Analysis, Characterization and Visualization of Freeway Traffic Data in Los Angeles

Alain L. KornhauserProfessor, Operations Research & Financial Engineering

Director, Transportation Research Program

Princeton University

Presented at 53rd Annual Meeting Transportation Research ForumTampa, FlMarch, 2012

Scott H. ChaconAnalyst, 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 kth link travelTimek

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 lengthDelay(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

1 Mon 8/22/08

2 Tue 8/23/08

3 Wed 8/24/08

4 Thu 8/25/08

5 Fri 8/26/08

6 Sat 8/27/08

7 Sun 8/28/08

Delay(t, x) at consecutive stations, x

Station #

Station ID

1 717029

2 717031

3 717033

4 763330

Animated Visualization of Delay• BarArea(x) = Delay(t,x)

Early morningRush Hour

• Observation:– Delay(t): Summation of three humps:

Delay(t) humps in the Morning, early Afternoon, late Afternoon

– kth Hump characterized• Time of center (μ)• Breath of hump (σ)• Height of hump (C) • Gausian Prob density function:

Time-of-Day Function

Time-of-Day Function

8 Days of curve Fitted data

10 Classes of Recurring Delay1AM AMpm

amPMAMPM

3PeaksAllDay

2PM

2AM

None

PM

Proportion(% of 1,500 locations)

byCongestion Classification

Forecasting: Exponential Smoothing

Application of Forecasting Method

Thank You