Session 20 Joel P. Franklin
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Transcript of Session 20 Joel P. Franklin
![Page 1: Session 20 Joel P. Franklin](https://reader036.fdocuments.us/reader036/viewer/2022070317/5562fefbd8b42a275f8b4d90/html5/thumbnails/1.jpg)
13 January 2010, 1
Congestion and Travel Time Reliability:
Comparing a Random Bottleneck to Empirical Data
Joel P. FranklinKungliga Tekniska Högskolan
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13 January 2010, 2
Overview
• Investigate the Role of Travel Time Variability in Costs/Benefits Estimation
• Case of Interest:• Future demand is known• Traveler preferences are known• Future travel time variability is unknown
• What tools can we use to predict future variability?
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13 January 2010, 3
Background
• Travel Time Variabilty Matters to Travelers
• It Matters in a Particular Way – Implications for Measurement
• Lateness matters more than Earliness• i.e. standard deviation can be misleading
• We can assume people try to optimize departure time
• Hence, total costs are a mixture of:• Early departure from previous activity*• Travel time in itself*• Expected late arrival to next activity: ”Mean Lateness”*• *Given optimized departure time
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13 January 2010, 4
Hour of Day
Tra
vel T
ime
/ M
ea
n T
rave
l Tim
e
1
2
3
5 6 7 8 9 10 11
What does our congestion look like?
Hour of Day (morning)
Bergslagsvägen, Inbound
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13 January 2010, 5
5 6 7 8 9 10 11
20
04
00
60
08
00
(a)
Hour of Day
Tra
vel T
ime
(se
c.)
How does it vary?
Hour of Day (morning)
Bergslagsvägen, Inbound
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13 January 2010, 6
What features are important to us?
• Take a person who wants to arrive on-time 20% of the time• Value of Lost Time at Home: 1/hr• Value of Lost Time at Work: 5/hr• Additional Cost of Travel Time: 1/hr
• Where: ”mean lateness” is the average time late• Mean Travel Time – predicted by standard demand models• Mean Lateness…?
1 1 Mean Travel Time 5 Mean LatenessU
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13 January 2010, 7
Theoretical Framework(Fosgerau & Karlström, 2009)
ChosenDeparture Time
PreferredArrival Time
Actual Arrival Time
15
1/5
Marginal Utilities
CDF of Travel Time
Area = Mean Lateness
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13 January 2010, 8
1.0 1.2 1.4 1.6 1.8 2.0
0.0
50
.10
0.1
50
.20
0.2
50
.30
Mean / Freeflow Travel Time
La
ten
ess
K /
Fre
eflo
w T
rave
l Tim
e
56
7
89
1011121314
15
1617
18192021
How do those features vary?
Mean Time / Freeflow Time
Bergslagsvägen, Inbound
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13 January 2010, 9
Results
1.0 1.2 1.4 1.6 1.8 2.0 2.2
0.1
0.2
0.3
0.4
(c)34 Centralbr.--Slussen-Klarastr.svia.
Mean / Freeflow Travel Time
La
ten
ess
K /
Fre
eflo
w T
rave
l Tim
e
56
7
89
10
111213
14
15
1617
18
19
20
21
Static Approach (for comparison):• Scale is 50% low• Looping pattern is absent
(mostly)• No Peak at Shoulders
Effect:• Role of Variability is
understated by about 50%• Difference in Variability at
Times of Day is Lost
Conclusion:• May need a Dynamic
approach
Results of Static Approach
Centralbron, Inbound
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13 January 2010, 10
Research Question
• How well can a random bottleneck model predict mean lateness?
• Why?• Could be a very simple way to forecast
improvements in travel time variability• Incorporates time-dependent congestion
dynamics
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13 January 2010, 11
Bottleneck Approach
• Fixed capacity
• Demand surpasses capacity at time ”0”
• Demand later subsides below capacity
• For an arrival at t:• Queue Length
measured by ”Q(t)”• Queue Time measured
by ”q(t)”Time of Day0
Q(t)
q(t)
t
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13 January 2010, 12
Random Bottleneck
• Demand in each period is random
• Queue time ”q” is random, depending on random variation in demand up to time ”t”
Time of Day0
Q(t)
q(t)
t
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13 January 2010, 13
Procedure
1. Selected Stockholm Highway Segments:• Example shown here: Centralbron—Northbound
2. Observed Delay Distributions by 15-Min Periods
3. Simulate Bottleneck Delay Distributions• Started with observed flow by 15-minute periods• Simulate random deviations in each period, using exponential distribution
• Also tested log-normal, poisson, negative-binomial• Manually Calibrate for Capacity, Random Dispersion
4. Compute Optimal Expected Lateness by 15-Min Periods• Also, Mean and Standard Devation
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13 January 2010, 14
20 40 60 80
02
46
81
0
Time Period
Re
lativ
e L
eve
l
Results
5 10 15 20
0.0
0.2
0.4
0.6
0.8
1.0
Hour of Day
Tra
vel T
ime
/ Mea
n T
rave
l Tim
e
Observed Travel Times (Segment)Random Bottleneck Travel Times (Point)
Centralbron, Northbound Centralbron, Northbound
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13 January 2010, 15
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Mean Travel Time
Sta
nd
ard
De
via
tion
Results
Bottleneck Approach:
• Looping effect exaggerated
• Peaks not separated• No peaks at shoulders
• Scale different by nature (point delay vs. link delay)
Centralbron, Northbound
9:00
16:45
1.0 1.2 1.4 1.6 1.8 2.0 2.2
0.1
0.2
0.3
0.4
(c)34 Centralbr.--Slussen-Klarastr.svia.
Mean / Freeflow Travel Time
La
ten
ess
K /
Fre
eflo
w T
rave
l Tim
e
56
7
89
10
111213
14
15
1617
18
19
20
21
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13 January 2010, 16
Main Conclusions
• Dynamic approach of the bottleneck reproduces the cyclical behavior behind ”mean lateness”
• Scale issues need to be better-calibrated• Maximum Capacity• Freeflow Travel Time• Random Characteristics of Traffic Demand
• Pure Bottleneck may be too simple• E.g. Demand just under capacity gives zero delay
• Overall:• The Bottleneck doesn’t give better predict than a static approach (yet)• But better random-demand data can give better forecasts
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13 January 2010, 17
Other Observations
• Under the Random Bottleneck Model:• Mean Lateness tracks very
closely with Standard Deviation
For facilities that truly operate as a bottleneck, standard deviation (multiplied by a constant) may be a good approximation to mean lateness
20 40 60 80
01
23
45
Time Period
Re
lativ
e L
eve
l
Mean FlowMean Travel TimeStd. Dev. Travel TimeMean LatenessMean Lateness / Std. Dev.
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13 January 2010, 18
Future Directions
• Mixed congestion models:• Uncongested volume-to-capacity relationship of static models• Congested time-dependency of bottleneck models
• Data on traffic volume variations:• Needed to appropriately simulate randomness• Potential Source: California highway data (day-to-day flows and travel times)
• Theoretical Exploration of Bottleneck Model• Why do Standard Deviation and Mean Lateness often track so closely?