Analysis, Characterization and Visualization of Freeway Traffic Data in Los Angeles Alain L. Kornhauser Professor, Operations Research & Financial Engineering Director, Transportation Research Program Princeton University Presented at 53 rd Annual Meeting Transportation Research Forum Tampa, Fl March, 2012 Scott H. Chacon Analyst, Wells Fargo Investment Banking and

Overview A methodology for parsimonious characterization of the time-of-day and day-of-week variation of recurring traffic congestion in roadway segments Want something that is appropriate for generating dynamic real-time minimum estimated-time-of- arrival turn-by-turn navigation instructions.

Overview Conceptually, travel time is straight forward to estimate. – It is simply the ensemble of travel time experienced on each of the route segments (aka links) that assemble to take you from where you are to where you are going. The challenge is the satisfactory estimation of that travel time when you will be traversing that segment. – Required is estimation of the time at which the segment is traversed and the time to traverse that segment at that time.

Overview Intent: to utilize the characterization to assist in the ranking of alternative routes in a turn-by-turn navigation system. – Such systems assess many routes each having many segments; – consequently, the estimation of time-of –arrival must be efficient in: – Data availability and Memory – Parallelization – computation of k th link travelTime k

Overview Focus on recurring congestion – as represented by PeMS ready availability of time series data for many locations – 8,915 individual lanes flow, occupancy and implied speed every twice a minute) Reviewed are other aspects – weather, special events, incidents – more appropriate data such as individual vehicle travel histories (aka “GPS Tracks”): observed travel times are explicitly exposed. These elements are beyond the scope of this paper Note – While the PeMS data are but surrogates for segment travel times, their recurring and special characteristics are arguably very similar to actual segment travel times. The ready availability of PeMS data for many locations is why they were used in this study to characterize and classify roadway segments

Sensor Locations Used data from 1,500 “mainline” detectors – Excluded on/off ramps, freeway2freeway connectors and HOV lanes

Sensor Locations Length of segment = Distance Btwn MidPoint of neighboring sensors AverageLength = 0.70 miles; StdDv = 0.64 Speed: Relatively constant btwn neighboring sensors

Congestion Measure: Delay(t) Delay defined as additional vehicle hours per time period per segment unit length Delay(t) = SegLength*Flow(t)*Max{(1/PeMS_Speed (t)) –(1/targetSpeed), 0} Jia et al. showed max throughput for LA Freeways occur at 60 mph = TargetSpeed

Congestion Measure: Delay(t, DoW) Consistency by Day-of-Week (DoW) Day of Week Date 1Mon 8/22/08 2Tue 8/23/08 3Wed 8/24/08 4Thu 8/25/08 5Fri 8/26/08 6Sat 8/27/08 7Sun 8/28/08

Delay(t, x) at consecutive stations, x Station # Station ID

Animated Visualization of Delay BarArea(x) = Delay(t,x) Early morning Rush Hour

Observation: – Delay(t): Summation of three humps: Delay(t) humps in the Morning, early Afternoon, late Afternoon – k th Hump characterized Time of center (μ) Breath of hump (σ) Height of hump (C) Gausian Prob density function: Time-of-Day Function

8 Days of curve Fitted data

10 Classes of Recurring Delay 1AM AMpm amPM AMPM 3Peaks AllDay 2PM 2AM None PM

Proportion (% of 1,500 locations) by Congestion Classification Proportion (% of 1,500 locations) by Congestion Classification

Forecasting: Exponential Smoothing

Application of Forecasting Method

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