Dirk Helbing

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Dirk Helbing, Jan Stigmeier and Stefan Lämmer. 2007 Self-organized network flows. NETWORKS AND HETEROGENEOUS MEDIA 2(2):191-210.

Abstract. A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers, and load-dependent transportation times. Furthermore, conflicts or coordination problems of intersecting or merging flows are considered as well. Making assumptions regarding the permeability of the intersection as a function of the conflicting flows and the queue lengths, we find self-organized oscillations in the flows similar to the operation of traffic lights.

For implementation see: Sayyed Amin Mazhoumian.

Stefan Lämmer and Dirk Helbing 2007 Self-control of traffic lights and vehicle flows in urban road networks Online at: Journal of Statistical Mechanics: Theory and Experiments

Abstract. Based on fluid-dynamic and many-particle (car-following) simulations of traffic flows in (urban) networks, we study the problem of coordinating incompatible traffic flows at intersections. Inspired by the observation of self-organized oscillations of pedestrian flows at bottlenecks, we propose a selforganization approach to traffic light control. The problem can be treated as a multi-agent problem with interactions between vehicles and traffic lights. Specifically, our approach assumes a priority-based control of traffic lights by the vehicle flows themselves, taking into account short-sighted anticipation of vehicle flows and platoons. The considered local interactions lead to emergent coordination patterns such as ‘green waves’ and achieve an efficient, decentralized traffic light control. While the proposed self-control adapts flexibly to local flow conditions and often leads to non-cyclical switching patterns with changing service sequences of different traffic flows, an almost periodic service may evolve under certain conditions and suggests the existence of a spontaneous synchronization of traffic lights despite the varying delays due to variable vehicle queues and travel times. The self-organized traffic light control is based on an optimization and a stabilization rule, each of which performs poorly at high utilizations of the road network, while their proper combination reaches a superior performance. The result is a considerable reduction not only in the average travel times, but also of their variation. Similar control approaches could be applied to the coordination of logistic and production processes.

Keywords: flow control, traffic and crowd dynamics, traffic models, self-driven particles

How individuals learn to take turns: Emergence of alternating cooperation in a congestion game and the prisoner's dilemma Dirk Helbing, Martin Schonhof, Hans-Ulrich Stark, Janusz A. Holyst. Advances in Complex Systems. (c) World Scientific Publishing Company

Abstract: 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.

Supply and Production Networks: From the Bullwhip Effect to Business Cycles. Dirk Helbing and Stefan Lämmer. Chapter 1, in ---

Abstract: Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of power grids remains to be explored. Based on a simple model of supply networks, we offer an interpretation of instabilities and oscillations observed in biological, ecological, economic, and engineering systems. We find that most supply networks display damped oscillations, even when their units - and linear chains of these units - behave in a non-oscillatory way. Moreover, networks of damped oscillators tend to produce growing oscillations. This surprising behavior offers, for example, a new interpretation of business cycles and of oscillating or pulsating processes. The network structure of material flows itself turns out to be a source of instability, and cyclical variations are an inherent feature of decentralized adjustments. In particular, we show how to treat production and supply networks as transport problems governed by balance equations and equations for the adaptation of production speeds. The stability and dynamic behavior of supply networks is investigated for different topologies, including sequential supply chains, "supply circles", "supply ladders", and "supply hierarchies". Moreover, analytical conditions for absolute and convective instabilities are derived. The empirically observed bullwhip effect in supply chains is explained as a form of convective instability based on resonance effects. An application of this theory to the optimization of production networks has large optimization potentials.

Self-Organized Network Flows 2007. Dirk Helbing, Jan Siegmeier, Stefan Lämmer.

Abstract: A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers, and load-dependent transportation times. Furthermore, conflicts or coordination problems of intersecting or merging flows are considered as well. Making assumptions regarding the permeability of the intersection as a function of the conflicting flows and the queue lengths, we find self-organized oscillations in the flows similar to the operation of traffic lights.

(2007) Efficient response to cascading disaster spreading. Lubon Buzna, K. Peters, H. Ammoser, C. Kühnert and D. Helbing. Physical Review E 75, 056107]

Stark, Hans-Ulrich, Helbing, Dirk, Schönhof, Martin, Holyst, Janusz A.: Alternating cooperation strategies in a Route Choice Game: Theory, experiments and effects of a learning scenario, in: Games, Rationality and Behaviour (Eds. A. Innocenti, P. Sbriglia), New York: Palgrave Macmilllian, (2008), pp. 256-273.

Comment: For related work see http://www.helbing.org

http://www.soms.ethz.ch/people/dhelbing/publications_new