Texas A&M University Analysis of Patterns in Traffic Congestion Tom Ioerger, Paul Nelson Department...

Texas A&M University

Analysis of Patterns in Traffic Congestion

Tom Ioerger, Paul Nelson

Department of Computer Science


Support provided by a grant from the Southwest Region University Transportation Research Center and the Texas Transportation Institute


Motivation

• Fundamental Diagram– What causes departure from linearity?– What is flow a function of, besides density?

• Phases of Traffic Flow– Free flow– “Synchronized flow” (Kerner)– “Phantom/emergent” traffic jams

• Gazis & Herman, Nagel & Paczuski, Helbing & Treiber, etc.

– Phase transitions?


Videogrammetric Data• Turner-Fairbanks (TFHRC) web site

– 5 data sets– basic sections (no on/off ramps, etc.), ~2000 ft.– 1 hour of data captured by camera on plane– digitized 1 second per frame– individual velocities and position within section – vehicles labeled for comparing between frames– compute flow (count 5s), vel (avg), dens (400ft)– each var. smoothed over windows of 10-60 sec.

• Finer granularity than induction-loop data


I-405 in L.A. (near Mulholland Dr.)• Some congestion:

– high density regions, and low velocities– disabled vehicles on right shoulder at 22

minutes, and left shoulder at 38 minutes


Correlation of Vel. And Dens. vel=-0.96*dens+92.8 r2=0.829

Quadratic Fit: flow=dens*vel =dens*(-0.96*dens+92.8) =-0.96*dens2+92.8*dens


Microanalysis

• Space-time diagram suggests existence of “constrictions”– very high density– tend to propagate backwards– different from platoons (which move forward)– hypothesis: tend to “trigger” slow-downs– theory:

• front of “shock wave”

• Lighthill-Whitham model (&kinematic wave theory)

• queue formation from events down-stream?


Convolutions

• How to detect ‘constrictions’ in data stream?

• Use time-series/signal-analysis techniques

• Template convolution– let f(t) be signal (discrete samples)– let g(t) be a pattern to be searched for (e.g. pulse)– C(f,g)(t) = f(t-u)g(u) du– gives peaks in spatial domain where tmplt. matches– efficient computation based on Fourier transforms:

• C(f,g)(t) = T-1(F(v)*G(v)) where F(v)=T(f), G(v)=T(g)


• Template 1: – sin wave in gradient of density - anticipation

– subtract waves for forward-moving platoons

• Template 2: – spike up in density (Gaussian)– coupled with sharp drop in velocity

time

gradient

time

density

time

velocity


New Observations in Mulh. Data

• Seems qualitatively different...

• Examine plots of flow, velocity, and flow

• Notice difference between <1300 and >1300– [0..1300]:

• Flow tracks density, velocity unrelated

– [1300..3600]: • velocity inverse to density, flow roughly constant

• Correlation coefficients


0

10

20

30

40

50

60

70

0 20 40 60 80 100

Series1

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Series1

Frames [0..1300] correlation of vel and dens: r2=0.373

Frames [1300..3600] correlation of vel and dens: r2=0.826

Density

Density

Velocity

Velocity


05101520253035404550

0 20 40 60 80 100

Density

Flow

Series1

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100

Density

Flow

Series2

Frames [0..1300] correlation of flow and density: r2=0.698

Frames [1300..3600] correlation of flow and density: r2=0.034


Phase Separation on Fundamental Diagram


New Phases?

• Phase 1: free flow - flow coupled to density

• Phase 2: – characteristic of congested traffic– velocity reacts inversely to density– contains constrictions (extremes)

• Appearance in other datasets:– free flow: US101 (White Oak, Van Nuys), I-495

(Montgom. Cnty., MD), I-10 (near La Brea Blvd., L.A.)

– mixture?: I-395 (near Duke St., in Alexandria VA)


Conclusions

• Video data is good for fine-grained analysis of traffic behavior (greater length desired)

• Can use signal analysis techinques

• Discovery of two unique behaviors (phases)

• Future Work– relation to other “phases” in lit. (sync. flow?)– cluster analysis techniques, adjacent lanes?– explanation by kinematic wave models– design detection methods for ind. loop sensors

Texas A&M University Analysis of Patterns in Traffic Congestion Tom Ioerger, Paul Nelson Department...

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