Kai Nagel

Two-lane traffic rules for cellular automata: A systematic approach

Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automation model for two-lane traffic was able to overcome some of these problems and to produce a correct density inversion at densities somewhat below the maximum flow density. In this paper, the authors summarize different approaches to lane changing and their results, and propose a general scheme, according to which realistic lane changing rules can be developed. They test this scheme by applying it to several different lane changing rules, which, in spite of their differences, generate similar and realistic results. The authors thus conclude that, for producing realistic results, the logical structure of the lane changing rules, as proposed here, is at least as important as the microscopic details of the rules.

Two lane traffic simulations using cellular automata

We examine a simple two-lane cellular automaton based upon the single-lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of stochastic elements with respect to real life traffic.

Particle hopping models and traffic flow theory

This paper shows how particle hopping models fit into the context of traffic flow theory, that is, it shows connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes-equation, and particle hopping models. In some cases, these connections are exact and have long been established, but have never been viewed in the context of traffic theory. In other cases, critical behavior of traffic jam clusters can be compared to instabilities in the partial differential equations. Finally, it is shown how all this leads to a consistent picture of traffic jam dynamics.---In consequence, this paper starts building a foundation of a comprehensive dynamic traffic theory, where strengths and weaknesses of different models (fluid-dynamical, car- following, particle hopping) can be compared, and thus allowing to systematically choose the appropriate model for a given question.

Discrete stochastic models for traffic flow.

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow vs.\ density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with maximum velocity 1 the simplest non-trivial approximation gives the exact result. For higher velocities the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.

TRANSIMS: TRansportation ANalysis and SIMulation System

This paper summarizes the TRansportation ANalysis and SIMulation System (TRANSIMS) Project, the system`s major modules, and the project`s near-term plans. TRANSIMS will employ advanced computational and analytical techniques to create an integrated regional transportation systems analysis environment. The simulation environment will include a regional population of individual travelers and freight loads with travel activities and plans, whose individual interactions will be simulated on the transportation system, and whose environmental impact will be determined. We will develop an interim operational capability (IOC) for each major TRANSIMS module during the five-year program. When the IOC is ready, we will complete a specific case study to confirm the IOC features, applicability, and readiness.

Emergent traffic jams.

We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic jams with a power law distribution {ital P}({ital t}){similar_to}{ital t}{sup {minus}3/2} of lifetimes {ital t}. On varying the vehicle density in a closed system, this critical state separates lamellar and jammed regimes and exhibits 1/{ital f} noise in the power spectrum. Using random walk arguments, in conjunction with a cascade equation, we develop a phenomenological theory that predicts the critical exponents for this transition and explains the self-organizing behavior. These predictions are consistent with all of our numerical results.

Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

Certain aspects of traffic flow measurements imply the existence of a phase transition. Models known from chaos and fractals, such as nonlinear analysis of coupled differential equations, cellular automata, or coupled maps, can generate behavior which indeed resembles a phase transition in the flow behavior. Other measurements point out that the same behavior could be generated by geometrical constraints of the scenario. This paper looks at some of the empirical evidence, but mostly focuses on different modeling approaches. The theory of traffic jam dynamics is reviewed in some detail, starting from the well-established theory of kinematic waves and then veering into the area of phase transitions. One aspect of the theory of phase transitions is that, by changing one single parameter, a system can be moved from displaying a phase transition to not displaying a phase transition. This implies that models for traffic can be tuned so that they display a phase transition or not.This paper focuses on microscopic modeling, i.e., coupled differential equations, cellular automata, and coupled maps. The phase transition behavior of these models, as far as it is known, is discussed. Similarly, fluid-dynamical models for the same questions are considered. A large portion of this paper is given to the discussion of extensions and open questions, which makes clear that the question of traffic jam dynamics is, albeit important, only a small part of an interesting and vibrant field. As our outlook shows, the whole field is moving away from a rather static view of traffic toward a dynamic view, which uses simulation as an important tool.

Realistic multi-lane traffic rules for cellular automata

Abstract A set of lane changing rules for cellular automata simulating multi-lane traffic is proposed. It reproduces qualitatively that the passing lane becomes more crowded than the one for slower cars if the flux is high enough, which is true for motorways in countries like Germany where passing should be done on a specified lane as a rule. The rules have two parameters allowing to adjust the inversion point of the lane-usage distribution and to calibrate the model.

Agent-Based Demand-Modeling Framework for Large-Scale Microsimulations

Microsimulation is becoming increasingly important in traffic demand modeling. The major advantage over traditional four-step models is the ability to simulate each traveler individually. Decision-making processes can be included for each individual. Traffic demand is the result of the different decisions made by individuals; these decisions lead to plans that the individuals then try to optimize. Therefore, such microsimulation models need appropriate initial demand patterns for all given individuals. The challenge is to create individual demand patterns out of general input data. In practice, there is a large variety of input data, which can differ in quality, spatial resolution, purpose, and other characteristics. The challenge for a flexible demand-modeling framework is to combine the various data types to produce individual demand patterns. In addition, the modeling framework has to define precise interfaces to provide portability to other models, programs, and frameworks, and it should be suitable for large-scale applications that use many millions of individuals. Because the model has to be adaptable to the given input data, the framework needs to be easily extensible with new algorithms and models. The presented demand-modeling framework for large-scale scenarios fulfils all these requirements. By modeling the demand for two different scenarios (Zurich, Switzerland, and the German states of Berlin and Brandenburg), the framework shows its flexibility in aspects of diverse input data, interfaces to third-party products, spatial resolution, and last but not least, the modeling process itself.

Deterministic models for traffic jams

We study several deterministic one-dimensional traffic models. For integer positions and velocities we find the typical high and low density phases separated by a simple transition. If positions and velocities are continuous variables the model shows self-organized critically driven by the slowest car.