A freeway with vehicles transmitting traffic-related messages via short-range broadcasting is a technological example of coupled material and information flows in complex networks: information on traffic flows is propagated via a dynamically changing ad hoc network based on local interactions....

We generalize a wide class of time-continuous microscopic traffic models to include essential aspects of driver behaviour not captured by these models. Specifically, we consider (i) finite reaction times, (ii) estimation errors, (iii) looking several vehicles ahead (spatial anticipation), and...

Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner's three-phase traffic theory with the phase diagram approach for traffic models with...

An extended open system such as traffic flow is said to be convectively unstable if perturbations of the stationary state grow but propagate in only one direction, so they eventually leave the system. By means of data analysis, simulations, and analytical calculations, we give evidence that this...

Traffic flow at low densities (free traffic) is characterized by a quasi-one-dimensional relation between traffic flow and vehicle density, while no such fundamental diagram exists for ‘synchronized’ congested traffic flow. Instead, a two-dimensional area of widely scattered flow-density...

We present a gas-kinetic (Boltzmann-like) traffic equation that is not only suited for low vehicle densities, but also for the high-density regime, as it takes into account the forwardly directed interactions, effects of vehicular space requirements like increased interaction rates, and effects...

When simulating trajectories by integrating time-continuous car-following models, standard integration schemes such as the fourth-order Runge–Kutta method (RK4) are rarely used while the simple Euler method is popular among researchers. We compare four explicit methods both analytically and...

The essential distinction between the Fundamental Diagram Approach (FDA) and Kerner’s three-phase theory (KTPT) is the existence of a unique gap–speed (or flow–density) relationship in the former class. In order to verify this relationship, empirical data are analyzed with the following...

We propose a simple cellular automaton for traffic flow within the fundamental diagram, which could reproduce aspects of the three-phase theory. This so-called average space gap model (ASGM) is based on the Nagel–Schreckenberg model with additional slow-to-start and anticipation rules. The...

Although pedestrians have individual preferences, aims, and destinations, the dynamics of pedestrian crowds is surprisingly predictable. Pedestrians can move freely only at small pedestrian densities. Otherwise their motion is affected by repulsive interactions with other pedestrians, giving...