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L35‐B Local Methods for Modeling, Economic Evaluation,
Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Sponsor:Transportation Research Board of the National Academies
Strategic Highway Research Program (SHRP II)
Contractors:University of Maryland
Center for Advanced Transportation Technology (CATT)National Center for Smart Growth (NCSG)
Sub‐Contractors:Cambridge Systematics, Inc.
Dunbar Transportation Consulting
Supporting/ Implementing Agency:Maryland State Highway Administration
SHRP 2 TCC for Reliability Workshop:Wednesday, October 30, 2013
Presentation Outline
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
2
• Introduction– Review of L35B Research goals– Overview of Research Approach & Tasks
• Early Findings & Lessons Learned– Overview of Maryland SHA’s Existing Project Prioritization Process– Summary of Methodologies to Estimate VOTTR (from the literature)– Approach to Travel Time Reliability Valuation – Binary Trees
• Identify Measure of Reliability• Determine Value of Travel Time• Present Random Walk Metaphor for Valuation Process• Present Computation of VOR by Application of Random Walk Metaphor
• Review of Project Schedule & Deliverables
• Question & Answer Session
Research Goals
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
3
• Select and defend a value or range of values for travel time reliability for the Maryland State Highway network
• Use the VTTR in the Maryland SHA project development process to prioritize operational and capital improvements and determine if (and how) the ranking of projects changes due to the addition of VTTR
• Report for the benefit of others the step‐by‐step process used to develop, justify, apply, and assess the use of VTTR in the Maryland SHA project evaluation and decision process
Overview of Research Tasks
1. Describe how your established processes to prioritize operational and capital improvements (baseline approach) meet the special evaluation criteria for this project. This includes analytical methods used to obtain performance metrics and a prioritization/evaluation process.
2. Develop and apply a methodology to select a travel time reliability performance measure and a value or range of values for travel time reliability.
3. Incorporate this performance and the value of travel time reliability into your project evaluation process and use that information to inform policy decisions about transportation alternatives.
4. Analyze and compare alternatives using the baseline approach and the revised method that includes VTTR.
5. Explore the sensitivity of priorities to changes/ranges of the VTTR.
6. Brief management and/or policy board on the results of Task 4 and 5 and assess the reaction of members.
7. Prepare a Draft Final Report including lessons learned from tasks 1‐6
8. Prepare Final Report.
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Task 1• Describe how your established process to prioritize operational and capital improvements (baseline approach) meet the special evaluation criteria for this project. This includes analytical methods used to obtain performance metrics and a prioritization/evaluation process.
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Overview of Existing Process(es)
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Overview of Existing Process(es)
Graphic from SHRP2 LO5 Presentation by Anita Vandervalk, September 17, 2013
SHA Congestion Relief Project Decision Making Process
Congestion Relief Project DM
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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In addition to safety and congestion, transportation system reliability is another key factor to providing our customers with a good travel experience.
From Forward 2013 SHA Mobility Report
Melinda B. Peters, SHA Administrator
Congestion Relief Project DM• Step 1 ‐Diagnosis
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Congestion Relief Project DM• Step 2 – Analysis
– Review– Simulate– B/C
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Congestion Relief Project DM• Some Step 2 Analysis Details
– VISSIM Model Calibration• Traffic volumes must be within 10% of the input volume;
• Auto speeds must be +/‐ 5MPH of the vehicle probe data speed; and
• Auto travel times must be within 10% of the vehicle probe data travel time
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Congestion Relief Project DM
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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• Some Step 2 Analysis Details– Benefits: VOT and VTTR
Saving Type Parameter Unit Categories SHA Value*
Travel time VOT $/hrPassenger 29.82Truck driver 20.21Cargo 45.40
Travel time reliability VTTR $/hrPassenger 22.36Truck driver 15.16Cargo 34.05
Fuel cost $/galGasoline 3.69Diesel 3.97
Value of Time (VOT)• Passenger: U.S. Census Bureau data• Truck driver: Bureau of Labor Statistics, US DOT,
and FHWA’s HERS • Cargo: TTI, and other studies
Value of Travel Time Reliability (VTTR)• Reliability Ratio (RR=0.75)• Based on literature review and current practice in
other parts of the world
*Parameters used by SHA in project benefit estimation (2012 values)
Congestion Relief Project DM• Step 3 ‐
Selection
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Location Project DescriptionTotal Savings
Construction Cost
O&M Cost
Total Cost B/C
All Values in (1000’s)I‐695 Outer Loop: MD 144 on ramp continuing to MD 372
Provide additional through lane from on ramp at MD 144 to end of acceleration lane from MD 372. Includes widening and restriping and removal and replacement of retaining wall. Total project length is 2,500ft.
$27,165 $16,500 $1,650 $18,150 150%
I‐695 Inner Loop: US 40 Interchange
Extend inner loop aux lane prior to interchange to connect deceleration lane to WB US40. Widen I‐695 inner loop to provide exclusive decel lane for EB US40. Includes retaining wall construction. Total length is 2,200ft.
$14,558 $10,900 $1,090 $11,990 121%
I‐695 Outer Loop: US 40 Interchange
Extend outer loop aux lane prior to interchange to connect decel lane to eastbound US 40. Widen I‐695 outer loop to provide exclusive decel lane for WB US 40. Total length is 2,200ft.
$32,894 $5,000 $500 $5,500 598%
I‐695 Outer Loop: I‐70/MD 122 to Windsor Mill Rd
Extend I‐70 WB to I‐695 NB acceleration lane by 500 ft. Extend MD 122 to I‐695 NB accel lane by 1,250ft. Requires restriping of I‐695, widening to accommodate accel lane and construction of retaining wall.
$26,665 $13,300 $1,330 $14,630 182%
Congestion Relief Project DM
• Step 4 –Assessment
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Prioritization ProcessInitial Lessons Learned
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Graphic from SHRP2 LO5 Presentation by Anita Vandervalk, September 17, 2013
• Many Project DM Processes Involved
• Travel Time Reliability Becoming Increasingly Popular Performance Measure
• TTR Used in One Current Project Prioritization Process
Task 2• Task 2: Develop and apply a methodology to select a travel time reliability performance measure and a value or range of values for travel time reliability
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Objective of Project L35B• Provide a means for valuing travel time reliability to enhance standard procedures for evaluating the benefits and costs of operations and other highway expenditures
• Provide the ability to develop local, defensible values of reliability that decision makers embrace when considering choices and tradeoffs in reaching expenditure decisions
17L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Valuation– General Approach Identify the measure of reliabilityDetermine the value of travel timeObtain data on how travel time varies over time and determine the type of process describing the variation
Create a metaphor for the valuation process that has exact counterparts in the physical world
Compute the economic value of reliability by applying the metaphor and calculate the value of reliability relative to the value of time
18L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Potential Use for MD‐SHA• Value of Reliability
– Validate the currently adopted RR (0.75)– Specify a value/range of values for RR for different
• Highway modes (auto, truck)• Corridors/regions• Time of day (AM/PM peak)
• Tool to analyze travel time data and to evaluate customized RR– Input raw travel time data– Estimate travel time process parameters– Characterize travel time distribution and relevant metrics from its histogram– Perform hypothesis testing– Evaluate travel time insurance value and reliability ratios
• Annual Mobility Report– Reliability profile along significant corridors– Include unreliability cost estimates
• Maryland Statewide Transportation Model (MSTM)– Update volume‐delay functions considering certainty‐equivalent extra travel times– Potentially improve mode/route choice sub‐models’ performance
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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0 20 40 60 80 100 1200
0.2
0.4
0.6
0.8
1
TIME (MINUTES)
RE
LIA
BIL
ITY
RA
TIO
(UN
ITLE
SS
)
AM PEAK PERIOD
0 20 40 60 80 100 1200
0.2
0.4
0.6
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1
TIME (MINUTES)
RE
LIA
BIL
ITY
RA
TIO
(UN
ITLE
SS
)
PM PEAK PERIOD
0 2 4 6 8 10 12 14 160
0.2
0.4
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LENGTH (MILES)
RE
LIA
BIL
ITY
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TIO
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ITLE
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)
0 2 4 6 8 10 12 14 160
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LENGTH (MILES)
RE
LIA
BIL
ITY
RA
TIO
(UN
ITLE
SS
)
RELIABILITY RATIOS (RR)PATH LEVEL & INTERDAY (ACROSS DAYS)
CORRIDOR NAME: I495 CW
RR=0.75?
Outline• Travel time reliability performance measure• Travel time reliability value• Overview and criticism of L11• Some background• Proposed valuation approach• How proposed approach is different from L11?• Some numerical results and simplifying relationships• Ideas for implementation/application (Task 3)• Summary• Q&A
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Travel Time ReliabilityPerformance Measure
• Currently used by MD‐SHA– Planning Time Index (PTI)
• Reliable (PTI<1.5)• Moderately Reliable (1.5<PTI<2.5)• Highly Unreliable (PTI>2.5)
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Methodology to Select a Value forTravel Time Reliability
• Survey based methods– Expensive and time consuming– Difficult to update/generalize/localize
• Literature review– Survey type/method/year– Choice mode/route/joint– Trip purpose/length/time
• Real options method– Based on statistical/financial concepts– Advantages
• Data driven• Easy to update/generalize/localize• Well‐known in transportation project management
– Disadvantages• Unfamiliar terminology • Only one application so far! (PSRC, L11, L17)
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Source: Carrion & Levinson (2012)
Source: KiM Netherlands Report (2013)
Overview of L11• Input:
– Speed data– Volume data
• Caution: applicable to data where the variation in speed can be characterized by a log‐normal distribution
• Steps:1) Characterize the recurring congestion problem2) Calculate the certainty‐equivalent value of unreliability (closed form
Black‐Scholes equation)3) Evaluate the treatment that reduces unreliability4) Calculate the value of the reliability improvement to the road user5) Calculate the reliability measures and the benefit‐cost ratio6) Compare the results with other similar treatments
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Overview of L11• Let’s take another look at the options theoreticapproach for travel time reliability valuation
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
24
L11 Criticisms
Analogy: Premium set for an insurance policy on guaranteed speed levels
Speed is not directly related to travel cost; therefore speed can not be discounted!
Requirement: Speed is log‐normally distributed
What if speed/travel time is not log‐normallydistributed?
Solution: Closed form Black‐Scholes
Black box approach:• What is the riskless interest rate and how it should be set?• Why slowest speed used to specify the length of option?
Some Background• Travel Utility, Reliability Ratio, and Real Options• Travel Cost and Travel Time• Penalty/Reward associated with Unreliability• Geometric Brownian Motion (GBM) w/ Drift• Random Walk and Binary Tree Representation• Binomial Distribution & Normal Distribution• GBM and Binary Tree Representation• Certainty‐Equivalent Conditions
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Utility Based Estimates
General case:
, ,⁄⁄⁄⁄
⁄⁄
Special case: additive‐linear utility function
⁄
⁄
⁄(Carrion & Levinson, 2012)
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making 26
Why Real Options?Special case: additive‐linear utility function
⁄
⁄
⁄Challenge: Estimate parameters!
Certainty‐equivalent additional average travel time
⁄
Challenge: Estimate !
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making 27
Some Background• Travel Utility, Reliability Ratio, and Real Options• Travel Cost and Travel Time• Penalty/Reward associated with Unreliability• Geometric Brownian Motion (GBM) w/ Drift• Random Walk and Binary Tree Representation• Binomial Distribution & Normal Distribution• GBM and Binary Tree Representation• Certainty‐Equivalent Conditions
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Travel Cost• Travel time and travel cost are closely related• In most practical applications, it is commonly assumed they
are linearly related with a constant factor representing Value Of Time (VOT)
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
29
$
1
Some Background• Travel Utility, Reliability Ratio, and Real Options• Travel Cost and Travel Time• Penalty/Reward associated with Unreliability• Geometric Brownian Motion (GBM) w/ Drift• Random Walk and Binary Tree Representation• Binomial Distribution & Normal Distribution• GBM and Binary Tree Representation• Certainty‐Equivalent Conditions
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Reliability Measure:Deviation from Estimated Time of Arrival (ETA)
• Cost=max[VOT*(Travel Time – ETA),0]• Value of Reliability depends on the pattern of deviations of
travel time from the mean, the probability of each deviation, and a penalty/reward function for being late and possibly early
• Any other functioncan be adopted!
– Socio‐economicattributes
– Trip purpose– Time of day
31
Penalty/Reward Function
1
0
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Some Background• Travel Utility, Reliability Ratio, and Real Options• Travel Cost and Travel Time• Penalty/Reward associated with Unreliability• Geometric Brownian Motion (GBM) w/ Drift• Random Walk and Binary Tree Representation• Binomial Distribution & Normal Distribution• GBM and Binary Tree Representation• Certainty‐Equivalent Conditions
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
32
The Random Process• Geometric Brownian Motion (GBM) w/ Drift
; ~ ≡
∆ ~ 2 ∆ , ∆
2 ∆ ∆ ,
• Parameters:– : long‐term trend– : standard deviation
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
33
0 2 4 6 8 10 12 14 16 18 200
10
20
30
40
50
60
70
80
ALPHA=0.05SIGMA=0.1
Time (Minute)
Trav
el T
ime
(Min
ute)
Geometric Brownian Motion (GBM) Process
Travel TimeTrendLower 95% CIUpper 95% CI
(Dixit & Pindyck, 1993)
Some Background• Travel Utility, Reliability Ratio, and Real Options• Travel Cost and Travel Time• Penalty/Reward associated with Unreliability• Geometric Brownian Motion (GBM) w/ Drift• Random Walk and Binary Tree Representation• Binomial Distribution & Normal Distribution• GBM and Binary Tree Representation• Certainty‐Equivalent Conditions
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
34
Random Walk and Binary Tree Representation
• A gentle metaphor
– A person goes up and down a ladder– At the end of each time interval he can either take one step up (probability p) or one
step down (probability 1‐p)– His position on the ladder over time can be depicted using a grid like network where
street corners represent times at which he flips a (generally biased) coin to take either one step up or one step down along the ladder
– In this grid network• The horizontal distance from his initial position represents the time passed• The vertical distance from his initial position represents his relative distance from where he
started
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
35
Random WalkPossible Waypoints and Their Probabilities
36L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Some Background• Travel Utility, Reliability Ratio, and Real Options• Travel Cost and Travel Time• Penalty/Reward associated with Unreliability• Geometric Brownian Motion (GBM) w/ Drift• Random Walk and Binary Tree Representation• Binomial Distribution & Normal Distribution• GBM and Binary Tree Representation• Certainty‐Equivalent Conditions
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
37
• Start with Binary Trees that make up the Random Walk
• Binary Trees converge to a Binomial distribution. Each trial has probabilities of p and 1‐p.
• A Binomial distribution with enough time steps converges to a normal probability density function (PDF)
• The normal distributions derived in this manner are directly useful in valuation problems..
Random Walk Approaches Normal Distribution
38L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Some Background• Travel Utility, Reliability Ratio, and Real Options• Travel Cost and Travel Time• Penalty/Reward associated with Unreliability• Geometric Brownian Motion (GBM) w/ Drift• Random Walk and Binary Tree Representation• Binomial Distribution & Normal Distribution• GBM and Binary Tree Representation• Certainty‐Equivalent Conditions
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
39
GBM and Binary Tree Representation• GBM w/ drift
– Log‐normal distribution– Source of random behavior ( ) represented by a random walk
• Modified Binary Tree Representation– Recall that GBM process implies a log‐normal distribution
• In that case up and down moves become multiplication operations instead of summations
– Useful properties of a binary tree representation of random walk will remain intact
– Increasing the number of time steps (reducing size of time intervals), Binomial distribution converges to a Normal distribution
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
40
Some Background• Travel Utility, Reliability Ratio, and Real Options• Travel Cost and Travel Time• Penalty/Reward associated with Unreliability• Geometric Brownian Motion (GBM) w/ Drift• Random Walk and Binary Tree Representation• Binomial Distribution & Normal Distribution• GBM and Binary Tree Representation• Certainty‐Equivalent Conditions
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
41
Certainty‐Equivalent Conditions• What does certainty mean?
– Over a given time period , expected travel times do not increase at a rate higher than a certain tolerable threshold
• How certainty‐equivalent conditions are determined?
| 1| 1 ∆
∴1 ∆
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
42
p
1‐p
Proposed Valuation Approach• Obtain necessary data over a substantial time period (at least 6 months)
– Travel time data• Probe based• Converted from spot speed detectors
– Volume data• Characterize the travel time data
– Mean & Standard Deviation– Find out which random process model best describes the observed variability in data (GBM,
etc.)– Determine the longest trip time observed in data (95 percentile travel time)
• Use binary tree to represent travel time variability over time• Evaluate penalty/rewards of arriving earlier/later than expected at the end of
longest trip time• Calculate certainty‐equivalent probabilities and use them to discount future
penalty/reward values to determine insurance premiums at any intermediate point in time as well as at initial time
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
43
Forward TimeBinary Tree Construction
• q: probability based on “real‐world” observations
44L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Backward Time (Recursive)Reliability Valuation
p:probabilityreplicating“artificial”riskless/reliable/certainconditions
45L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
How is the proposed approach different from L11?
Proposed Approach L11
Analogy used? Insurance premium Insurance premium
What is being insured? Travel Time Travel Speed
What is being discounted? Travel Cost Travel Speed
Length of insurance policy? 95 percentile trip time 95 percentile trip time
What statistical process is used to describe travel time variations/unreliability?
Relaxed GBM (log‐normal dist.)
How forward/backward projections are described?
Binary Tree Closed form cumulative normal distribution
Penalty/reward evaluations? Relaxed Bilinear function
Certainty‐equivalent discounting of future policy value?
Fully described using “tolerance level” concept
Applicability? General (Monte CarloSimulation)
Special case (Black‐Scholes)
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
46
Binary Tree vs. Black‐Scholes
47L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Some Numerical Results• Maryland travel time data• VPP suite (probe based, provided by INRIX™)
– www.RITIS.org• 2011 data at one minute resolution• AM peak (7AM‐9AM)• PM peak (4PM‐6PM)• Five major corridors in the Baltimore/ Washington metro area
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
48
Major Corridors• I‐95 (b/w Washington and Baltimore beltways)
– 22 mile (21 minute)• I‐270 (Beltway to Frederick)
– 41 mile (42 minute)• I‐495 (I‐95 to I‐270 spur)
– 16 mile (18 minute)• MD‐295 (DC line to Baltimore)
– 29 mile (32 minute)• US‐29 (Beltway to I‐70)
– 21 mile (22 minute)
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
49
Comparisons• US‐29/I‐95/MD‐295
– Direction• Northbound• Southbound
– Peak Period• AM• PM
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
50
ComparisonsUS‐29/I‐95/MD‐295
Northbound
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Average Travel Time (Minute)
Rel
iabi
lity
Rat
io -
RR
(Uni
tless
)
AM Peak Period
I-95MD-295US-29
0 10 20 30 40 50 600
0.2
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1
Average Travel Time (Minute)
Rel
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Rat
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(Uni
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PM Peak Period
I-95MD-295US-29
0 5 10 15 20 25 300
0.1
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Length (Mile)
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io -
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(Uni
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AM Peak Period
I-95MD-295US-29
0 5 10 15 20 25 300
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1
Length (Mile)
Rel
iabi
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Rat
io -
RR
(Uni
tless
)
PM Peak Period
I-95MD-295US-29
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
51
ComparisonsUS‐29/I‐95/MD‐295
Southbound
0 5 10 15 20 25 30 35 40 450
0.2
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0.6
0.8
1
Average Travel Time (Minute)
Rel
iabi
lity
Rat
io -
RR
(Uni
tless
)
AM Peak Period
I-95MD-295US-29
0 5 10 15 20 25 30 35 400
0.1
0.2
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0.8
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Average Travel Time (Minute)
Rel
iabi
lity
Rat
io -
RR
(Uni
tless
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PM Peak Period
I-95MD-295US-29
0 5 10 15 20 25 300
0.2
0.4
0.6
0.8
1
Length (Mile)
Rel
iabi
lity
Rat
io -
RR
(Uni
tless
)
AM Peak Period
I-95MD-295US-29
0 5 10 15 20 25 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Length (Mile)
Rel
iabi
lity
Rat
io -
RR
(Uni
tless
)
PM Peak Period
I-95MD-295US-29
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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95 Percentile Travel Time vs.Average Travel Time
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70
80
90
100
Y=-0.291+1.320XR2=0.971
Average Travel Time (Minute)
95 P
erce
ntile
Tra
vel T
ime
(Min
ute)
Path Level / Across Days
AM PeakPM Peak
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Reliability Ratio (RR) vs.Average Travel Time
0 10 20 30 40 50 60 700
0.1
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Gompertz Function:
Y=1-e17.355(e-0.004X-1)
MSE=0.001
Average Travel Time (Minute)
Rel
iabi
lity
Rat
io -
RR
(U
nitl
ess)
Path Level / Across Days
AM PeakPM Peak
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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Estimated vs. ObservedReliability Ratio (RR)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
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Y=0.006+0.987XR2=0.98
Observed Reliability Ratio - RR (Unitless)
Estim
ated
Rel
iabi
lity
Rat
io -
RR
(Uni
tless
)
Path Level / Across Days
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
55
Summary Valuation Approach for Travel Time Reliability
– Data driven– Actuarial as opposed to perception‐based– Understandable/simple
• Exploits the ups and downs of travel time• Uses a Random Walk
– Flexible• Underlying process• Termination function
– Equivalent Solutions• Numerical methods, especially a binary tree • Closed form
56L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Potential Use for MD‐SHA• Value of Reliability
– Validate the currently adopted RR (0.75)– Specify a value/range of values for RR for different
• Highway modes (auto, truck)• Corridors/regions• Time of day (AM/PM peak)
• Tool to analyze travel time data and to evaluate customized RR– Input raw travel time data– Estimate travel time process parameters– Characterize travel time distribution and relevant metrics from its histogram– Perform hypothesis testing– Evaluate travel time insurance value and reliability ratios
• Annual Mobility Report– Reliability profile along significant corridors– Include unreliability cost estimates
• Maryland Statewide Transportation Model (MSTM)– Update volume‐delay functions considering certainty‐equivalent extra travel times– Potentially improve mode/route choice sub‐models’ performance
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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RELIABILITY RATIOS (RR)PATH LEVEL & INTERDAY (ACROSS DAYS)
CORRIDOR NAME: I495 CW
RR=0.75?
Subrat MahapatraTransportation Engineering ManagerOffice of Planning and Preliminary
EngineeringMaryland State Highway Administration
Thomas H. JacobsDirector
Kaveh FarokhiFaculty Research Assistant
Center for Advanced Transportation Technology (CATT)
University of MarylandCollege Park, MD 20742
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making 58
Frederick W. DuccaSenior Research Scientist
Sevgi ErdoganFaculty Research Associate
National Center for Smart Growth (NCSG)
University of MarylandCollege Park, MD 20742
List of Appendices• Option valuation (travel time vs. speed)• Binary tree vs. closed form (Black‐Scholes) solution
• Numerical example (binary tree’s convergence to BS)
• Corridor examples
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
59
Travel Time vs. Speed
Travel Time Process
•
• ∆ log ~ ∆ , ∆t
• ∆ ∆ ,
~ 0,1
Speed Process
•
• ∆ log ~ ∆ , ∆t
• ∆ ∆ ,~ 0,1
60
Trends: Same magnitude, but opposite signsStandard Deviations: Equal
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Travel Time vs. SpeedTravel Time ProcessBinomial Tree Representation
• 1 ∆
• ∆ ∆
• ∆ ∆
• ,– 1,… , ; 0,1,… ,
Speed ProcessBinomial Tree Representation
• 1 ∆
• ∆ ∆
• ∆ ∆
• ,– 1,… , ; 0,1,… ,
61
Probabilities: 1Factors: 1; 1
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Travel Time vs. SpeedTravel Time ProcessRisk Valuation
• , max , , 0– 0,1,… ,
• ∆
• ,, ,
∆– 1,… , 1; 0,1, … ,
Speed ProcessRisk Valuation
• , max,
, 0
– 0,1,… ,
• ∆
• ,, ,
∆– 1,… , 1; 0,1, … ,
62
Terminal Values: Note unconventional valuation in speed processProbabilities: Discounted expected values: 1; 1
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Binary Tree – Mathematical MagicLeads to Essentially Same Answer as other Formulations
63L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Example Valuation• A simple binary example
• 1; 1;∆ ⁄ 1• 0.2; 0.4
• ∆ ∆ 1.13
• ∆ ∆ 0.51
• 1 ∆ 0.25• 5%; 112
• ∆ 0.87
•∆
. ∗.
0.83
64
100
q
1‐q
113
51
?
p
1‐p
max 113 112,0 1
max 51 112,0 0
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Example Valuation• A simple binary example
• 1; 2;∆ ⁄ 0.5• 0.2; 0.4
• ∆ ∆ 1.15
• ∆ ∆ 0.65
• 1 ∆ 0.32• 5%; 112
• ∆ 0.74
•∆
. ∗ .. ∗ .
11.04
65
100
q
1‐q
133
43
115
6576
VOR ?
p
1‐p
21
0
15.25
00
L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Example Valuation• Black‐Scholes formula
• 1• 0.2; 0.4• 5%; 112
•⁄ . .
.0.042
• 0.042 0.4 1 0.358• 100 0.042 112 . 0.358 13.30
66L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Binary Tree vs. Black‐Scholes
67L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
Analysis Mode7:00 7:01 7:02 . . 9:00
Day 1
Day 2
Day 3
Day 4
Day 5
.
.
.
.
.
Across W
eek‐Da
ys
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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I‐495 Innerloop
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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I‐495 Outerloop
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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L35‐B Local Methods for Modeling, Economic Evaluation, Justification, and Use of the Value of Travel Time Reliability in Transportation Decision Making
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