Microscopic traffic simulation is an invaluable tool for traffic research. In recent years, both the scope of research and the capabilities of the tools have been extended considerably. This article presents the latest developments concerning intermodal traffic solutions, simulator coupling and model development and validation on the example of the open source traffic simulator SUMO.

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Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton 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, we summarize different approaches to lane changing and their results, and propose a general scheme, according to which realistic lane changing rules can be developed. We test this scheme by applying it to several different lane changing rules, which, in spite of their differences, generate similar and realistic results. We 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.

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.

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Summary. The aim of this paper is to present recent progress in calibrating ten microscopic traffic flow models. The models have been tested using data collected via DGPS-equipped cars (Differential Global Positioning System) on a test track in Japan. To calibrate the models, the data of a leading car are fed into the model under consideration and the model is used to compute the headway time series of the following car. The deviations between the measured and the simulated headways are then used to calibrate and validate the models. The calibration results agree with earlier studies as there are errors of 12 % to 17 % for all models and no model can be denoted to be the best. The differences between individual drivers are larger than the differences between different models. The validation process leads to errors from 17 % to 22 %. But for special data sets with validation errors up to 60 % the calibration process has reached what is known as "overfitting": because of the adaptation to a particular situation, the models are not capable of generalizing to other situations.

Summary. The aim of this paper is to present recent progress in calibrating ten microscopic traffic flow models. The models have been tested using data collected via DGPS-equipped cars (Differential Global Positioning System) on a test track in Japan. To calibrate the models, the data of a leading car are fed into the model under consideration and the model is used to compute the headway time series of the following car. The deviations between the measured and the simulated headways are then used to calibrate and validate the models. The calibration results agree with earlier studies as there are errors of 12 % to 17 % for all models and no model can be denoted to be the best. The differences between individual drivers are larger than the differences between different models. The validation process leads to errors from 17 % to 22 %. But for special data sets with validation errors up to 60 % the calibration process has reached what is known as "overfitting": because of the adaptation to a particular situation, the models are not capable of generalizing to other situations.

Abstract. We derive some rigorous results concerning the backflow operator introduced by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not compact. Thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator. From the position representation of the backflow operator we obtain a more efficient method to determine the backflow constant. Finally, detailed position probability flow properties of a numerical approximation to the (perhaps improper) wave function of maximal backflow are displayed.