traffic flow, incorporating factors like fuel consumption and emissions. The kinematic wave model, introduced by Lighthill and Whitham in 1955, is a cornerstone of traffic flow theory, describing the propagation of traffic waves and impact of bottlenecks. Bottlenecks, whether stationary or moving, significantly disrupt flow and reduce roadway capacity. The Federal Highway Authority attributes 40% of congestion to bottlenecks. Classical traffic flow theories include the Lighthill-Whitham-Richards model and various car-following models that describe how vehicles interact...