Mechanical restriction versus human overreaction triggering congested traffic states

A new cellular automaton (CA) traffic model is presented. The focus is on mechanical restrictions of vehicles realized by limited acceleration and deceleration capabilities. These features are incorporated into the model in order to construct the condition of collision-free movement. The strict collision-free criterion imposed by the mechanical restrictions is softened in certain traffic situations, reflecting human overreaction. It is shown that the present model reliably reproduces most empirical findings including synchronized flow, the so-called {\it pinch effect}, and the time-headway distribution of free flow. The findings suggest that many free flow phenomena can be attributed to the platoon formation of vehicles ({\it platoon effect})Comment: 5 pages, 3 figures, to appear in PR

Optimizing Traffic Lights in a Cellular Automaton Model for City Traffic

We study the impact of global traffic light control strategies in a recently proposed cellular automaton model for vehicular traffic in city networks. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nagel-Schreckenberg model for highway traffic. The city network has a simple square lattice geometry. All streets and intersections are treated equally, i.e., there are no dominant streets. Starting from a simple synchronized strategy we show that the capacity of the network strongly depends on the cycle times of the traffic lights. Moreover we point out that the optimal time periods are determined by the geometric characteristics of the network, i.e., the distance between the intersections. In the case of synchronized traffic lights the derivation of the optimal cycle times in the network can be reduced to a simpler problem, the flow optimization of a single street with one traffic light operating as a bottleneck. In order to obtain an enhanced throughput in the model improved global strategies are tested, e.g., green wave and random switching strategies, which lead to surprising results.Comment: 13 pages, 10 figure

Fuzzy cellular model for on-line traffic simulation

This paper introduces a fuzzy cellular model of road traffic that was intended for on-line applications in traffic control. The presented model uses fuzzy sets theory to deal with uncertainty of both input data and simulation results. Vehicles are modelled individually, thus various classes of them can be taken into consideration. In the proposed approach, all parameters of vehicles are described by means of fuzzy numbers. The model was implemented in a simulation of vehicles queue discharge process. Changes of the queue length were analysed in this experiment and compared to the results of NaSch cellular automata model.Comment: The original publication is available at http://www.springerlink.co

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.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://www.theo2.physik.uni-stuttgart.de/treiber.htm

A stochastic cellular automaton model for traffic flow with multiple metastable states

A new stochastic cellular automaton (CA) model of traffic flow, which includes slow-to-start effects and a driver's perspective, is proposed by extending the Burgers CA and the Nagel-Schreckenberg CA model. The flow-density relation of this model shows multiple metastable branches near the transition density from free to congested traffic, which form a wide scattering area in the fundamental diagram. The stability of these branches and their velocity distributions are explicitly studied by numerical simulations.Comment: 11 pages, 20 figures, submitted for publicatio

Optimised Traffic Flow at a Single Intersection: Traffic Responsive signalisation

We propose a stochastic model for the intersection of two urban streets. The vehicular traffic at the intersection is controlled by a set of traffic lights which can be operated subject to fix-time as well as traffic adaptive schemes. Vehicular dynamics is simulated within the framework of the probabilistic cellular automata and the delay experienced by the traffic at each individual street is evaluated for specified time intervals. Minimising the total delay of both streets gives rise to the optimum signalisation of traffic lights. We propose some traffic responsive signalisation algorithms which are based on the concept of cut-off queue length and cut-off density.Comment: 10 pages, 11 eps figs, to appear in J. Phys.

Cellular Automata Simulating Experimental Properties of Traffic Flows

A model for 1D traffic flow is developed, which is discrete in space and time. Like the cellular automaton model by Nagel and Schreckenberg [J. Phys. I France 2, 2221 (1992)], it is simple, fast, and can describe stop-and-go traffic. Due to its relation to the optimal velocity model by Bando et al. [Phys. Rev. E 51, 1035 (1995)], its instability mechanism is of deterministic nature. The model can be easily calibrated to empirical data and displays the experimental features of traffic data recently reported by Kerner and Rehborn [Phys. Rev. E 53, R1297 (1996)].Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://traffic.comphys.uni-duisburg.de/member/home_schreck.htm

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

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