The lectures present mathematical models of human coordination in space and time, addressing subjects like pedestrian motion, crowd dynamics, freeway traffic and material flows in networks. Particular attention is paid to the spontaneous formation (emergent self-organization) and breakdown of cooperative spatio-temporal patterns of motion.
Objective
Students should gain an overview over the many interesting phenomena observed in traffic flows, crowds, and other multi-component systems characterized by interactive motion in space and time, such as material flows in logistics and production. Moreover, participants of the course should learn how to set up mathematical models describing such systems. Finally, one should be able to derive in mathematical terms typical spatio-temporal characteristics of the systems under consideration. It is expected that the corresponding formalisms can be well formulated and explained.
Content
The lectures present mathematical models of human coordination in space and time, addressing subjects like pedestrian motion, crowd dynamics, freeway traffic and material flows in networks. A particular focus will be on the spontaneous formation (emergent self-organization) and breakdown of cooperative spatio-temporal patterns of motion. We will answer questions such as: Why are vehicles sometimes stopped by so-called ``phantom traffic jams'', although they 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 of the traffic volume cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize in lanes, while similar systems are ``freezing by heating''? How do pedestrians manage to cross different flow directions smoothly, often without stopping? Why do self-organizing systems tend to reach an optimal state? What is layer formation and the ``zipper effect''? Why do panicking pedestrians produce dangerous deadlocks or phenomena like ``crowd turbulence''? Can one understand business cycles through unstable material flows in networks? How can one describe the interaction of traffic flows in urban street networks? And how can those flows be optimally coordinated by a self-organized traffic light control?
Lecture notes
The script is a copyrighted and preliminary first draft of an upcoming book on traffic dynamics intended for publication. Feedback on this script is strongly encouraged. (Please report unclear paragraph and mistakes.)
Literature
[1] Dirk Helbing, Verkehrsdynamik (Springer, Berlin, 1997). [2] Dirk Helbing, Traffic and related self-driven many-particle systems. Reviews of Modern Physics 73(4), 1067-1141 (2001). [3] Additional references will be given in each chapter of the lecture/script.
Prerequisites / Notice
The number of participants is limited due to the small size of the lecture hall. There are no tutored exercises, but example exercises will be displayed on the course's webpage to allow students to test and train their skills. Good mathematical skills are required.
Performance assessment
Performance assessment information (valid until the course unit is held again)
The performance assessment is only offered at the end after the course unit. Repetition only possible after re-enrolling.
Additional information on mode of examination
Depending on the number of exam candidates, a written exam (90min, if more than 5 candidates) or individual oral exams (30min each, if less than 6 candidates) will be offered (not optional). In exceptional cases, a seminar thesis (simulation study) will be considered alternatively.
Learning materials
No public learning materials available.
Only public learning materials are listed.
Groups
No information on groups available.
Restrictions
There are no additional restrictions for the registration.