Mohammad Ansari

Travel Time Reliability of Signalized Arterials – MacLeod Trail Case Study

University of Calgary

May 01,2016

What is Travel Time Reliability?

Measures the extend of the unexpected delay

Consistency or dependability in travel times measured from:• Vehicle to vehicle (spatial)• Across different times of day• Day-to-day (temporal)

Why Travel Time Reliability?

Jan. Dec.July

Traveltime

How traffic conditions havebeen communicated

Annual average

Jan. Dec.July

Traveltime

What travelers experience

Travel times varygreatly day-to-day

What theyremember

Average is not a good measure of reliability

http://ops.fhwa.dot.gov/perf_measurement/reliability_measures/index.htm

Why Travel Time Reliability?

It captures the benefits of traffic management

Traveltime

Before After

Avg. day

Small improvement inaverage travel times

Larger improvement intravel time reliability

Traveltime

Before After

Worst dayof month

http://ops.fhwa.dot.gov/perf_measurement/reliability_measures/index.htm

Problem Statement

There are many travel time reliability analysis for freeways

None for signalized arterials

Traffic flow interrupted by: Signals Speed limit Presence of parking Construction Pedestrian crossing Transit stops

No analysis for extreme travel time

Evaluating travel time reliability of signalized arterials (Casestudy: Macleod Trail, Calgary, AB)

Vehicle-to-vehicle distribution for:• All events• Extreme events

Objective of the Study

• Time of day• Road segment• Uncongested travel time• Average speed• Segment length

Data Source

Travel timeTravel delay

• 6 month data• Travel Data updated every 5 minutes• 6 AM – 12 PM• 880,000 data entries in total• 13,000 data entries for Macleod Trail

Data Source

FrameworkD

ays

Time of Day

Kim, J., & Mahmassani, H. S. (2015). Compound Gamma representation for modeling travel time variability in a traffic network. Transportation Research Part B: Methodological, 80, 40-63.

Framework

Vehicle-to-vehicle distribution of individual travel time at t

Kim, J., & Mahmassani, H. S. (2015). Compound Gamma representation for modeling travel time variability in a traffic network. Transportation Research Part B: Methodological, 80, 40-63.

Framework

Day-to-day distribution of mean travel time at t

Kim, J., & Mahmassani, H. S. (2015). Compound Gamma representation for modeling travel time variability in a traffic network. Transportation Research Part B: Methodological, 80, 40-63.

Framework

Overall vehicle-to-vehicle distribution of individual travel times at t

Kim, J., & Mahmassani, H. S. (2015). Compound Gamma representation for modeling travel time variability in a traffic network. Transportation Research Part B: Methodological, 80, 40-63.

Framework

0

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12 17 22

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12 13 14 15 16 17 18

July 16

July 17

Jan 16

....... .

6:00-10:00 am

Freeway

Linear relationship between standard deviation (SD) andmean for

• Travel time• Travel delay

Kim, J., & Mahmassani, H. S. (2014). Compound Gamma Representation for Modeling 2 Vehicle-to-vehicle and Day-to-day Travel Time Variability in a 3 Traffic Network 4. Traffic, 4, 5.

Signalized arterial

y = 0.2995x + 0.0023

R² = 0.7269

0

0.05

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0.25

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0 0.2 0.4 0.6 0.8 1

SD

of

TD

PM

(m

in/k

m)

Mean TDPM (min/km)

y = 0.2805x - 0.2899

R² = 0.3427

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0 0.5 1 1.5 2

SD

of

TT

PM

(m

in/k

m)

Mean TTPM (min/km)

Same linear relationship between standard deviation (SD)and mean for

• Travel time• Travel delay

Extreme Delay Analysis

Extremes events:

Located on the tail of PDF

Very low probable events

1. Block Maxima

2. Rth order statistic

3. Extremes exceed a high threshold

Models of extreme values:

Artificial block selection

PDF: Weibull, Frechet or Gumbel

PDF: Exponential, Pareto or Beta

Extreme Delay Analysis : Block Maxima

1. Block Maxima (event based)

Block length of 1 hour 6 blocks each day, 384 blocks in total

Choosing highest travel time and delay event in each block

Gumbel

F x = exp −exp0.31 − x

0.042

MAE= 0.062

Histogram Gumbel Max

Extreme Delay0.480.440.40.360.320.280.240.20.16

Fre

quency o

f extr

em

e d

ela

y

0.12

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Extreme Delay Analysis : Block Maxima

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Cum

ula

tive

pro

bab

ilit

y

Delay (min/km)

Empirical Frechet (2p) Frechet (3p) Weibull (2p) Weibull (3p) Gumble Max

Distribution FRECHET (2P) (FRECHET 3P) WEIBULL (2P) WEIBULL (3P) GUMBLE

MAE 0.119 0.585 0.071 0.063 0.062

Extreme events

y = 0.3076x - 0.0209

R² = 0.2345

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SD

of

TD

PM

(m

in/k

m)

Mean TDPM (min/km)

y = 0.3244x - 0.373

R² = 0.264

0

0.02

0.04

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0.08

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0.12

0.14

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0.18

0 0.5 1 1.5 2

SD

of

TT

PM

(m

in/k

m)

Mean TTPM (min/km)

linear relationship between standard deviation (SD) andmean for

• Travel time• Travel delay

Conclusions & Keynotes

Vehicle-to-vehicle distribution of signalized arterials is evaluated using INRIX data

Linear relationship between SD and mean of all travel time and delay were observed

• Highly positive correlation for travel time (R2 = 0.727)• Low positive correlation for travel delay (R2 = 0.343)

Linear relationship between SD and mean of extreme travel time and delay were observed

• Low positive correlation for travel time (R2 = 0.235)• Low positive correlation for travel delay (R2 = 0.264)

Gumbel distribution fits the best to the extreme vehicle-to-vehicle travel delays

Thank you

Questions??