KraussModell

KraussModell, commonly referred to as the Krauss car-following model, is a microscopic traffic flow model used to simulate the longitudinal motion of individual vehicles on single-lane roads. It is part of the family of car-following models and is widely employed in microsimulations and academic studies to analyze how driver behavior influences traffic dynamics, stability, and congestion patterns.

The model updates each vehicle’s speed in discrete time steps by computing a safe velocity that ensures collision-free operation given the gap to the vehicle ahead, the ahead vehicle’s speed, and the vehicle’s own acceleration and deceleration limits. The actual speed is determined as the minimum of the vehicle’s velocity after applying allowed acceleration, the computed safe velocity, and any external speed constraints. A stochastic component is often included to reflect driver heterogeneity, whereby with a certain probability a vehicle experiences a random slowdown or more cautious adjustment.

Key parameters include the maximum acceleration, comfortable deceleration, the time step, maximum speed, and the probability of random deceleration. The safe-velocity rule is designed to prevent crashes under varying traffic conditions and vehicle behaviors. The Krauss model has been used to study phenomena such as stop-and-go waves, metastability, and the impact of driver reaction variability on macroscopic traffic states, and it is frequently compared with other microscopic models such as the Intelligent Driver Model and the Nagel-Schreckenberg model.

Originating in the late 1990s, the Krauss model remains a standard reference in traffic-flow literature for understanding how local interaction rules shape global traffic patterns.