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Dirk Helbing

Publications and source records attributed to Dirk Helbing.

At least 109 records · Page 6Linked to original sources
arXiv2009

Experimental study of the behavioural mechanisms underlying self-organization in human crowds

In animal societies as well as in human crowds, many observed collective behaviours result from self-organized processes based on local interactions among individuals. However, models of crowd dynamics are still lacking a systematic individual-level experimental verification, and the local mechanisms underlying the formation of collective patterns are not yet known in detail. We have conducted a set of well-controlled experiments with pedestrians performing simple avoidance tasks in order to determine the laws ruling their behaviour during interactions. The analysis of the large trajectory dataset was used to compute a behavioural map that describes the average change of the direction and speed of a pedestrian for various interaction distances and angles. The experimental results reveal features of the decision process when pedestrians choose the side on which they evade, and show a side preference that is amplified by mutual interactions. The predictions of a binary interaction model based on the above findings were then compared to bidirectional flows of people recorded in a crowded street. Simulations generate two asymmetric lanes with opposite directions of motion, in quantitative agreement with our empirical observations. The knowledge of pedestrian behavioural laws is an important step ahead in the understanding of the underlying dynamics of crowd behaviour and allows for reliable predictions of collective pedestrian movements under natural conditions.

physics.soc-ph↗
arXiv2009

On the Controversy around Daganzo's Requiem for and Aw-Rascle's Resurrection of Second-Order Traffic Flow Models

Daganzo's criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277-286 (1995)] and Aw and Rascle's proposal how to overcome them [A. Aw and M. Rascle, SIAM J. Appl. Math. 60, 916-938 (2000)] have stimulated an intensive scientific activity in the field of traffic modeling. Here, we will revisit their arguments and the interpretations behind them. We will start by analyzing the linear stability of traffic models, which is a widely established approach to study the ability of traffic models to describe emergent traffic jams. Besides deriving a collection of useful formulas for stability analyses, the main attention is put on the characteristic speeds, which are related to the group velocities of the linearized model equations. Most macroscopic traffic models with a dynamic velocity equation appear to predict two characteristic speeds, one of which is faster than the average velocity. This has been claimed to constitute a theoretical inconsistency. We will carefully discuss arguments for and against this view. In particular, we will shed some new light on the problem by comparing Payne's macroscopic traffic model with the Aw-Rascle model and macroscopic with microscopic traffic models.

physics.soc-ph↗
arXiv2009

Reply to "What Faster-than-traffic Characteristic Speeds Mean for Vehicular Traffic Flow"

This contribution replies to H. M. Zhang's paper "What Faster-than-traffic Characteristic Speeds Mean for Vehicular Traffic Flow", which comments on the manuscript "On the Controversy around Daganzo's Requiem for and Aw-Rascle's Resurrection of Second-Order Traffic Flow Models" published in this issue of Eurpean Physical Journal B. The author clarifies several points and agrees that suitable experiments can be a way of deciding the controversy on the existence of propagation speeds faster than the speed of vehicles. Moreover, he proposes to aim at an integrated theory, which is both, theoretically consistent and practically relevant.

physics.soc-ph↗
arXiv2009

The outbreak of cooperation among success-driven individuals under noisy conditions

According to Thomas Hobbes' Leviathan [1651; 2008 (Touchstone, New York), English Ed], "the life of man [is] solitary, poor, nasty, brutish, and short," and it would need powerful social institutions to establish social order. In reality, however, social cooperation can also arise spontaneously, based on local interactions rather than centralized control. The self-organization of cooperative behavior is particularly puzzling for social dilemmas related to sharing natural resources or creating common goods. Such situations are often described by the prisoner's dilemma. Here, we report the sudden outbreak of predominant cooperation in a noisy world dominated by selfishness and defection, when individuals imitate superior strategies and show success-driven migration. In our model, individuals are unrelated, and do not inherit behavioral traits. They defect or cooperate selfishly when the opportunity arises, and they do not know how often they will interact or have interacted with someone else. Moreover, our individuals have no reputation mechanism to form friendship networks, nor do they have the option of voluntary interaction or costly punishment. Therefore, the outbreak of prevailing cooperation, when directed motion is integrated in a game-theoretical model, is remarkable, particularly when random strategy mutations and random relocations challenge the formation and survival of cooperative clusters. Our results suggest that mobility is significant for the evolution of social order, and essential for its stabilization and maintenance.

physics.soc-ph↗
arXiv2009

Game Theoretical Interactions of Moving Agents

Game theory has been one of the most successful quantitative concepts to describe social interactions, their strategical aspects, and outcomes. Among the payoff matrix quantifying the result of a social interaction, the interaction conditions have been varied, such as the number of repeated interactions, the number of interaction partners, the possibility to punish defective behavior etc. While an extension to spatial interactions has been considered early on such as in the "game of life", recent studies have focussed on effects of the structure of social interaction networks. However, the possibility of individuals to move and, thereby, evade areas with a high level of defection, and to seek areas with a high level of cooperation, has not been fully explored so far. This contribution presents a model combining game theoretical interactions with success-driven motion in space, and studies the consequences that this may have for the degree of cooperation and the spatio-temporal dynamics in the population. It is demonstrated that the combination of game theoretical interactions with motion gives rise to many self-organized behavioral patterns on an aggregate level, which can explain a variety of empirically observed social behaviors.

physics.soc-ph↗
arXiv2009

Pattern Formation, Social Forces, and Diffusion Instability in Games with Success-Driven Motion

A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the spreading and disappearance of strategies. In this paper, it is shown that success-driven motion can trigger such local agglomeration and may, therefore, be used to supplement other mechanisms supporting cooperation, like reputation or punishment. Success-driven motion is formulated here as a function of the game-theoretical payoffs. It can change the outcome and dynamics of spatial games dramatically, in particular as it causes attractive or repulsive interaction forces. These forces act when the spatial distributions of strategies are inhomogeneous. However, even when starting with homogeneous initial conditions, small perturbations can trigger large inhomogeneities by a pattern-formation instability, when certain conditions are fulfilled. Here, these instability conditions are studied for the prisoner's dilemma and the snowdrift game. Furthermore, it is demonstrated that asymmetrical diffusion can drive social, economic, and biological systems into the unstable regime, if these would be stable without diffusion.

physics.soc-ph↗
arXiv2009

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.

physics.soc-ph↗
arXiv2009

Operation Regimes and Slower-is-Faster-Effect in the Control of Traffic Intersections

The efficiency of traffic flows in urban areas is known to crucially depend on signal operation. Here, elements of signal control are discussed, based on the minimization of overall travel times or vehicle queues. Interestingly, we find different operation regimes, some of which involve a "slower-is-faster effect", where a delayed switching reduces the average travel times. These operation regimes characterize different ways of organizing traffic flows in urban road networks. Besides the optimize-one-phase approach, we discuss the procedure and advantages of optimizing multiple phases as well. To improve the service of vehicle platoons and support the self-organization of "green waves", it is proposed to consider the price of stopping newly arriving vehicles.

physics.soc-ph↗
arXiv2009

Derivation of a Fundamental Diagram for Urban Traffic Flow

Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and the travel time. In the past, empirical measurements have primarily been described by fit curves. Here, we derive expected fundamental relationships from a model of traffic flows at intersections, which suggest that the recently measured fundamental diagrams for urban flows can be systematically understood. In particular, this allows one to derive the average travel time and the average vehicle speed as a function of the utilization and/or the average number of delayed vehicles.

physics.soc-ph↗
arXiv2008

Analytical and Numerical Investigation of Ant Behavior Under Crowded Conditions

Swarm intelligence is widely recognized as a powerful paradigm of self-organized optimization, with numerous examples of successful applications in distributed artificial intelligence. However, the role of physical interactions in the organization of traffic flows in ants under crowded conditions has only been studied very recently. The related results suggest new ways of congestion control and simple algorithms for optimal resource usage based on local interactions and, therefore, decentralized control concepts. Here, we present a mathematical analysis of such a concept for an experiment with two alternative ways with limited capacities between a food source and the nest of an ant colony. Moreover, we carry out microscopic computer simulations for generalized setups, in which ants have more alternatives or the alternative ways are of different lengths. In this way and by variation of interaction parameters, we can get a better idea, how powerful congestion control based on local repulsive interactions may be. Finally, we will discuss potential applications of this design principle to routing in traffic or data networks and machine usage in supply systems.

physics.soc-ph↗
arXiv2008

From Crowd Dynamics to Crowd Safety: A Video-Based Analysis

The study of crowd dynamics is interesting because of the various self-organization phenomena resulting from the interactions of many pedestrians, which may improve or obstruct their flow. Besides formation of lanes of uniform walking direction and oscillations at bottlenecks at moderate densities, it was recently discovered that stop-and-go waves [D. Helbing et al., Phys. Rev. Lett. 97, 168001 (2006)] and a phenomenon called "crowd turbulence" can occur at high pedestrian densities [D. Helbing et al., Phys. Rev. E 75, 046109 (2007)]. Although the behavior of pedestrian crowds under extreme conditions is decisive for the safety of crowds during the access to or egress from mass events as well as for situations of emergency evacuation, there is still a lack of empirical studies of extreme crowding. Therefore, this paper discusses how one may study high-density conditions based on suitable video data. This is illustrated at the example of pilgrim flows entering the previous Jamarat Bridge in Mina, 5 kilometers from the Holy Mosque in Makkah, Saudi-Arabia. Our results reveal previously unexpected pattern formation phenomena and show that the average individual speed does not go to zero even at local densities of 10 persons per square meter. Since the maximum density and flow are different from measurements in other countries, this has implications for the capacity assessment and dimensioning of facilities for mass events. When conditions become congested, the flow drops significantly, which can cause stop-and-go waves and a further increase of the density until critical crowd conditions are reached. Then, "crowd turbulence" sets in, which may trigger crowd disasters.

physics.soc-ph↗
arXiv2008

Approximate Hamiltonian Statistics in One-dimensional Driven Dissipative Many-Particle Systems

This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring. We will compare two different situations: (i) symmetrical interaction forces fulfilling Newton's law of "actio = reactio" and (ii) asymmetric, forwardly directed interactions as, for example in vehicular traffic. Surprisingly, the steady-state velocity and distance distributions for asymmetric interactions and driving terms agree with the equilibrium distributions of classical many-particle systems with symmetrical interactions, if the system is large enough. This analytical result is confirmed by computer simulations and establishes the possibility of approximating the steady state statistics in driven many-particle systems by Hamiltonian systems. Our finding is also useful to understand the various departure time distributions of queueing systems as a possible effect of interactions among the elements in the respective queue [D. Helbing et al., Physica A 363, 62 (2006)].

physics.data-an↗
arXiv2008

Analytical Calculation of Critical Perturbation Amplitudes and Critical Densities by Non-Linear Stability Analysis of a Simple Traffic Flow Model

Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerically in the past. Here, we present an analytical study for the optimal velocity model with a stepwise specification of the optimal velocity function and a simple kind of perturbation. Despite various approximations, the analytical results are shown to reproduce numerical results very well.

physics.soc-ph↗
arXiv2008

A Power Law for the Duration of High-Flow States in Heterogeneous Traffic Flows

We study the duration of "high-flow states" in freeway traffic, defined as the time periods for which traffic flows exceed a given flow threshold. Our empirical data are surprisingly well represented by a power law. Moreover, the power law exponent is approximately 2, in dependently of the chosen flow threshold. In order to explain this discovery, we investigate a simple theoretical model of heterogeneous traffic with overtaking maneuvers, which is able to reproduce both, the empirical power law and its exponent.

physics.soc-ph↗
arXiv2008

Derivation of Non-Local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use a smooth particle hydrodynamic approach and to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the ``traffic pressure'', which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others.

physics.soc-ph↗
arXiv2008

Agents for Traffic Simulation

Vehicular traffic is a classical example of a multi-agent system in which autonomous drivers operate in a shared environment. The article provides an overview of the state-of-the-art in microscopic traffic modeling and the implications for simulation techniques. We focus on the short-time dynamics of car-following models which describe continuous feedback control tasks (acceleration and braking) and models for discrete-choice tasks as a response to the surrounding traffic. The driving style of an agent is characterized by model parameters such as reaction time, desired speed, desired time gap, anticipation etc. In addition, internal state variables corresponding to the agent's "mind" are used to incorporate the driving experiences. We introduce a time-dependency of some parameters to describe the frustration of drivers being in a traffic jam for a while. Furthermore, the driver's behavior is externally influenced by the neighboring vehicles and also by environmental input such as limited motorization and braking power, visibility conditions and road traffic regulations. A general approach for dealing with discrete decision problems in the context of vehicular traffic is introduced and applied to mandatory and discretionary lane changes. Furthermore, we consider the decision process whether to brake or not when approaching a traffic light turning from green to amber. Another aspect of vehicular traffic is related to the heterogeneity of drivers. We discuss a hybrid system of coupled vehicle and information flow which can be used for developing and testing applications of upcoming inter-vehicle communication techniques.

physics.soc-ph↗
arXiv2008

Dynamic Effects Increasing Network Vulnerability to Cascading Failures

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure (triggering event). It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. We obtain {\em upper} and {\em lower} limits to network robustness, and it is shown that {\it two} time scales $τ$ and $τ_0$, defined by the network dynamics, are important to consider prior to accurately addressing network robustness or vulnerability. The robustness of networks showing cascading failures is generally determined by a complex interplay between the network topology and flow dynamics, where the ratio $χ=τ/τ_0$ determines the relative role of the two of them.

physics.soc-ph↗