Theoretical vs. Empirical Classification and Prediction of Congested Traffic States

Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss the terminology of traffic phases and give empirical evidence for the existence of a phase diagram of traffic states. In contrast to previously presented phase diagrams, it is shown that "widening synchronized patterns" are possible, if the maximum flow is located inside of a metastable density regime. Moreover, for various kinds of traffic models with different instability diagrams it is discussed, how the related phase diagrams are expected to approximately look like. Apart from this, it is pointed out that combinations of on- and off-ramps create different patterns than a single, isolated on-ramp.Comment: See http://www.helbing.org for related wor

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.Comment: Comments are welcome. For related work see http://www.helbing.or

Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts

Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner's three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram. We discuss the inconsistent use of the term "traffic phase" and show that patterns demanded by three-phase traffic theory can be reproduced with simple two-phase models, if the model parameters are suitably specified and factors characteristic for real traffic flows are considered, such as effects of noise or heterogeneity or the actual freeway design (e.g. combinations of off- and on-ramps). Conversely, we demonstrate that models created to reproduce three-phase traffic theory create similar spatiotemporal traffic states and associated phase diagrams, no matter whether the parameters imply a fundamental diagram in equilibrium or non-unique flow- density relationships. In conclusion, there are different ways of reproducing the empirical stylized facts of spatiotemporal congestion patterns summarized in this contribution, and it appears possible to overcome the controversy by a more precise definition of the scientific terms and a more careful comparison of models and data, considering effects of the measurement process and the right level of detail in the traffic model used.Comment: 18 pages in the published article, 13 figures, 2 table

Volatile Decision Dynamics: Experiments, Stochastic Description, Intermittency Control, and Traffic Optimization

The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on aggregate rather than complete information, such as TV news or stock market indices. In related experiments, we have observed a volatile decision dynamics and far-from-optimal payoff distributions. We have also identified ways of information presentation that can considerably improve the overall performance of the system. In order to determine optimal strategies of decision guidance by means of user-specific recommendations, a stochastic behavioural description is developed. These strategies manage to increase the adaptibility to changing conditions and to reduce the deviation from the time-dependent user equilibrium, thereby enhancing the average and individual payoffs. Hence, our guidance strategies can increase the performance of all users by reducing overreaction and stabilizing the decision dynamics. These results are highly significant for predicting decision behaviour, for reaching optimal behavioural distributions by decision support systems, and for information service providers. One of the promising fields of application is traffic optimization.Comment: For related work see http://www.helbing.or

Criticism of three-phase traffic theory

After introducing the history and main points of three-phase traffic theory, we continue with a critical discussion based on its theoretical features and empirical traffic data. Our data originate from the German freeway A5 close to Frankfurt, i.e. from the same freeway section that has been the basis for the development of three-phase traffic theory. Despite of this, we end up with partially different interpretations of the observations. In particular, we highlight findings that are inconsistent with three-phase traffic theory and facts that question the concept of a "general pattern" of congested traffic flow. Finally, we discuss some open problems that call for the development of improved traffic models and further empirical studies.Traffic breakdowns and congestion Three-phase traffic theory General pattern Synchronized flow Pinch effect Wide scattering

HOW INDIVIDUALS LEARN TO TAKE TURNS: EMERGENCE OF ALTERNATING COOPERATION IN A CONGESTION GAME AND THE PRISONER'S DILEMMA

In many social dilemmas, individuals tend to generate a situation with low payoffs instead of a system optimum ("tragedy of the commons"). Is the routing of traffic a similar problem? In order to address this question, we present experimental results on humans playing a route choice game in a computer laboratory, which allow one to study decision behavior in repeated games beyond the Prisoner's Dilemma. We will focus on whether individuals manage to find a cooperative and fair solution compatible with the system-optimal road usage. We find that individuals tend towards a user equilibrium with equal travel times in the beginning. However, after many iterations, they often establish a coherent oscillatory behavior, as taking turns performs better than applying pure or mixed strategies. The resulting behavior is fair and compatible with system-optimal road usage. In spite of the complex dynamics leading to coordinated oscillations, we have identified mathematical relationships quantifying the observed transition process. Our main experimental discoveries for 2- and 4-person games can be explained with a novel reinforcement learning model for an arbitrary number of persons, which is based on past experience and trial-and-error behavior. Gains in the average payoff seem to be an important driving force for the innovation of time-dependent response patterns, i.e. the evolution of more complex strategies. Our findings are relevant for decision support systems and routing in traffic or data networks.Game theory, reinforcement learning, multi-agent simulation