L35B-SHRP2 TCC for Reliability Workshop 10302013-consolidated … › uploaded_files ›...

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

• 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

• 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.

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.

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

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

Congestion Relief Project DM• Step 2 – Analysis

– Review– Simulate– B/C

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

• 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

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%

• Step 4 –Assessment

Prioritization ProcessInitial Lessons Learned

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

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

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

0 20 40 60 80 100 1200

TIME (MINUTES)

AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 2 4 6 8 10 12 14 160

LENGTH (MILES)

0 2 4 6 8 10 12 14 160

LENGTH (MILES)

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

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)

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)

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

Overview of L11• Let’s take another look at the options theoreticapproach for travel time reliability valuation

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

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 !

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)

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

Penalty/Reward Function

The Random Process• Geometric Brownian Motion (GBM) w/ Drift

; ~ ≡

∆ ~ 2 ∆ , ∆

2 ∆ ∆ ,

• Parameters:– : long‐term trend– : standard deviation

0 2 4 6 8 10 12 14 16 18 200

ALPHA=0.05SIGMA=0.1

Time (Minute)

Geometric Brownian Motion (GBM) Process

Travel TimeTrendLower 95% CIUpper 95% CI

(Dixit & Pindyck, 1993)

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

Random WalkPossible Waypoints and Their Probabilities

• 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

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

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 ∆

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

Forward TimeBinary Tree Construction

• q: probability based on “real‐world” observations

Backward Time (Recursive)Reliability Valuation

p:probabilityreplicating“artificial”riskless/reliable/certainconditions

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)

Binary Tree vs. Black‐Scholes

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

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)

Comparisons• US‐29/I‐95/MD‐295

– Direction• Northbound• Southbound

– Peak Period• AM• PM

ComparisonsUS‐29/I‐95/MD‐295

Northbound

0 5 10 15 20 25 30 350

Average Travel Time (Minute)

AM Peak Period

I-95MD-295US-29

0 10 20 30 40 50 600

PM Peak Period

I-95MD-295US-29

0 5 10 15 20 25 300

Length (Mile)

AM Peak Period

I-95MD-295US-29

0 5 10 15 20 25 300

Length (Mile)

PM Peak Period

I-95MD-295US-29

ComparisonsUS‐29/I‐95/MD‐295

Southbound

0 5 10 15 20 25 30 35 40 450

AM Peak Period

I-95MD-295US-29

0 5 10 15 20 25 30 35 400

PM Peak Period

I-95MD-295US-29

0 5 10 15 20 25 300

Length (Mile)

AM Peak Period

I-95MD-295US-29

0 5 10 15 20 25 300

Length (Mile)

PM Peak Period

I-95MD-295US-29

95 Percentile Travel Time vs.Average Travel Time

0 10 20 30 40 50 60 700

Y=-0.291+1.320XR2=0.971

Path Level / Across Days

AM PeakPM Peak

Reliability Ratio (RR) vs.Average Travel Time

0 10 20 30 40 50 60 700

Gompertz Function:

Y=1-e17.355(e-0.004X-1)

MSE=0.001

AM PeakPM Peak

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

Y=0.006+0.987XR2=0.98

Observed Reliability Ratio - RR (Unitless)

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

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

0 20 40 60 80 100 1200

TIME (MINUTES)

AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 2 4 6 8 10 12 14 160

LENGTH (MILES)

0 2 4 6 8 10 12 14 160

LENGTH (MILES)

RR=0.75?

Subrat MahapatraTransportation Engineering ManagerOffice of Planning and Preliminary

EngineeringMaryland State Highway Administration

smahapatra@sha.state.md.us410.545.5649

Thomas H. JacobsDirector

tjacobs@umd.edu301.405.7328

Kaveh FarokhiFaculty Research Assistant

kfarokhi@umd.edu301.405.1352

Center for Advanced Transportation Technology (CATT)

University of MarylandCollege Park, MD 20742

Frederick W. DuccaSenior Research Scientist

fducca@umd.edu301.405.1945

Sevgi ErdoganFaculty Research Associate

serdogan@umd.edu301.405.9877

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

Travel Time vs. Speed

Travel Time Process

• ∆ log ~ ∆ , ∆t

• ∆ ∆ ,

Speed Process

• ∆ log ~ ∆ , ∆t

• ∆ ∆ ,~ 0,1

Trends: Same magnitude, but opposite signsStandard Deviations: Equal

Travel Time vs. SpeedTravel Time ProcessBinomial Tree Representation

• 1 ∆

• ∆ ∆

• ,– 1,… , ; 0,1,… ,

Speed ProcessBinomial Tree Representation

• 1 ∆

• ∆ ∆

• ,– 1,… , ; 0,1,… ,

Probabilities: 1Factors: 1; 1

Travel Time vs. SpeedTravel Time ProcessRisk Valuation

• , max , , 0– 0,1,… ,

• ∆

• ,, ,

∆– 1,… , 1; 0,1, … ,

Speed ProcessRisk Valuation

• , max,

– 0,1,… ,

• ∆

• ,, ,

∆– 1,… , 1; 0,1, … ,

Terminal Values: Note unconventional valuation in speed processProbabilities: Discounted expected values: 1; 1

Binary Tree – Mathematical MagicLeads to Essentially Same Answer as other Formulations

Example Valuation• A simple binary example

• 1; 1;∆ ⁄ 1• 0.2; 0.4

• ∆ ∆ 1.13

• ∆ ∆ 0.51

• 1 ∆ 0.25• 5%; 112

• ∆ 0.87

•∆

. ∗.

max 113 112,0 1

max 51 112,0 0

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

•∆

. ∗ .. ∗ .

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

Binary Tree vs. Black‐Scholes

Analysis Mode7:00 7:01 7:02 . . 9:00

Across W

eek‐Da

I‐95 North

0 5 10 15 20 250

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: I95 NB (LENGTH = 22.0677 MILES)

AM PEAKPM PEAK

I‐95 North

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 5 10 15 20 250

LENGTH (MILES)

0 5 10 15 20 250

LENGTH (MILES)

CORRIDOR NAME: I95 NB

I‐95 South

0 5 10 15 20 250

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: I95 SB (LENGTH = 21.797 MILES)

AM PEAKPM PEAK

I‐95 South

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 5 10 15 20 250

LENGTH (MILES)

0 5 10 15 20 250

LENGTH (MILES)

CORRIDOR NAME: I95 SB

I‐270 North

0 5 10 15 20 25 30 35 40 450

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: I270 NB (LENGTH = 40.9652 MILES)

AM PEAKPM PEAK

I‐270 North

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 5 10 15 20 25 30 35 40 450

LENGTH (MILES)

0 5 10 15 20 25 30 35 40 450

LENGTH (MILES)

CORRIDOR NAME: I270 NB

I‐270 South

0 5 10 15 20 25 30 35 40 450

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: I270 SB (LENGTH = 41.1712 MILES)

AM PEAKPM PEAK

I‐270 South

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 5 10 15 20 25 30 35 40 450

LENGTH (MILES)

0 5 10 15 20 25 30 35 40 450

LENGTH (MILES)

CORRIDOR NAME: I270 SB

I‐495 Innerloop

0 2 4 6 8 10 12 14 160

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: I495 CW (LENGTH = 15.0123 MILES)

AM PEAKPM PEAK

I‐495 Innerloop

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 2 4 6 8 10 12 14 160

LENGTH (MILES)

0 2 4 6 8 10 12 14 160

LENGTH (MILES)

I‐495 Outerloop

0 2 4 6 8 10 12 14 16 180

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: I495 CCW (LENGTH = 16.0245 MILES)

AM PEAKPM PEAK

I‐495 Outerloop

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 2 4 6 8 10 12 14 16 180

LENGTH (MILES)

0 2 4 6 8 10 12 14 16 180

LENGTH (MILES)

CORRIDOR NAME: I495 CCW

MD‐295 North

0 5 10 15 20 25 300

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: MD295 NB (LENGTH = 29.4831 MILES)

AM PEAKPM PEAK

MD‐295 North

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 5 10 15 20 25 300

LENGTH (MILES)

0 5 10 15 20 25 300

LENGTH (MILES)

CORRIDOR NAME: MD295 NB

MD‐295 South

0 5 10 15 20 25 300

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: MD295 SB (LENGTH = 29.3012 MILES)

AM PEAKPM PEAK

MD‐295 South

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 5 10 15 20 25 300

LENGTH (MILES)

0 5 10 15 20 25 300

LENGTH (MILES)

CORRIDOR NAME: MD295 SB

US‐29 North

0 5 10 15 20 250

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: US29 NB (LENGTH = 20.6504 MILES)

AM PEAKPM PEAK

US‐29 North

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 5 10 15 20 250

LENGTH (MILES)

0 5 10 15 20 250

LENGTH (MILES)

CORRIDOR NAME: US29 NB

US‐29 South

0 5 10 15 20 250

LENGTH (MILES)

AVERAGE TRAVEL TIMESCORRIDOR NAME: US29 SB (LENGTH = 20.7763 MILES)

AM PEAKPM PEAK

US‐29 South

0 20 40 60 80 100 1200

TIME (MINUTES)

)AM PEAK PERIOD

0 20 40 60 80 100 1200

TIME (MINUTES)

PM PEAK PERIOD

0 5 10 15 20 250

LENGTH (MILES)

0 5 10 15 20 250

LENGTH (MILES)

CORRIDOR NAME: US29 SB

L35B-SHRP2 TCC for Reliability Workshop 10302013-consolidated … › uploaded_files ›...

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BROCHURE L30B L35B pro DE 25 3 430 5588 - … · The smoothness of the hydraulic control valve provides precise control during all hydraulic operations. ... potential with the Z-bar

ApresentaçãO Tcc

Old Company Name in Catalogs and Other Documentspdf.searchdatasheet.com/datasheets-1/renesas_electronics/R5F2L3... · Old Company Name in Catalogs and Other Documents ... R8C/L35B

Www.fateczl.edu.Br TCC 2009-1 Tcc-221

Tcc cooling

TCC Publicidade e Propaganda // Book TCC // 2014 - Uninove