Carfollowing

Car-following refers to the set of mathematical and behavioral models that describe how a driver responds to the vehicle directly ahead in the same traffic lane. In microscopic traffic flow theory, car-following models specify a vehicle’s longitudinal acceleration as a function of the gap to the lead vehicle, the relative speed to that vehicle, and the follower’s own speed, with the aim of reproducing realistic driving and inter-vehicle dynamics.

Historically, car-following models date from mid-20th century research in traffic engineering. Notable continuous-time, time-and-space models include the Gazis–Herman–Rothery (GHR) model, Gipps’ model, and the Intelligent Driver Model (IDM). Other influential families include Krauss-type models and Wiedemann-type models. These models can be deterministic or incorporate stochastic elements to reflect human variability, and they may operate in continuous time or discretized time steps for use in simulations.

A typical car-following formulation expresses acceleration as a function a = F(s, v, Δv), where s is the gap or headway to the lead vehicle, v is the follower’s speed, and Δv is the relative speed to the lead vehicle. Drivers also respond to safety constraints, desired speed, and maximum deceleration. Key concepts include time headway, desired gap, and safe following distance, all of which influence stability and the emergence of traffic patterns such as stop-and-go waves.

Applications of car-following models include microscopic traffic simulation, traffic management and safety analysis, and the development of automated driving and platooning systems. Their insights help explain phenomena like string stability, jam formation, and capacity under varying driver behavior.