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Session 42 Joel Franklin
1. The Importance of Lateness:
Travel Time Reliability on Stockholm
Roadways
Joel P. Franklin & Anders Karlström
Dept. of Transport & Economics
Royal Institute of Technology
Stockholm, Sweden
2. Outline
1. Background:
Theory behind Value of Reliability
To do it right, need the “Mean Lateness”
2. Exploratory Analysis:
Bergslagsvägen, Stockholm
Mean Lateness has its own peaks over the day, varies by at
least a factor of 5
3. Modeling Exercise:
What factors seem to be important?
All the suspected factors are important, but not enough
Transport Forum, 2009 2/23
3. Motivation
Transport investments affect average travel
times, and variations in travel times
Reliability improvements might be worth 10-
15% the worth of travel time savings
Points toward different kinds of policies, e.g.
incident management, traveler information
What is the trade-off from users’ perspective?
How can we use this in Benefit-Cost Analysis?
Transport Forum, 2009 3/23
4. Conceptual Framework:
Modeling Reliability
As usual, we combine:
Traveler Preferences
Observable Data
To make:
Estimators for Cost/Utility/Benefit
Choice Modeling
User Benefit Estimation
Transport Forum, 2009 4/23
5. Conceptual Framework:
Two Standard Approaches
Mean-Variance Approach
(Hollander 2006, Noland & Polak 2002, Small
2005)
U = γ C + ημ + ρσ
Cost Mean Std. Dev.
Time Time
Uses Observable (and Predictable) Data
No Supporting Theory behind Preferences
Transport Forum, 2009 5/23
6. Conceptual Framework:
Two Standard Approaches
Scheduling Approach
(Small 1982, Noland & Small 1995)
EU ( th ) = γ C + ημ + λ E ( SDE ) + δ E ( SDL ) + θ PL
Cost Mean Early Late Prob.
Time Delay Delay Being
Late
Good for Identifying Preferences
Difficult to know what the Delays really are
Transport Forum, 2009 6/23
7. New Approach
Fosgerau & Karlström
Start with Scheduling Approach:
Opportunity Cost of Leaving Early, α
Time-Cost of Travel Itself, ω
Cost for Late Delays, β
By the way: α/β = optimal probability of being late
Assume: no fixed penalty for being late (θ = 0)
Allow any Distribution of Travel Times, Φ
Can express expected utility in terms of Mean, Std.
Dev. and H, i.e. Mean Lateness (given being late):
H = f (α/β, Φ)
Transport Forum, 2009 7/23
8. New Approach
Fosgerau & Karlström
Utility can be expressed:
⎛α ⎞
E (U ) = (α + ω ) μ + β H ⎜ , Φ ⎟ σ
⎝β ⎠
Value of Value of
Time Reliability
Where H is:
⎛α ⎞ 1
H ⎜ , Φ ⎟ = ∫ α Φ ( x ) dx
−1
⎝β ⎠ 1− β
for any standardized travel time distribution Φ
Transport Forum, 2009 8/23
9. New Approach
Fosgerau & Karlström
⎛α ⎞ 1
H ⎜ , Φ ⎟ = ∫ α Φ −1 ( x ) dx
⎝β ⎠ 1− β
Optimal Φ, Standardized
Probability Pr Distribution of Travel Time
of Being late
x
0 1 – α/β
Transport Forum, 2009 9/23
10. New Approach
What’s the Advantage?
In Practice of User Benefit Analysis:
Relying only on Mean and Std. Dev.:
E (U ) = ημ + ρσ
ρ = βH
Preference Feature of
Parameter Distribution Φ
If we can estimate H (i.e. Mean Lateness) then we
have transferability
But can we estimate Mean Lateness?
Transport Forum, 2009 10/23
11. This Project…
Research Questions:
Is the standardized travel time distribution, Φ,
constant?
If not, how does it vary?
Can we predict the Mean Lateness, H?
We examine:
44 Arterial & Highway Segments
15-minute camera-based travel time observations,
June-Oct, 2005-2007
2507 “good” observations
Transport Forum, 2009 11/23
15. Model of Mean Lateness:
Methodology
“Mean Lateness” as a function of:
Roadway Characteristics:
Freeflow Speed
Number of Lanes
Direction of Travel
{Inward, Outward, Circumferential}
Location
{Inner City, Connector, Suburban}
Transport Forum, 2009 15/23
16. Model of Mean Lateness:
Methodology
…and as a function of:
Traffic Flow Characteristics:
Standard Deviation of Travel Time
Relative Delay
Peak Period Stage
{Early Morning, Up-Shoulder, Peak, Down-Shoulder, Midday}
Interaction Terms
Transport Forum, 2009 16/23
18. Modeling Results:
Significant Factors
Direct Effects:
Speed, Location, Log of Std. Dev. Travel Time, Log
Congestion, Peak Stage
Two-Way Interactions:
Direction with: Speed, Lanes
Location with: Speed, Lanes, Log Std. Dev. TT, Log
Congestion, Peak Stage
Peak Stage with: Lanes
Three-Way Interactions:
Direction with Location with Lanes
Transport Forum, 2009 18/23
19. Modeling Results: Mean Lateness
vs. Direction & Peak Stage
0.700
0.600
0.500
Intercept for Mean Lateness
0.400 Inward (base)
Outward
0.300 Circumferential
0.200
0.100
0.000
Early (base) Up-Shoulder Peak Down-Shoulder Midday
Peak Stage
Transport Forum, 2009 19/23
20. Modeling Results: Mean Lateness
vs. Location & Peak Stage
0.900
0.800
0.700
Intercept for Mean Lateness
0.600
0.500 Inner City (base)
Connector
0.400 Outer
0.300
0.200
0.100
0.000
Early (base) Up-Shoulder Peak Down-Shoulder Midday
Peak Stage
Transport Forum, 2009 20/23
21. Summary of Findings
The Mean Lateness Does Vary…
Across different roadway segments
Across time of day
Can often lead to bias of a factor of 5 for the Value of
Reliability
The Mean Lateness can be partially explained by:
Time of Day, Location, Orientation, Size, Traffic Level
Interactions between Time of Day, Location, Orientation
Not enough for predictive modeling
Transport Forum, 2009 21/23
22. Issues for Future Research
Stronger mechanistic basis for why mean
lateness changes over time
Simulate the distribution of Φ using traffic flow
theory, e.g. the standard “bottleneck” model
What happens with a fixed penalty for being
late?
Direct modeling of (σ·H), the “unstandardized
mean lateness”, instead of modeling them
separately
Transport Forum, 2009 22/23
23. Thanks to…
Centre for Transport Studies, KTH
Vägverket
Questions to…
Joel Franklin
joelfr@kth.se
