Post on 01-Apr-2015
Texas A&M University
Analysis of Patterns in Traffic Congestion
Tom Ioerger, Paul Nelson
Department of Computer Science
Texas A&M University
Support provided by a grant from the Southwest Region University Transportation Research Center and the Texas Transportation Institute
Texas A&M University
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?
Texas A&M University
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
Texas A&M University
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
Texas A&M University
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
Texas A&M University
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?
Texas A&M University
Texas A&M University
Texas A&M University
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)
Texas A&M University
• 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
Texas A&M University
Texas A&M University
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
Texas A&M University
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
Texas A&M University
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
Texas A&M University
Phase Separation on Fundamental Diagram
Texas A&M University
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)
Texas A&M University
Texas A&M University
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