arXiv subjects

Martin Treiber

Publications and source records attributed to Martin Treiber.

66 records · Page 4Linked to original sources

arXiv2001

Modelling Widely Scattered States in `Synchronized' Traffic Flow and Possible Relevance for Stock Market Dynamics

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 data is observed as a consequence of a complex traffic dynamics. For an explanation of this phenomenon and transitions between the different traffic phases, we propose a new class of molecular-dynamics-like, microscopic traffic models based on times to collisions and discuss the properties by means of analytical arguments. Similar models may help to understand the laminar and turbulent phases in the dynamics of stock markets as well as the transitions among them.

cond-mat.stat-mech↗

arXiv2000

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.

cond-mat.stat-mech↗

arXiv2000

Micro- and Macrosimulation of Freeway Traffic

We present simulations of congested traffic in circular and open systems with a non-local, gas-kinetic-based traffic model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro- and macrosimulations with these models for identical vehicles on a single lane produce the same traffic states, which also qualitatively agree with empirical traffic observations. Moreover, the phase diagrams of traffic states in the presence of bottlenecks for the microscopic car-following model and the macroscopic gas-kinetic-based model almost agree. In both cases, we found metastable regimes, spatially coexistent states, and a small region of tristability. The distinction of different types of vehicles (cars and long vehicles) yields additional insight and allows to reproduce empirical data even more realistically, including the observed fluctuation properties of traffic flows like the wide scattering of congested traffic data. Finally, as an alternative to the gas-kinetic approach, we propose a new scheme for deriving non-local macroscopic traffic models from given microscopic car-following models. Assuming identical (macroscopic) initial and boundary conditions, we show that there are microscopic models for which the corresponding macroscopic version displays an almost identical dynamics. This enables us to combine micro- and macrosimulations of road sections by simple algorithms, and even to simulate them simultaneously.

cond-mat.stat-mech↗

arXiv1999

Numerical Simulation of Macroscopic Traffic Equations

Macroscopic traffic simulations are based on coupled non-linear partial differential equations, the solutions of which are either shock-like or inhomogeneous with steep gradients, at least in the interesting density regime. We discuss several suitable explicit integration schemes, including their advantages and disadvantages, their numerical robustness and errors. We compare the effects of diffusion with that of nonlocal terms. In addition, we investigate different possibilities of treating realistic open boundary conditions. The theoretical considerations are illuminated by many examples of simulation results.

cond-mat.soft↗

arXiv1999

Gas-Kinetic-Based Traffic Model Explaining Observed Hysteretic Phase Transition

Recently, hysteretic transitions to `synchronized traffic' with high values of both density and traffic flow were observed on German freeways [B. S. Kerner and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)]. We propose a macroscopic traffic model based on a gas-kinetic approach that can explain this phase transition. The results suggest a general mechanism for the formation of probably the most common form of congested traffic.

cond-mat.stat-mech↗

arXiv1999

Phase Diagram of Traffic States in the Presence of Inhomogeneities

We present a phase diagram of the different kinds of congested traffic that are triggered by disturbances when passing ramps or other spatial inhomogeneities of a freeway. The simulation results obtained by the nonlocal, gas-kinetic-based traffic model are in good agreement with empirical findigs. They allow to understand the observed trasitions between free and various kinds of congested traffic, among them localized clusters, stop-and-go waves, and different types of ``synchronized'' traffic. The proposed conditions for the existence of these states suggest that the phase diagram is universal for a class of different microscopic and macroscopic traffic models.

cond-mat.stat-mech↗

arXiv1999

Explanation of Observed Features of Self-Organization in Traffic Flow

Based on simulations with the ``intelligent driver model'', a microscopic traffic model, we explain the recently discovered transition from free over ``synchronized'' traffic to stop-and-go patterns [B. S. Kerner, Phys. Rev. Lett. 81, 3797 (1998)]. We obtain a nearly quantitative agreement with empirical findings such as the ``pinch effect'', the flow-density diagram, the emergence of stop-and-go waves from nonhomogeneous congested traffic, and the dimensions of their wavelength.

cond-mat.stat-mech↗

arXiv1999

Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average velocity contain a non-local interaction term which is very favorable for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. The model parameters can be easily calibrated by means of empirical data. They are directly related to the quantities characterizing individual driver-vehicle behavior, and their optimal values have the expected order of magnitude. Therefore, they allow to investigate the influences of varying street and weather conditions or freeway control measures. Simulation results for realistic model parameters are in good agreement with the diverse non-linear dynamical phenomena observed in freeway traffic.

cond-mat.stat-mech↗

arXiv1999

Macroscopic Simulation of Widely Scattered Synchronized Traffic States

Recently, a phase transition to synchronized congested traffic has been observed in empirical highway data [B. S. Kerner and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)]. This hysteretic transition has been described by a non-local, gas-kinetic-based traffic model [D. Helbing and M. Treiber, Phys. Rev. Lett. 81, 3042 (1998)] that, however, did not display the wide scattering of synchronized states. Here, it is shown that the latter can be reproduced by a mixture of different vehicle types like cars and trucks. The simulation results are in good agreement with Dutch highway data.

cond-mat.stat-mech↗

arXiv1998

Jams, Waves, and Clusters

Have you been suffering from traffic jams lately and asking yourself why freeways are no free ways anymore? After several great advances in traffic theory, Korean physicists have now offered an interpretation of a recently discovered state of congested traffic, called ``synchronized'' traffic. Their fluid-dynamic simulations can be a useful tool for an optimization of traffic flow on motorways.

cond-mat.stat-mech↗

arXiv1997

Travelling waves in electroconvection of the nematic Phase 5: A test of the weak electrolyte model

We investigated travelling waves appearing as the primary pattern-forming instability in the nematic Phase 5 (Merck) in the planar geometry in order to test the recently developed weak electrolyte model of ac-driven electroconvection [M. Treiber and L. Kramer, Mol. Cryst. Liq. Cryst 261, 311 (1995)]. Travelling waves are observed over the full conductive range of applied frequencies for three cells of different layer thickness d. We also measured the elastic constants, the electric conductivity, and the dielectric constant. The other parameters of Phase 5 are known, apart from the (relatively unimportant) viscosity $α_1$ and the two parameters of the weak electrolyte model that are proportional to the geometric mean of the mobilities, and the recombination rate, respectively. Assuming a sufficiently small recombination rate, the predicted dependence of the frequency of the travelling waves at onset (Hopf frequency) on d and on the applied frequency agreed quantitatively with the experiments, essentially without fit parameters. The absolute value of the Hopf frequency implies that the geometric mean of the mobilities amounts to $1.1 \times 10^{-10} m^2/(Vs)$.

patt-sol↗

arXiv1994

Bipolar Electrodiffusion model for Electroconvection in Nematics

The common description of the electrical behavior of a nematic liquid crystal as an anisotropic dielectric medium with (weak) ohmic conductivity is extended to an electrodiffusion model with two active ionic species. Under appropriate, but rather general conditions the additional effects can lead to a distinctive change of the threshold behavior of the electrohydrodynamic instability, namely to travelling patterns instead of static ones. This may explain the experimentally observed phenomena.

patt-sol↗