Dirk Helbing

Traffic and related self-driven many-particle systems

Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by “phantom traffic jams” even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems “freeze by heating”? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Growth, innovation, scaling, and the pace of life in cities

Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be societys predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution, and disease. The inexorable trend toward urbanization worldwide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development. Here we present empirical evidence indicating that the processes relating urbanization to economic development and knowledge creation are very general, being shared by all cities belonging to the same urban system and sustained across different nations and times. Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, β, that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have β ≈1.2 >1 (increasing returns), whereas those accounting for infrastructure display β ≈0.8 <1 (economies of scale). We predict that the pace of social life in the city increases with population size, in quantitative agreement with data, and we discuss how cities are similar to, and differ from, biological organisms, for which β<1. Finally, we explore possible consequences of these scaling relations by deriving growth equations, which quantify the dramatic difference between growth fueled by innovation versus that driven by economies of scale. This difference suggests that, as population grows, major innovation cycles must be generated at a continually accelerating rate to sustain growth and avoid stagnation or collapse.

Generalized Force Model of Traffic Dynamics

Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been carried out, e.g., of a moving car which approaches a stopped car. It turned out that, in order to manage such kinds of situations without producing accidents, improved traffic models are needed. Good results were obtained with the proposed generalized force model.

Self-Organizing Pedestrian Movement

Although pedestrians have individual preferences, aims, and destinations, the dynamics of pedestrian crowds is surprisingly predictable. Pedestrians can move freely only at small pedestrian densities. Otherwise their motion is affected by repulsive interactions with other pedestrians, giving rise to self-organization phenomena. Examples of the resulting patterns of motion are separate lanes of uniform walking direction in crowds of oppositely moving pedestrians or oscillations of the passing direction at bottlenecks. If pedestrians leave footprints on deformable ground (for example, in green spaces such as public parks) this additionally causes attractive interactions which are mediated by modifications of their environment. In such cases, systems of pedestrian trails will evolve over time. The corresponding computer simulations are a valuable tool for developing optimized pedestrian facilities and way systems.

The Walking Behaviour of Pedestrian Social Groups and Its Impact on Crowd Dynamics

Human crowd motion is mainly driven by self-organized processes based on local interactions among pedestrians. While most studies of crowd behaviour consider only interactions among isolated individuals, it turns out that up to 70% of people in a crowd are actually moving in groups, such as friends, couples, or families walking together. These groups constitute medium-scale aggregated structures and their impact on crowd dynamics is still largely unknown. In this work, we analyze the motion of approximately 1500 pedestrian groups under natural condition, and show that social interactions among group members generate typical group walking patterns that influence crowd dynamics. At low density, group members tend to walk side by side, forming a line perpendicular to the walking direction. As the density increases, however, the linear walking formation is bent forward, turning it into a V-like pattern. These spatial patterns can be well described by a model based on social communication between group members. We show that the V-like walking pattern facilitates social interactions within the group, but reduces the flow because of its “non-aerodynamic” shape. Therefore, when crowd density increases, the group organization results from a trade-off between walking faster and facilitating social exchange. These insights demonstrate that crowd dynamics is not only determined by physical constraints induced by other pedestrians and the environment, but also significantly by communicative, social interactions among individuals.

How simple rules determine pedestrian behavior and crowd disasters

With the increasing size and frequency of mass events, the study of crowd disasters and the simulation of pedestrian flows have become important research areas. However, even successful modeling approaches such as those inspired by Newtonian force models are still not fully consistent with empirical observations and are sometimes hard to calibrate. Here, a cognitive science approach is proposed, which is based on behavioral heuristics. We suggest that, guided by visual information, namely the distance of obstructions in candidate lines of sight, pedestrians apply two simple cognitive procedures to adapt their walking speeds and directions. Although simpler than previous approaches, this model predicts individual trajectories and collective patterns of motion in good quantitative agreement with a large variety of empirical and experimental data. This model predicts the emergence of self-organization phenomena, such as the spontaneous formation of unidirectional lanes or stop-and-go waves. Moreover, the combination of pedestrian heuristics with body collisions generates crowd turbulence at extreme densities—a phenomenon that has been observed during recent crowd disasters. By proposing an integrated treatment of simultaneous interactions between multiple individuals, our approach overcomes limitations of current physics-inspired pair interaction models. Understanding crowd dynamics through cognitive heuristics is therefore not only crucial for a better preparation of safe mass events. It also clears the way for a more realistic modeling of collective social behaviors, in particular of human crowds and biological swarms. Furthermore, our behavioral heuristics may serve to improve the navigation of autonomous robots.

How social influence can undermine the wisdom of crowd effect

Social groups can be remarkably smart and knowledgeable when their averaged judgements are compared with the judgements of individuals. Already Galton [Galton F (1907) Nature 75:7] found evidence that the median estimate of a group can be more accurate than estimates of experts. This wisdom of crowd effect was recently supported by examples from stock markets, political elections, and quiz shows [Surowiecki J (2004) The Wisdom of Crowds]. In contrast, we demonstrate by experimental evidence (N = 144) that even mild social influence can undermine the wisdom of crowd effect in simple estimation tasks. In the experiment, subjects could reconsider their response to factual questions after having received average or full information of the responses of other subjects. We compare subjects’ convergence of estimates and improvements in accuracy over five consecutive estimation periods with a control condition, in which no information about others’ responses was provided. Although groups are initially “wise,” knowledge about estimates of others narrows the diversity of opinions to such an extent that it undermines the wisdom of crowd effect in three different ways. The “social influence effect” diminishes the diversity of the crowd without improvements of its collective error. The “range reduction effect” moves the position of the truth to peripheral regions of the range of estimates so that the crowd becomes less reliable in providing expertise for external observers. The “confidence effect” boosts individuals’ confidence after convergence of their estimates despite lack of improved accuracy. Examples of the revealed mechanism range from misled elites to the recent global financial crisis.

Globally networked risks and how to respond

Today’s strongly connected, global networks have produced highly interdependent systems that we do not understand and cannot control well. These systems are vulnerable to failure at all scales, posing serious threats to society, even when external shocks are absent. As the complexity and interaction strengths in our networked world increase, man-made systems can become unstable, creating uncontrollable situations even when decision-makers are well-skilled, have all data and technology at their disposal, and do their best. To make these systems manageable, a fundamental redesign is needed. A ‘Global Systems Science’ might create the required knowledge and paradigm shift in thinking.

The Hidden Geometry of Complex, Network-Driven Contagion Phenomena

Predicting Disease Dissemination In combating the global spread of an emerging infectious disease, answers must be obtained to three crucial questions: Where did the disease emerge? Where will it go next? When will it arrive? Brockmann and Helbing (p. 1337; see the Perspective by McLean) analyzed disease spread via the “effective distance” rather than geographical distance, wherein two locations that are connected by a strong link are effectively close. The approach was successfully applied to predict disease arrival times or disease source using data from the the 2003 SARS viral epidemic, 2009 H1N1 influenza pandemic, and the 2011 foodborne enterohaemorrhagic Escherichia coli outbreak in Germany. A model based on effective rather than geographical distance can reveal the origin, timing, and likely spread of epidemics. [Also see Perspective by McLean] The global spread of epidemics, rumors, opinions, and innovations are complex, network-driven dynamic processes. The combined multiscale nature and intrinsic heterogeneity of the underlying networks make it difficult to develop an intuitive understanding of these processes, to distinguish relevant from peripheral factors, to predict their time course, and to locate their origin. However, we show that complex spatiotemporal patterns can be reduced to surprisingly simple, homogeneous wave propagation patterns, if conventional geographic distance is replaced by a probabilistically motivated effective distance. In the context of global, air-traffic–mediated epidemics, we show that effective distance reliably predicts disease arrival times. Even if epidemiological parameters are unknown, the method can still deliver relative arrival times. The approach can also identify the spatial origin of spreading processes and successfully be applied to data of the worldwide 2009 H1N1 influenza pandemic and 2003 SARS epidemic.

General Lane-Changing Model MOBIL for Car-Following Models

A general model (minimizing overall braking induced by lane change, MOBIL) is proposed to derive lane-changing rules for discretionary and mandatory lane changes for a wide class of car-following models. Both the utility of a given lane and the risk associated with lane changes are determined in terms of longitudinal accelerations calculated with microscopic traffic models. This determination allows for the formulation of compact and general safety and incentive criteria for both symmetric and asymmetric passing rules. Moreover, anticipative elements and the crucial influence of velocity differences of these car-following models are automatically transferred to the lane-changing rules. Although the safety criterion prevents critical lane changes and collisions, the incentive criterion takes into account the advantages and disadvantages of other drivers associated with a lane change via the “politeness factor.” The parameter allows one to vary the motivation for lane changing from purely egoistic to more cooperative driving behavior. This novel feature allows one first to prevent lane changes for a marginal advantage if they obstruct other drivers and second to let an aggressive driver induce the lane change of a slower driver ahead in order to no longer be obstructed. This phenomenon is common for asymmetric passing rules with a dedicated lane for passing. The model is applied to traffic simulations of cars and trucks with the intelligent driver model as the underlying car-following model. An open system with an on-ramp is studied, and the resulting lane-changing rate is investigated as a function of the spatial coordinate as well as a function of traffic density.