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 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 r 2 =0.829 Quadratic Fit: flow=dens*vel =dens*(-0.96*dens+92.8) =-0.96*dens *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?

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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

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New Observations in Mulh. Data Seems qualitatively different... Examine plots of flow, velocity, and flow Notice difference between 1300 –[ ]: Flow tracks density, velocity unrelated –[ ]: velocity inverse to density, flow roughly constant Correlation coefficients

Texas A&M University Frames [ ] correlation of vel and dens: r 2 =0.373 Frames [ ] correlation of vel and dens: r 2 =0.826 Density Velocity

Texas A&M University Frames [ ] correlation of flow and density: r 2 =0.698 Frames [ ] correlation of flow and density: r 2 =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)

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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