Traffic Jams, Pedestrian Streams, Escape Panics, and Supply Chains

Transcription

1 Taffic Jams, Pedestian Steams, Escape Panics, and Supply Chains New Insights fom Many-Paticle-Physics Pof. D. e. nat. habil. Dik Helbing Institute fo Economics and Taffic Faculty of Taffic Sciences Desden Univesity of Technology Liteatue: D.H., Taffic and elated self-diven many paticle systems, Reviews of Moden Physics 73 (4), (2001).

2 Some Analogies between Pedestian Cowds and Fluids Footpints in snow look simila to steamlines of fluids. Thee ae gaseous (fee), fluid (obstucted), and solid (immobile) states. Passing though a standing pedestian cowd leads to ive-like steams. In pushy pedestian cowds one can obseve shock waves. Similaities with ganula media ae dominating at high pedestians densities.

3 Ae thee Regula Phenomena, i.e. Laws of Natue?

4 Fluid-Induced Paticle Size Segegation in Sheaed Ganula Media S. B. Santa, S. Schwaze, and H. J. Hemann, Phys. Rev. E 54, 5066 (1996).

5 Social Foce Concept Pedestians ae confonted with standad situations. The eactions to these ae athe automatic. We assume a moe oe less optimized behavio egading the avoidance of collision and time delays. This allows us to descibe the aveage behavio in a mathematical way. In addition, we have to conside fluctuations. We model the systematic contibution to the acceleation by a supeposition of seveal (Non-Newtonian) foces eflecting diffeent motivations and influence factos.

6 Expeiments Regading the Supeposition of Foces in Conflict Situations

7 Social Foce Model Equation of Motion: dxi ( t) dt Acceleation Equation fo Pedestians: dvi ( t) mi 123 dt v ( t) i Acceleation m i τ 123 i k ( ( ) ( ) ww ) ( ) b ( ) att v e t v t F t F t F ( t ) { ( t ) i i i + + i + ik + ξi Diving Foce j( i) Inteactions Bodes, Fie Attactions Fluctuations 0 x i Place; t Time; vi Speed; mi Mass; τi Acceleation Time; vi e i Desied Diection F psy ph att ( t) F ( t) + F ( t) F ( t) ww + Psychological Repulsion Physical Inteactions Attactions between People Desied Velocity;

8 Social Foce Model Specification of the Inteaction Foces: ( ) ) ( ) ( ) ( ) ( ) ( ] ) / exp[( ) ( )], ( ) ( )],[ ( ) ( [ ) ( i j i j att t ji ph i j i j ì psy psy x x x x C t F t v d n d k t F n B d A t v t v t v t x t x F t F Θ + Θ e.g. e.g. e.g. κ Lage Constants Velocity; Relative Tangential ;, othewise fo ; Distance; Radii; Sum of Attaction Stength; Inteaction; Range of Repulsion; + > Θ,κ ) ( 0 0 ) (, ) / ( k t v v v x x x n t d x x n x x d C B A i j t ji j i j i j i Compession Fiction

9 Self-Oganization of Pedestians

10 Optimization of Pedestian Facilities Conventional Impoved

11 Evolutionay Optimization Oiginal Multiplication Selection Evaluation Pefomance Citeion: Efficiency 1 v E N α α ( t) e 0 v α α Mutation (Random Vaiations) Test (Simulation)

12 Evolutionay Optimization of a Bottleneck

13 Noise-Induced Odeing Small Noise Medium Noise Lage Noise

14 Role of Fluctuations Small Fluctuations: Lane Fomation Ensemble-Aveaged Efficiency Lage Fluctuations: Feezing by Heating Reminde: The tempeatue is popotional to the velocity vaiance. D.H., I. Fakas, T. Viscek, Phys. Rev. Lett. 84, 1240 (2000).

15 Escape Panics Physical Inteactions and Fiction Effects due to Uncontolled Rush and Pushy Behavio Faste-is-Slowe Effect Phantom Panics Application to the Simulation of Evacuation Scenaios

16 Optimal Escape Stategy and Collective Poblem Solving Mixtue of Individualistic Behavio and Heding: Inefficient Usage of Doos due to Heding Effect D. H., I. Fakas, and T. Viscek, Natue 407, 487 (2000).

17 Emegence of a Phantom Taffic Jam J. Teitee et al. (1966, 1970, 1974).

18 Velocity-Density-Relation Speed Limit 1-min-Aveages Mean Values Fit Function

19 Instability of Taffic Flow

20 Sub- and Supecitical Petubations subcitical supecitical J.M. de Castillo, TGF 97 (1998).

21 Metastability of Taffic Flow

22 Beakdown of Taffic due to a Supecitical Reduction of Taffic Flow

23 Phase Diagam of Taffic States at Bottlenecks D. H. et al., Science 282, 2001 (1998); Physical Review Lettes 82, 4360 (1999).

24 Empiical Repesentatives of Congested Taffic States

25 Avoidance of Taffic Beakdowns - Intelligent Speed Limits - On-Ramp Contol Beakdown of Taffic With Contol Illustation of an On-Ramp-Contol - Dive-Assistance Systems

26 Model Ingedients Many simila units (paticles, pedestians, vehicles, individuals, ). The units ae extenally o intenally diven, i.e. thee is some enegy input, e.g. they can move. Units ae non-lineay inteacting, i.e., unde cetain conditions, small vaiations can have lage effects. The system behavio is then dominated by the inteactions athe than by the bounday conditions (the extenal contol). Thee is a competition fo limited essouces such as space, time, enegy, o money. Each unit has a cetain extension in space o time. When units come too close, they have fictional effects and/o obstuct each othe. Conclusions fom taffic models ae elevant fo the functionality, stability, eliability, and efficieny of societies, oganizations, administations, companies, poduction pocesses, etc.

27 Paadoxical Phenomena Phantom taffic jams Phantom panics Faste-is-slowe effect Noice-induced self-oganization and odeing Feezing by heating Attaction effects in diven systems with epulsive foces Moe efficiency with less essouces Simila beakdown, jamming and heding effects can be obseved in biological systems, oganizations, companies, makets, administations, societies, politics, economy and science. Conclusions: The theoetical undestanding of taffic dynamics is a good statingpoint fo studying elementay human inteactions unde expeimental conditions. It is also suitable fo managing logistic poblems (e.g. optimizing the thoughput in the poduction of compute chips).

28 Physical Popeties and Phenomena (Auto-)Solitons (Bose-Einstein-)Condensation Catalysis Chaos Clogging Complex Dynamics Cystallization Dislocations Ganula Flows Histoy-/Path-Dependence Hysteesis Indiect Inteactions Meta-/Multi-Stability Noise-Induced Odeing Non-Equilibium States Non-Linea Waves Optimal Self-Oganization Pai Inteactions Phase Tansitions Powe Laws Reaction-Diffusion-Dynamics Rotation Scaling Laws Segegation Self-Oganization Shock Waves Synchonization Univesality

29 Physical Concepts Active Bownian Paticles Boltzmann Equation Cellula Automata Diven Many-Paticle Systems Fokke-Planck Equation Ginzbug-Landau Equation Koteweg-de-Vies Equation Langevin Equation Maste Equation Mico-Maco-Link Molecula Dynamics Phase Diagam Self-Oganized Citicality Spin-Systems

30 Physical Fields Fluid Dynamics Kinetic Gas Theoy Mechanics Non-Equilibium Themodynamics Non-Linea Dynamics Quantum Theoy Soft Matte Solid State Physics Statistical Physics