Characterizing correlations of flow oscillations at bottlenecks

"Oscillations" occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. We present a model of pedestrian motion that is able to reproduce oscillations with different characteristics. The Wald-Wolfowitz test and Gillis' correlated random walk are shown to hold observables that can be used to characterize different kinds of oscillations

Traffic Instabilities in Self-Organized Pedestrian Crowds

In human crowds as well as in many animal societies, local interactions among individuals often give rise to self-organized collective organizations that offer functional benefits to the group. For instance, flows of pedestrians moving in opposite directions spontaneously segregate into lanes of uniform walking directions. This phenomenon is often referred to as a smart collective pattern, as it increases the traffic efficiency with no need of external control. However, the functional benefits of this emergent organization have never been experimentally measured, and the underlying behavioral mechanisms are poorly understood. In this work, we have studied this phenomenon under controlled laboratory conditions. We found that the traffic segregation exhibits structural instabilities characterized by the alternation of organized and disorganized states, where the lifetime of well-organized clusters of pedestrians follow a stretched exponential relaxation process. Further analysis show that the inter-pedestrian variability of comfortable walking speeds is a key variable at the origin of the observed traffic perturbations. We show that the collective benefit of the emerging pattern is maximized when all pedestrians walk at the average speed of the group. In practice, however, local interactions between slow- and fast-walking pedestrians trigger global breakdowns of organization, which reduce the collective and the individual payoff provided by the traffic segregation. This work is a step ahead toward the understanding of traffic self-organization in crowds, which turns out to be modulated by complex behavioral mechanisms that do not always maximize the group's benefits. The quantitative understanding of crowd behaviors opens the way for designing bottom-up management strategies bound to promote the emergence of efficient collective behaviors in crowds.Comment: Article published in PLoS Computational biology. Freely available here: http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.100244

Validated force-based modeling of pedestrian dynamics

This dissertation investigates force-based modeling of pedestrian dynamics. Having the quantitative validation of mathematical models in focus principle questions will be addressed throughout this work: Is it manageable to describe pedestrian dynamics solely with the equations of motion derived from the Newtonian dynamics? On the road to giving answers to this question we investigate the consequences and side-effects of completing a force-based model with additional rules and imposing restrictions on the state variables. Another important issue is the representation of modeled pedestrians. Does the geometrical shape of a two dimensional projection of the human body matter when modeling pedestrian movement? If yes which form is most suitable? This point is investigated in the second part while introducing a new force-based model. Moreover, we highlight a frequently underestimated aspect in force-based modeling which is to what extent the steering of pedestrians influences their dynamics? In the third part we introduce four possible strategies to define the desired direction of each pedestrian when moving in a facility. Finally, the effects of the aforementioned approaches are discussed by means of numerical tests in different geometries with one set of model parameters. Furthermore, the validation of the developed model is questioned by comparing simulation results with empirical data

Computer simulation of pedestrian dynamics at high densities

The increasing importance and magnitude of large-scale events in our society calls for continuous research in the field of pedestrian dynamics. This dissertation investigates the dynamics of pedestrian motion at high densities using computer simulations of stochastic models. The first part discusses the successful application of the Floor Field Cellular Automaton (FFCA) in an evacuation assistant that performs faster than real-time evacuation simulations of up to $50,000$ persons leaving a multi-purpose arena. A new interpretation of the matrix of preference improves the realism of the FFCA simulation in U-turns, for instance at the entrance to the stands. The focus of the second part is the experimentally observed feature of phase separation in pedestrian dynamics into a slow-moving and a completely jammed phase. This kind of phase separation is fundamentally different to known instances of phase separation in e.g. vehicular traffic. Different approaches to modeling the phase separation are discussed and an investigation of both established and new models of pedestrian dynamics illustrates the difficulties of finding a model able to reproduce the phenomenon. The Stochastic Headway Dependent Velocity Model is introduced and extensively analyzed, simulations of the model evolve into a phase-separated state in accordance with the experimental data. Key components of the model are its slow-to-start rule, minimum velocity, and large interaction range

Der Fußgängerverkehr - Simulation und Experimente

In recent years and decades the development of ever more powerful computer hardware has been accompanied by the evolution of simulational or computer physics as a third element of physics next to theory and experiment. This thesis deals with the simulation of pedestrian traffic with a focus on evacuation processes. While theory and experiment, respectively empiricism, relied on each other since the dawn of modern physics, they do not necessarily rely on simulations, although they have begun to make heavy use of it. Simulations on the contrary can never be carried out meaningfully without theories and experiments backing them and making use of them in the interpretation process of the results. This dependence is reflected in this thesis, which includes elements of all three operation methods. It begins with an overview of elements that are necessary to build reliable simulation models. The interrelation between simulation, theory and experiment is set out in more detail there. Then a survey of existing models of pedestrian evacuation dynamics is given. The second chapter deals with the semantic - and therefore rather theoretical - problem of how a cellular automaton model can evolve toward a model which is better referred to as “discrete” model when the model is extended. This question is irrelevant for the issue of reliability, yet it is often asked. In the third chapter a discrete model of pedestrian evacuation dynamics is constructed and tested. The tests of the various elements of the model focus on the elements’ influence on the fundamental diagram, yet there are also some other tests which include some background from theory. The main results of this chapter are the construction of the model itself, the proof that it is very well able to reproduce a widely accepted empirical fundamental diagram up to a density of roughly four persons per square meter, and that - concerning computing times - the model is applicable to scenarios with a few million persons. The fourth chapter deals with the analysis of two observations and two experiments. The first observation was done during an evacuation exercise in a primary school. The empirical data was partly used to calibrate the parameters of the simulation and partly to compare them with the results of simulations which were done using these parameters. The second observation is a study of upstairs walking speed distributions on a long stair. In the counterflow experiment a rich variety of self-organisational structures showed up, which will be a challenge to model in the future. The finding that the sum of flux and counterflux is always larger than the flux in no counterflow situations may be seen as the most interesting result of this experiment. The main results of the “bottleneck experiment” is that the flux is neither a linear nor especially a step function of the width of a bottleneck and that therefore some legal regulations are based upon wrong assumptions. Chapter five consists of five examples with diverse focuses for the application of crowd simulations. The appendix includes a record of crowd disasters as well as - following from that - some considerations on human behavior in dangerous situations.In den vergangenen Jahren und Jahrzehnten hat sich parallel zur rasanten Entwicklung der Rechnertechnologie die Simulations- bzw. Computer-Physik als drittes Element der Physik neben Theorie und Empirie entwickelt. Diese Arbeit handelt allgemein von der Simulation des Fußgängerverkehres und hierbei speziell von der Simulation von Evakuierungsprozessen. Während Theorie und Experiment bzw. Empirie während der gesamten Geschichte der modernen Physik wechselseitig aufeinander beruhten, bedürfen beide nicht unbedingt der Simulation, auch wenn in beiden Bereichen Simulationen zu den unterschiedlichsten Fragestellungen durchgeführt werden. Simulationen hingegen kommen weder ohne Theorie noch ohne Empirie aus, sofern ihre Ergebnisse in einem quantitativen Verhältnis zur Wirklichkeit stehen sollen. Diese Abhängigkeit spiegelt sich in dieser Arbeit wieder, die daher Elemente aller drei Arbeitsweisen enthält. Sie beginnt in der Einleitung mit einem Überblick über notwendige Elemente zur Konstruktion eines verlässlichen Personenstrom-Simulationsmodells. Hierbei wird auch der Zusammenhang zwischen Simulation, Theorie und Experiment etwas näher beleuchtet. Es schließt sich ein Überblick über existierende Modelle der Personen-Evakuierungsdynamik an. Im zweiten Kapitel wird der semantischen - und daher eher theoretischen - Frage nachgegangen, wie sich ein Zellularautomatenmodell durch Erweiterungen zu einem Modell entwickeln kann, das möglicherweise besser schlicht als ,,diskretes'' Modell bezeichnet werden sollte. Diese Frage ist für die Frage nach der Verlässlichkeit der Simulationsergebnisse ohne Belang, sie wird jedoch häufig gestellt. Im dritten Kapitel wird ein diskretes Modell zur Personen-Evakuierungsdynamik präsentiert und untersucht. Die Untersuchungen der einzelnen Elemente des Modells konzentrieren sich auf die Frage nach dem Einfluss des Elementes auf das Fundamentaldiagramm. Zu einigen Elementen gibt es jedoch zusätzliche Untersuchungen mit weitergehendem theoretischen Hintergrund. Als Hauptergebnis des dritten Kapitels seien die Konstruktion des Modells selbst, der Nachweis, dass es in der Lage ist, ein weithin anerkanntes empirisches Fundamentaldiagramm bis zu einer Dichte von ca. vier Personen pro Quadratmeter sehr präzise zu reproduzieren, und dass das Modell im Hinblick auf die Rechenzeiten beim derzeitigen Stand der Computertechnik auf Szenarien mit mehreren Millionen Agenten angewandt werden kann, genannt. Im vierten Kapitel werden zwei Beobachtungen und zwei Experimente analysiert. Bei der ersten Beobachtung handelt es sich um eine Feueralarmübung in einer Grundschule. Die gewonnenen Daten werden zum einen zur Kalibrierung der Simulationsparameter benutzt, zum anderen verwendet, um sie mit Ergebnissen von mit diesen Parametern durchgeführten weiteren Simulationen zu vergleichen. Es folgt die Auswertung von Beobachtungen zur Gehgeschwindigkeit von auf einer langen Treppe aufwärts gehenden Personen. Das anschließend ausgewertete Gegenstrom-Experiment zeigt eine große Bandbreite von Selbst-Organisationsstrukturen, deren Reproduktion in Simulationen eine Herausforderung darstellt. Dass sich die Summe aus Strom und Gegenstrom immer größer herausstellt als der Strom in Situationen ohne Gegenstrom, ist wohl das interessanteste Ergebnis dieses Experimentes. Das Hauptergebnis des Engstellen-Experimentes ist, dass der Fluss weder eine lineare noch eine Stufenfunktion der Durchgangsbreite ist. Dies bedeutet, dass einige gesetzlichen Regelwerke auf falschen Annahmen beruhen. Kapitel fünf besteht aus fünf Beispielen der Anwendung von Personenstrom-Simulationen. Der Anhang enthält eine Auflistung historischer Massenunglücken sowie - darauf aufbauend - einige Überlegungen zum Verhalten in gefährlichen Situationen