Macroscopic Dynamics of Multi-Lane Traffic

We present a macroscopic model of mixed multi-lane freeway traffic that can be easily calibrated to empirical traffic data, as is shown for Dutch highway data. The model is derived from a gas-kinetic level of description, including effects of vehicular space requirements and velocity correlations between successive vehicles. We also give a derivation of the lane-changing rates. The resulting dynamic velocity equations contain non-local and anisotropic interaction terms which allow a robust and efficient numerical simulation of multi-lane traffic. As demonstrated by various examples, this facilitates the investigation of synchronization patterns among lanes and effects of on-ramps, off-ramps, lane closures, or accidents.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Conductance noise in interacting Anderson insulators driven far from equilibrium

The combination of strong disorder and many-body interactions in Anderson insulators lead to a variety of intriguing non-equilibrium transport phenomena. These include slow relaxation and a variety of memory effects characteristic of glasses. Here we show that when such systems are driven with sufficiently high current, and in liquid helium bath, a peculiar type of conductance noise can be observed. This noise appears in the conductance versus time traces as downward-going spikes. The characteristic features of the spikes (such as typical width) and the threshold current at which they appear are controlled by the sample parameters. We show that this phenomenon is peculiar to hopping transport and does not exist in the diffusive regime. Observation of conductance spikes hinges also on the sample being in direct contact with the normal phase of liquid helium; when this is not the case, the noise exhibits the usual 1/f characteristics independent of the current drive. A model based on the percolative nature of hopping conductance explains why the onset of the effect is controlled by current density. It also predicts the dependence on disorder as confirmed by our experiments. To account for the role of the bath, the hopping transport model is augmented by a heuristic assumption involving nucleation of cavities in the liquid helium in which the sample is immersed. The suggested scenario is analogous to the way high-energy particles are detected in a Glaser's bubble chamber.Comment: 15 pages 22 figure

Single-Bottleneck Approximation for Driven Lattice Gases with Disorder and Open Boundary Conditions

We investigate the effects of disorder on driven lattice gases with open boundaries using the totally asymmetric simple exclusion process as a paradigmatic example. Disorder is realized by randomly distributed defect sites with reduced hopping rate. In contrast to equilibrium, even macroscopic quantities in disordered non-equilibrium systems depend sensitively on the defect sample. We study the current as function of the entry and exit rates and the realization of disorder and find that it is, in leading order, determined by the longest stretch of consecutive defect sites (single-bottleneck approximation, SBA). Using results from extreme value statistics the SBA allows to study ensembles with fixed defect density which gives accurate results, e.g. for the expectation value of the current. Corrections to SBA come from effective interactions of bottlenecks close to the longest one. Defects close to the boundaries can be described by effective boundary rates and lead to shifts of the phase transitions. Finally it is shown that the SBA also works for more complex models. As an example we discuss a model with internal states that has been proposed to describe transport of the kinesin KIF1A.Comment: submitted to J. Stat. Mec

Pedestrian, Crowd, and Evacuation Dynamics

This contribution describes efforts to model the behavior of individual pedestrians and their interactions in crowds, which generate certain kinds of self-organized patterns of motion. Moreover, this article focusses on the dynamics of crowds in panic or evacuation situations, methods to optimize building designs for egress, and factors potentially causing the breakdown of orderly motion.Comment: This is a review paper. For related work see http://www.soms.ethz.c

Congested Traffic States in Empirical Observations and Microscopic Simulations

We present data from several German freeways showing different kinds of congested traffic forming near road inhomogeneities, specifically lane closings, intersections, or uphill gradients. The states are localized or extended, homogeneous or oscillating. Combined states are observed as well, like the coexistence of moving localized clusters and clusters pinned at road inhomogeneities, or regions of oscillating congested traffic upstream of nearly homogeneous congested traffic. The experimental findings are consistent with a recently proposed theoretical phase diagram for traffic near on-ramps [D. Helbing, A. Hennecke, and M. Treiber, Phys. Rev. Lett. {\bf 82}, 4360 (1999)]. We simulate these situations with a novel continuous microscopic single-lane model, the ``intelligent driver model'' (IDM), using the empirical boundary conditions. All observations, including the coexistence of states, are qualitatively reproduced by describing inhomogeneities with local variations of one model parameter. We show that the results of the microscopic model can be understood by formulating the theoretical phase diagram for bottlenecks in a more general way. In particular, a local drop of the road capacity induced by parameter variations has practically the same effect as an on-ramp.Comment: Now published in Phys. Rev. E. Minor changes suggested by a referee are incorporated; full bibliographic info added. For related work see http://www.mtreiber.de/ and http://www.helbing.org