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Traffic Physics and Traffic Analysis

NOTE: This web page is sketchy, in near outline form, and comprised principally of links to websites or articles or simulations. It was constructed from a set of notes, in the form of logged websites, assembled out of curiosity about what's been happening in the modeling of traffic flow and not with the intent of developing a full or informed review of the field. Please expect a significant number of the referenced URL's to be dead, owing to instability of university and local government systems.

FOR A QUICK TOUR:

read sections C. and D. for orientation;
browse the "layman's language" articles of section E.1;
try out a simulation:
- http://www.traffic.uni-duisburg.de/model/index.html
play with the "global density" to see the strong dependence of the phase transition on this parameter;
browse either the Journal Articles, section E.5, or the Links, section E.2.

Measurement and Monitoring

The measurement and monitoring of automobile traffic levels and flows was begun in the early 1900's and since then has been increasingly with us.

References, history of FHWA and methods of traffic monitoring:

http://www.fhwa.dot.gov/ctdiv/history.htm

History FHWA

http://www.ops.fhwa.dot.gov/Travel/Traffic_Analysis_Tools/Proceedings.pdf

Workshop, Aug. 2000

http://www.fhwa.dot.gov/ohim/tmguide/tmg0.htm

Traffic monitoring guide

Theoretical Analysis

Theoretical analysis of traffic flow began in the 1930's. The post-WWII growth in automobile use produced growth also in analysis of traffic flow, which continues apace. There have been a wide variety of models applied to traffic analysis: probabilistic, fluid dynamic, microscopic (vehicle-/driver-based), simulation, etc.

References, primarily to classical approaches to traffic theory and analysis:

http://www.tfhrc.gov/its/tft/tft.htm

Traffic flow theory, revised monograph, ca 1997

http://www.tfhrc.gov/its/tft/chap1.pdf

ibid, Chap. 1, Introduction

http://tti.tamu.edu/product/catalog/reports/3943-1.pdf

Simuation...Dallas freeways, 1999

http://publish.uwo.ca/~jmalczew/gida_5/Pursula/Pursula.html

Simulation of Traffic Systems - An Overview

http://www.ite.org/

Institute of Transportation Engineers

http://www.ite.org/NationalSummit/vision/Congestion.pdf

Overview - Congestion and solutions

Cellular Automata and General Models of the Condensed Phase

The analyses described in the preceding paragraph often were carried out with the immediate engineering purpose of improving traffic flow, and so were tied as closely as possible to the real structures over which vehicles flow and to data on traffic flow.

One can take a different view, with the aim of understanding traffic as a particular expression of the general problem of the statistical physics of interacting objects. In this case one not uncommonly works with a model that encapsulates particular salient features of a problem. One can view such a model as a cartoon that is simple to work with but also relevant and effective because it abstracts what is most important.

The remainder of this note focuses largely on research undertaken from the latter viewpoint, that of statistical physics and complex systems theory.

Rationale

Which Approaches?

Apply standard statistical-physical and similar models, especially of the condensed phase, e.g. cellular automata, Ising model, lattice gas model, etc. Use simulation, and where possible, mathematical analysis. The models are "universal" in that they hold for systems of widely different type.

Why Study Models?

To gain understanding by isolating in a model a few principal features of the traffic problem and by comparing results obtained from the model with those for more completely understood systems (abstraction and analogy - powerful tools).

Results?

Lots, from an abundant recent literature on the analysis of traffic, referenced in web pages linked below.

Relevance?

Human social phenomena can and often do show the properties of a phase transition, a long-studied and deeply-understood event:

At a critical density (or velocity, or ...) a new structure with very different properties emerges explosively, i.e, following only a small increment in the density (or velocity, or ...);

Such behavior is "nonlinear".

It is also "universal". The most fundamental properties of phase transitions are independent of the material or system studied: ferromagnets and protein folding, forrest fires and growth of cities, etc.

Traffic jams are a commonly-experienced nonlinear phenomenon that is characteristically human.

Examples of phase transitions (nonlinear phenomena) in the inanimate world:

gelation (a small change in temperature or in gelatin concentration leads to an explosive change in amount of gel);

melting of ice (affected by a small change in temperature, pressure, salt or other solute concentration);

etc.

Relevance to the BIG BOX Ordinance?

The increased scale of a Big Box, though perhaps a relatively small increase, is nonlinear in its effect on adjacent neighborhoods (and adjacement businesses). Thinking about traffic jams, gelation, etc., should prepare one to accept nonlinearity in other phenomena, in this case large-scale commercial development within densely populated areas.

(Note: the increased scale of a Big Box is not just in floor area or wall area, but also in number of deliveries, hours of operation, number of customers traveling specifically to the store, etc.)

After all that relevance.... On to the physics:

Websites, Links, Etc.

Articles and Discussion Written in Layman's Language

http://www.theatlantic.com/issues/2000/12/budiansky.htm

THE PHYSICS OF GRIDLOCK, Stephen Budiansky

The Atlantic Online

Excellent layman's article that makes clear the spirit of the statistical physics approach to a problem. A good place to start (and even to end?)

http://www.villagevoice.com/issues/0144/davis.php

BOTTOMS UP, Erik Davis

Village Voice, Week of Oct. 31, 2001

Erik Davis reviews the book, Emergence: The Connected Lives of Ants, Brains, Cities, and Software, by Steven Johnson. The reviewer is trendy, even fatuous, but he gets the basics right: emergence, self-organization, and the parallels that can be drawn between the physics of inanimate matter and that of aggregates of organisms, including man. Off-topic for traffic, but worth a read (the review) as a different take.

http://www.sciencenews.org/20010908/mathtrek.asp

WAVES OF CONGESTION, Ivars Peterson

Science News, Week of Sept. 8, 2001; Vol. 160, No. 10

Layman's article on certain results of simulation of traffic. More focused than the Budiansky article, but worth reading as a second and shorter introduction.

http://rcswww.urz.tu-dresden.de/%7Ehelbing/foxtraffic.html

BEHIND EVERY TRAFFIC JAM IS AN ENDLESSLY COMPLEX PHYSICAL EQUATION

Amanda Onion

Fox News

Phase transitions in traffic.

http://www.inf.ethz.ch/research/next/nagel_k.html

MODELING AND SIMULATION

Prof. Kai Nagel

Overview of Kai Nagel's research (Department of Computer Science, ETH Zurich), notable for the clear statement of the logic behind the work; written for scientists not in the field and for prospective students, but likely readable by the layman.

http://amasci.com/amateur/traffic/traffic1.html

TRAFFIC WAVES

An amusing set of pages on traffic, written by an observant engineer in layman's language; somewhat lengthy, easily understood.

http://www.amasci.com/amateur/traffic/links.html

COLLECTION OF TRAFFIC-RELATED WEBSITES:

Resources - Links and References

http://vwisb7.vkw.tu-dresden.de/TrafficForum/

TRAFFIC FORUM

Univ. Dresden

Advisory Board

Wide-ranging, informative, thorough, technical, excellent. Focus on physics of interacting particles. Go to the following, for information as indicated:

Library

Quick Guide (references: tutorial, background, and basic)

References (comprehensive list)

Past Issues (preprints/articles; monthly collection, 1999-date)

Links

Institutes

Traffic Projects

Online Traffic Simulation or Visualization (Java Applets)

Granular Matter

General Articles in the Media

Econophysics and Other Related Websites

Other Useful Links

Internet Journal of Cooper@tive Tr@nsport@tion Dyn@mics

A new journal (Volume 1, 2002) that covers all subjects related to the analysis, modeling, simulation, and optimization of the spatio-temporal dynamics of traffic and transportation. Contributions addressing regional development, logistics, operations research, control strategies, and economic issues related to traffic and transportation are appreciated as well. Particularly welcome are manuscripts focussing on aspects like cooperation, communication, self-organization, synchronization, adaptation, collective intelligence, or decentralized control in multi-agent systems.

http://www.tu-dresden.de/vkiwv/vwista/index.html

HOMEPAGE OF DIRK HELBING - INSTITUTE FOR ECONOMICS AND TRAFFIC

Prof. Dr. rer. nat. Dirk Helbing(Managing Director) Chair for Traffic Modeling and Econometrics

Research:

Multi-Agent Simulation of Socio-Economic Systems;
Behavioral Models, Decision and Game Theory;
Self-Organization Phenomena in Space and Time;
Optimization of Vehicle, Pedestrian, and Air Traffic;
Stochastic Systems and Monte-Carlo Simulations;
Molecular Dynamic, Gas Kinetic, Fluid Dynamic Models;
Micro-Macro Link.

http://www.helbing.org/publist.html

PUBLICATIONS

http://www.tu-dresden.de/vkiwv/vwista/media.html

RESPONSE IN THE MEDIA (interesting - layman's discussions)

http://rcswww.urz.tu-dresden.de/~helbing/kluwer.html

QUANTITATIVE SOCIODYNAMICS: STOCHASTIC METHODS AND MODELS OF SOCIAL INTERACTION PROCESSES

Theory and Decision Library B: Mathematical and Statistical Methods 31

Kluwer Academic, Dordrecht, 1995, ISBN 0-7923-3192-3 Dirk Helbing, translated from the German by R. Calek and D. Helbing

http://rcswww.urz.tu-dresden.de/~helbing/springer.html

TRAFFIC DYNAMICS: NEW PHYSICAL MODELING CONCEPTS

Springer, Berlin, 1997. ISBN 3-540-61927-5. (German)

Dirk Helbing

http://www.zpr.uni-koeln.de/GroupBachem/VERKEHR.PG/

THE TRAFFIC SIMULATION GROUP AT THE ZPR

(ZPR = Center for Parallel Computing) (old site)

(Now has become the ZAIK = Center for Applied Computer Science)

Index page:

What are we doing?

What is traffic simulation good for?

Scientific Journals.

http://www.zpr.uni-koeln.de/GroupBachem/VERKEHR.PG/ca-info.html

THE CA MODEL

Good short introductory description of traffic

simulation with CA (Cellular Automata)

http://www.zpr.uni-koeln.de/GroupBachem/VERKEHR.PG/traffic-sim.ps

CA-SIMULATIONS WRITTEN IN POSTSCRIPT (NEAT!)

http://www.zpr.uni-koeln.de/GroupBachem/VERKEHR.PG/fundamental.html

THE FUNDAMENTAL DIAGRAM

http://www.zpr.uni-koeln.de/GroupBachem/VERKEHR.PG/VERBUND_NRW/Journals.html

SCIENTIFIC JOURNALS

http://www.uni-koeln.de/rrzk/Autoren/WF/traffic/OneLaneCA.html

VERKEHRSSIMULATION MIT HILFE EINES JAVA-APPLETS

Ralf Wimmershoff

(Traffic simulation with the help of a Java applet) (may be old code)

(RRZK = Regionales Rechenzentrum der Universität zu Köln)

http://www.uni-koeln.de/rrzk/projekte/berichte/Projektbericht_ising1.ps

MONTE CARLO SIMULATIONEN ZUM ISING-mODELL, Siegert, M. und Stauffer, D.

(paper, with the information: ISING B'DAY AT 95 IN PEORIA, IL, USA)

http://www.thp.Uni-Koeln.DE/

INSTITUTE FOR THEORETICAL PHYSICS, UNIVERSITY OF COLOGNE

Research Groups (esp. those related to social or biological problems:

Statistical Physics, Physics in Biology (M. Lassig)

Statistical Physics, Random Systems (T. NAttermann)

Computational Physics (D. Stauffer)

Statistical Physics, Field Theory (J. Zittartz)

http://www.thp.Uni-Koeln.DE/~as/as_engl.html

HOMEPAGE - Priv.-Doz. Dr. Andreas Schadschneider

Stochastic Processes, Nonequilibrium Systems

Stochastic Resonance and Ratchet Systems

Traffic Flow Theory

http://www.thp.Uni-Koeln.DE/~as/Mypage/verkehr.html

TRAFFIC FLOW THEORY = VERKEHRSMODELLE (introduction, in German)

http://www.thp.Uni-Koeln.DE/~as/Mypage/publication.html

PUBLICATIONS of Priv.-Doz. Dr. Andreas Schadschneider

http://www.thp.uni-koeln.de/personal/stauffer.html

HOMEPAGE - Dietrich Stauffer

COMPUTATIONAL PHYSICS, especially lattice models of everything:

Research:

Monte Carlo simulations in Statistical Physics (percolation,

Ising models, polymers)

Biologically motivated computer simulations (ageing)

Econophysics: microscopic models for stock markets (e.g. Cont-Bouchaud)

Sociophysics: Models on Bonabeau et al, Sznajd, ...

Books:

Introduction to Percolation Theory

From Newton to Mandelbrot

Computer Simulation and Computer Algebra

Evolution, Money, War, and Computers - Non-Traditional Applications of Computational Statistical Physics

Principles of Equilibrium Statistical Mechanics

Review Articles:

Getting Older -- Monte Carlo Simulations of Biological Aging

Percolation models of financial market dynamics ?

Why care about sex ? Some Monte Carlo justification

Monte Carlo simulations of Sznajd models

http://www.traffic.uni-duisburg.de/

PHYSICS OF TRANSPORT AND TRAFFIC

Prof. Dr. Michael Schreckenberg

LINKS ARE WORTH A LOOK....

http://www.moresimulation.com/Links_Frame.htm

VARIOUS MODELS AND SYSTEMS AND SIMULATION METHODS

http://www.fields.utoronto.ca/~hfuks/bibtraf.html

BIBLIOGRAPHY OF CA TRAFFIC MODELS

Online Simulations

http://www.traffic.uni-duisburg.de/model/index.html

TRAFFIC SIMULATION BASED ON CELLULAR AUTOMATA

(excellent; various options, selected by buttons or sliders)

Try this one first

http://www.uni-koeln.de/rrzk/Autoren/WF/traffic/OneLaneCA.html

VERKEHRSSIMULATION MIT HILFE EINES JAVA-APPLETS

Ralf Wimmershoff

(Traffic simulation with the help of a Java applet) (may be old code)

(RRZK = Regionales Rechenzentrum der Universität zu Köln)

[One of the simplest to run and understand; the following explanation holds closely for the other simulations listed.]

SIMULATION OF ONE LANE OF TRAFFIC:

7 possible velocities for a vehicle: 0 to maximum in unit steps;

density of vehicles approx. 25 percent;

for each vehicle in "road", at each time step:

1. increase velocity by 1 unit if not at maximum velocity;

2. if velocity so great as to overtake next car to within a set safe distance, reduce velocity to comply with safe distance;

3. with a set probability, reduce velocity by 1 unit.

increasing time is down the page;

increasing distance along road is across the page.

trajectory of each vehicle is a left-to-right, downward-trending, curved-&-stepped line across the page;

as vehicles exit right, new vehicles are injected left.

NOTE: the simulation shows a dynamical phase transition -

a traffic jam (red) forms and dissipates;

the jam moves backward along the road;

the fraction of vehicles in the "jam" phase is *very* sensitive to velocity and to density of the vehicles (data not shown)

http://www.zpr.uni-koeln.de/GroupBachem/VERKEHR.PG/traffic-sim.ps

CA-SIMULATIONS WRITTEN IN POSTSCRIPT (NEAT!)

Real-Time Cam Images and Traffic Maps

http://www.wsdot.wa.gov/PugetSoundTraffic/

WSDOT ---- PUGET SOUND TRAFFIC CONDITIONS

(map, with traffic level indicated by color)

http://www.wsdot.wa.gov/pugetsoundtrafficarchive/

WSDOT ---- PUGET SOUND AREA TRAFFIC CONGESTION MAP ARCHIVE

(try a Friday, at 5:00p.m. :->)

http://www.wsdot.wa.gov/pugetsoundtraffic/cameras/default.htm

WSDOT ---- PUGET SOUND AREA TRAFFIC CAMERAS

(snapshots and in some locations, video clips)

http://www.wsdot.wa.gov/traffic/current/mainbas.htm

WSDOT ---- TRAFFIC AND WEATHER-CURRENT WEATHER

(weather/pass info/travel routes==construction)

NOTE: some of the following azfms files (the most interesting) fail to display now on my Netscape browser (they left out several table end tags); one hopes for repair soon....

http://www.azfms.com/Travel/freeway.html

CURRENT PHOENIX FREEWAY CONDITIONS

(speed level indicated by color/construction areas/active warnings)

[if the above URL fails to display, try the following and wait 30'' for refresh:

/Current-Events/azfms-freeway.html]

http://www.azfms.com/HCRSv2/arizona.html

FREEWAY MANAGEMENT SYSTEM HIGHWAY CLOSURE AND RESTRICTION SYSTEM

(all state)

(roads closed or restricted, generally by construction)

http://www.azfms.com/Video/

FREEWAY MANAGEMENT SYSTEM LIVE VIDEO

http://www.azfms.com/index.html

ADOT FREEWAY MANAGEMENT SYSTEM

(index page, for above and more travel-related stuff)

Journal Articles

http://www.traffic.uni-duisburg.de/

PUBLICATIONS:PAPERS:GENERAL: (this is the way to "papers" web pages)

ftp://traf36.uni-duisburg.de/pub/paper/origca.pdf

A CELLULAR AUTOMATON MODEL FOR FREEWAY TRAFFIC

J. Phys. I France 2, 2221 (1992)

K. Nagel and M. Schreckenberg

Mathematisches Institute, Univ. Koln

Institut fur Theoretische Physik, Univ. Koln

(earliest (?) application of CA model to simulation of traffic transitions)

(as a rule, the first papers in a field are less difficult reading)

ftp://traf36.uni-duisburg.de/pub/paper/heraeus.pdf

STATISTICAL PHYSICS OF CELLULAR AUTOMATA MODELS FOR TRAFFIC FLOW

in: Computational Statistical Physics

eds. K. H. Hoffmann, M. Schreiber (Springer, Berlin, 2001), pp. 113-126

M. Schreckenberg, R. Barlovic, W. Knospe, and H. Klüpfel

Gerhard-Mercator-Universitat Duisberg,

Physik von Transport und Verkehr

(review; easy to understand)

http://cornell.mirror.aps.org/abstract/PRA/v46/i10/pR6124_1

SELF-ORGANIZATION AND A DYNAMICAL TRANSITION IN TRAFFIC-FLOW MODELS

Phys. Rev. A 46, R6124-R6127 (1992)

Ofer Biham and A. Alan Middleton

Department of Physics, Syracuse University, Syracuse, New York 13244

Dov Levine

Department of Physics, Technion, Israel Institute of Technology, Haifa 32000, Israel

(also one of the first to apply modern physical models to traffic)

http://cornell.mirror.aps.org/abstract/PRE/v48/i6/pR4175_1

PHASE TRANSITIONS IN TWO-DIMENSIONAL TRAFFIC-FLOW MODELS

Phys. Rev. E 48, R4175-R4178 (1993)

Jose A. Cuesta, Froilan C. Martinez, Juan M. Molera, and Angel Sanchez

Escuela Politecnica Superior, Universidad Carlos III de Madrid, Avda. Mediterraneo 20, E-28913 Legans, Madrid, Spain

http://www.thp.uni-duisburg.de/~sven/_publications/publications.html

LIST OF PUBLICATIONS OF SVEN LUBECK

(wide-ranging set of papers on condensed matter theory)

http://www.thp.Uni-Duisburg.DE/Paper/sven/preprint_1999_01.ps.gz

CRITICAL BEHAVIOR OF A TRAFFIC FLOW MODEL

Physical Review E 59, 2672 (1999)

L. Roters, S. Lübeck and K. D. Usadel

Theoretische Physik, Gerhard-Mercator-Universitat Duisberg

also

http://www.thp.Uni-Duisburg.DE/Paper/sven/preprint_1998_04.ps.gz

THE DYNAMICAL STRUCTURE FACTOR AND CRITICAL BEHAVIOR OF A TRAFFIC FLOW MODEL

proceedings of the conference Complexity and Fractals in the Sciences, edited by M. M. Novak (World Scientific, Singapore, 1998), p. 261.

[same authors]

(dynamical structure factor: analysis in transform space of the Nagel-Schreckenberg model)

http://www.thp.Uni-Duisburg.DE/Paper/sven/preprint_1998_01.ps.gz

DENSITY FLUCTUATIONS AND PHASE TRANSITION IN THE NAGEL-SCHRECKENBERG TRAFFIC FLOW MODEL

Physical Review E 57, 1171 (1998)

S. Lübeck, M. Schreckenberg and K. D. Usadel

Theoretische Physik, Gerhard-Mercator-Universitat Duisberg

also

http://www.thp.Uni-Duisburg.DE/Paper/sven/preprint_1998_02.ps.gz

DENSITY FLUCTUATIONS AND PHASE SEPARATION IN A TRAFFIC FLOW MODEL

in Traffic and Granular Flow 97, edited by D. E. Wolf and M. Schreckenberg (Springer, Singapore, 1998), p. 361

[same authors]

http://www.thp.Uni-Koeln.DE/~as/Mypage/publication.html

PUBLICATIONS of Priv.-Doz. Dr. Andreas Schadschneider

http://xxx.lanl.gov/abs/cond-mat/0007053

STATISTICAL PHYSICS OF VEHICULAR TRAFFIC AND SOME RELATED SYSTEMS

Physics Reports 329, 199 (2000)

Debashish Chowdhury, Ludger Santen, Andreas Schadschneider

(review; 170pp; 50pp on earlier methods, i.e., other than CA)

http://xxx.lanl.gov/abs/cond-mat/0007418

STATISTICAL PHYSICS OF TRAFFIC FLOW

Physica A285, 101 (2000)

Andreas Schadschneider

(review; 23pp; focus on work by A.S.)

http://xxx.lanl.gov/abs/cond-mat/9910173

VEHICULAR TRAFFIC: A SYSTEM OF INTERACTING PARTICLES DRIVEN FAR FROM EQUILIBRIUM

Current Science 77 (1999) 411-419

Debashish Chowdhury, Ludger Santen, Andreas Schadschneider

(review; 9pp; focus on recent (CA) work, with some perspective)

http://www.thp.Uni-Koeln.DE/~as/Mypage/PSfiles/altenberg.ps

TRAFFIC FLOW: A STATISTICAL PHYSICS POINT OF VIEW

Physica A

Andreas Schadschneider

(review; 40pp; 7pp on pre-CA work; focus on A.S.'s work, with some perspective)

http://www.tu-dresden.de/vkiwv/vwista/publications/rmp.pdf

TRAFFIC AND RELATED SELF-DRIVEN MANY-PARTICLE SYSTEMS.

Reviews of Modern Physics 73, 1067-1141 (2001)

D. Helbing

(review; 79pp)

http://www.tu-dresden.de/vkiwv/vwista/publications/experiment.pdf

VOLATILE DECISION DYNAMICS: EXPERIMENTS, STOCHASTIC DESCRIPTION, INTERMITTENCY CONTROL, AND TRAFFIC OPTIMIZATION.

New Journal of Physics 4, 33.1-33.16 (2002)

D. Helbing, M. Schönhof, and D. Kern

http://www.inf.ethz.ch/~nagel/papers/or-review/or-review.pdf

STILL FLOWING: OLD AND NEW APPROACHES TO TRAFFIC FLOW AND TRAFFIC JAM MODELING

preprint (2002)

K Nagel, P Wagner, R Woesler

(review; 40pp)

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Last revised: August 10, 2002
John Rupley: rupley@u.arizona.edu