Universalities in fundamental diagrams of cars, bicycles and pedestriansSymposium Celebrating 50 Years of Traffic Flow TheoryAugust 11 - 13, 2014, Portland, Oregon USA

Mitg

lied

de

r H

elm

ho

ltz-G

em

ein

sch

aft

Aug.11th 2014 Armin Seyfried University of Wuppertal

and

Forschungszentrum Jülich GmbH

Overview

Introduction

Setup of experiments

• Pedestrian

• Bicycles

• Cars

Comparison of results

• Trajectories and stop and go waves

• Speed-density and flow-density relations

• Scaling by particle size and free flow speed

Summary

Introduction

Systems with humans, like traffic (cars), crowds, bicycle traffic

are subject of a manifold of influences (in traffic human

factors).

E.g. Fundamental diagrams of pedestrian depend on

motivation, culture and other characteristics.

India (male) versus German I and II

U. Chattaraj, P. Chakroborty, A. Seyfried, Advances in Complex Systems 12(3), 393, 2009

Influence of Motivation*

*J. Lukowski, Masterthesis, Univ. Wuppertal (2009)

Introduction

Fundamental diagrams depend on motivation, awareness, culture

and other characteristics.

Moreover cars, bicycles and pedestrian have different sizes,

‘locomotion systems’, free flow speeds, speedup and slowdown

capabilities, …

BUT

Is the principle shape of the fundamental diagram of these

systems different?

Are the properties defining the principle shape different?

Pedestrians

Seyfried, A.; Boltes, M.; Kähler, J.; Klingsch, W.; Portz, A.; Rupprecht, T.;

Schadschneider, A.; Steffen, B. & Winkens A., Enhanced empirical data for the

fundamental diagram and the flow through bottlenecks. In Pedestrian and

Evacuation Dynamics 2008, Springer, 2010, 145

Portz, A. & Seyfried, A., Analyzing stop-and-go waves by experiment and

modeling. In: Pedestrian and Evacuation Dynamics 2010, Springer, 2011, 577

and many more

Setup details

• Closed system

• Oval shape circuit with length

L = 26 m

• Number of pedestrians

N = 14, 17, 20, 22,

25, 28, 34, 39,

45, 54, 62, 70

Pedestrians: Setup of experiment

N=56N=14 N=39N=25

N=70

Pedestrians: Trajectories

N=62

Voronoi triangulation (for 1d)

Density

Speed

Measurements of density and speed

𝜃𝑖 = 𝑑´𝑖/𝑑𝑖 𝜌 = 𝑖 in 𝑙𝑚 𝜃𝑖

𝑙𝑚

𝑑𝑖´

v = 𝑖 in 𝑙𝑚 𝜃𝑖v𝑖

𝑙𝑚v𝑖 =

𝑥𝑖 𝑡 + 𝑡0 2 − 𝑥𝑖 𝑡 − 𝑡0 2

𝑡0

Pedestrians: Fundamental diagram

Bicycles

Andresen, E.; Seyfried, A. & Huber, F.

Basic driving dynamics of cyclists

1st SUMO user conference 2013, 2013

Setup details

• Oval shape circuit with length

L = 86 m

• 6 runs with number of bicycles

N = 5, 10, 15,

18, 20, 33

Bicycles: Setup of the experiments

Bicycles: Trajectories

Bicycles: Fundamental diagram

Cars

Sugiyama, Y.; Fukui, M.; Kikuchi, M.; Hasebe, K.; Nakayama, A.; Nishinari, K.;

Tadaki, S.-i. & Yukawa, S. Traffic jams without bottlenecks - Experimental

evidence for the physical mechanism of the formation of a jam, New Journal of

Physics, 2008, 10, 1-7

and

Tadaki, S.-I.; Kikuchi, M.; Fukui, M.; Nakayama, A.; Nishinari, K.; Shibata, A.;

Sugiyama, Y.; Yosida, T. & Yukawa, S. Phase transition in traffic jam experiment

on a circuit, New Journal of Physics, 2013, 15, 103034

Setup details

• Circuit shape of length

L = 230 m and 312 m

• 21 runs with numbers

N230 = 22, 23

N312 = 10 - 40 (19 runs)

Cars: Setup of the experiments

Sources:

Sugiyama et al.; New Jour. Phys.; 2008

Tadaki et al.; New Jour. Phys.; 2013

Cars: Trajectories

Source: Tadaki, S. et al.; New Journal of Physics; 2013; 15; 103034

Cars: Fundamental diagram

Source:

Tadaki, S. et al.;

New Journal of Physics; 2013

Comparison

Instabilities (stop and go waves)

Cars

Pedestrians

Bicycles

Speed-density relations

Cars Bicycles

Pedestrians

Scaling factors

• Density

Ped: L0 = 0,40 m

Bicy: L0 = 1,73 m

Cars: L0 = 3,90 m

• Speed

Ped: v0 = 1.4 m/s

Bicy: v0 = 5.5 m/s

Cars: v0 = 11.1 m/s

𝜌 → ρρ0 = 𝜌𝐿0

v → v v0

Comparison and scaling

Comparison of scaled relations

Summary

Experiments with pedestrians, bicycles and cars in comparable

setups

• Oval or circular circuits

• Periodic boundaries (closed system)

• Comparable relation between system and object size

Comparison

• In all systems instabilities with stop and go waves are observable

• In all systems the speed decreases with the density

• Simple scaling of density and speed with reasonable number lead to an

correspondence (high density range excepted)

The basic property defining the principle shape of the fundamental

diagram in driven systems with humans is volume exclusion!

Research Centre Jülich• Lukas Arnold

• Maik Boltes

• Mohcine Chraibi

• Stefan Holl

• Kevin Drdzimski

• Ulrich Kemloh

• Gregor Lämmel

• Weichen Liao

• Wolfgang Mehner

• Daniel Salden

• Benjamin Schröder

• Antoine Tordeux

• My Linh Würzburger

• Jun Zhang

University of Wuppertal• Erik Andresen

• Andreas Meunders

Thank you for your interest

Further information

Pedestrian database (open source)

Movies, trajectories and data of other pedestrian experiments for

determining the fundamental diagram and flow characteristics:

http://www.asim.uni-wuppertal.de/datenbank.html

Pedestrian simulation model (open source)

You will also find some nice videos on our YouTube Channel at:

https://www.youtube.com/user/JuPedSim

Release notes (and source codes):

https://github.com/JuPedSim/JuPedSim/releases/