Analyzing the Effects of Tolls and Operating Costs on Statewide Travel Patterns

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Analyzing the Effects of Tolls and Operating
Costs on Statewide Travel Patterns
Vishal Gossain
Thomas A. Williams Joseph P. Savage
Jr. Christopher E. Mwalwanda
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OBJECTIVES

• Illustrate the application of the Generalized
  Cost Function (GCF) as a proxy to a toll
  diversion curve
• Investigate the use of Operating Costs in the GCF
• Highlight pros and cons of implementing the GCF
  for statewide modeling.
• The analysis presented here does not represent
  the WSA procedure for toll based revenue
  estimation.

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MODEL USED

• Texas Statewide Analysis Model (Texas Department
  of Transportation)
• Four Step Travel Demand Model
• Implemented in TransCAD using GISDK programming

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SALIENT FEATURES
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288 COUNTIES COVERED (Including some
outside Texas)
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4600 Zones 142 External Stations, 323,350
square miles
more than 35 million
population
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106,000 miles of network, 54,500 links with over
1 billion VMT
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Four Step Model

• 2030 horizon year chosen, base year data grown to
  2030 based on TDC forecasts and disaggregated.
• Passenger Trip Generation TripCAL5
• Passenger Trip Distribution ATOM2
• Passenger Mode Choice Nested logit

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Four Step Model

• Freight Trip Generation using regression
  equations developed based on Reebie and WEFA
• Freight Trip Distribution ATOM2
• Mode Choice Logit

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Assignments

• All or Nothing Assignment
• STOCH Assignment
• Incremental Assignment
• Capacity Restraint
• User Equilibrium
• Stochastic User Equilibrium
• System Optimum Assignment

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User Equilibrium Assignment

• TransCAD Multi Modal Multi Class Assignment
  utilized.
• All travelers have identical perceptions of time
  and cost.
• Equilibrium problem No traveler can reduce
  his/her travel time by switching to another path
  (Wardrop conditions)

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User Equilibrium Equation
Generalized Cost Function
Dummy variable
Number of vehicles from i to j
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Implementation
Compute GC for each link using seed values (Free
flow times)
Compute GC for each link with new solution
Compute shortest paths for every O-D minimizing
GC (Solcurr)
Assign all O-D trips to shortest path (Soltemp)
Solcurr (1-?) Solcurr ? Soltemp , ? chosen to
minimize new objective function (Frank-Wolfe
algorithm)
No
Solution converged?
Yes
Terminate
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Crux of Equilibrium VDF function

• Bureau of Public Records Function

Capacity
Free Flow Time
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Crux of Equilibrium VDF function

• Conical Volume Delay Function

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A Generalized Cost Delay Function
Value of Time for mode m
Passenger Car Equivalent
Volume Delay Function
Toll for Section i and mode m
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Toll Sensitivity

• What is the current and anticipated demand in the
  corridor?
• Toll Sensitivity as a proxy to potential demand
• How to incorporate sensitivities related to
  willingness to pay operating cost ?

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Key Variables

• Value of Time
• Operating Costs
• Volume Delay Curves Travel Time Savings (Urban
  vs. Rural)

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Toll Corridor
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Toll Corridor
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Toll Corridor

• A high speed (gt80 mph) competing toll corridor
• Separate Auto only (6 lanes) and Truck only
  Routes (4 lanes)
• Separate Toll Rates for Auto and Truck
• Limited Access (provided to only FM and above
  category roadways)

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Value of Time for Auto

• Urban versus Intercity Markets
• Income / Wage Rate Distribution
• Rural / Purpose Segmentation and Distribution
• Average 10-12 cents per minute (7.2 per
  hour) for rural interstate travel in 2005 dollars

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Variations in Value of Time for Auto
2004 Value of Time per Hour
2004 Value of Time per Hour
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Value of Time for Trucks

• Commercial Vehicle/Commodity Composition
• Fleet/Shipper versus Independent Operator
• Just-in-Time versus Flexible Scheduling
• Long versus Short Haul
• 26.7 per hour
• 17.4 - 22.6 per hour
• 23.4 per hour based on logit model
• Adopted Value of 42 cents per minute (25.2 per
  hour) in 2005 dollars

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Operating Costs

• Helps to control utilization of unrealistic paths
  compared to a pure time based GC function
• Full Costs versus Perceived Costs

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Operating Costs

• Direct Costs
• Importance of fuel costs with the current
  volatility in fuel prices.
• Indirect/Hidden Costs
• Maintenance (tires, oil and other work)
• Unanticipated repairs
• Depreciation in the value of the vehicle
• Depends on speed (magnitude and duration)
• Depends on pavement roughness

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Operating Costs

• 15.3 cents per mile recommended for auto and 43.4
  cents recommended for trucks
• City Driving conditions (19.1 cents and 52.9
  cents respectively)
• Poor pavement quality (17.9 cents and 48.9 cents)
• All costs mentioned in 2003 dollars 14 cents per
  mile for auto and 42 cents per mile for trucks
  used in 2005 dollars

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Modeling Criteria

• Values of Time and Operating Costs based on
  overall market averages
• Toll rates set at 0 to 30 cents per mile
• UE Assignment, BPR VDF
• Optimal number of iterations and convergence
  criteria

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Typical Toll Rates Ranges
2004 Cash Toll Rates per mile
Nationwide Toll Facilities Averages (USA - 75
Facilities)
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Toll Sensitivity Curve (12 runs)
UE BPR
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Sensitivities to Toll
Percentage of the total length of the corridor
which has traffic more than 1000 vehicles for the
considered toll rate
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UE Assessment

• Fixed point equilibrium cut off
• The same generalized cost function for all links
  (toll or non toll)
• Perfect perception of time and costs along each
  route by all drivers.

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Stochastic User Equilibrium

• No perfect information about network
  characteristics
• Different travel costs perception
• Eliminates zero volume roads
• Implemented in TransCAD (utilizes Method of
  Successive Averages)
• Requires large number of iterations and hence a
  longer run time

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Stochastic User Equilibrium

• Utility Maximization.
• Random error term added to the utility to mimic
  differences in perceived costs and imperfect
  information.

Randomly distributed error
Deterministic Utility
All influencing factors
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Stochastic User Equilibrium

• Estimate probability

• Multinomial Logit, Multinomial Probit etc.

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Stochastic User Equilibrium (8 runs)
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Stochastic User Equilibrium
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Conical Volume Delay Function (12 runs)
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Conical Volume Delay Function
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Operating Cost Analysis
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Operating Cost Analysis
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Operating Cost Analysis
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SUMMARY

• Toll road modeling using statewide models has its
  limitations.
• Inclusion of operating costs is beneficial and
  requires further analysis.
• Different assignment techniques should be
  evaluated on a case by case basis.
• The analysis presented here does not represent
  the WSA procedure for toll based revenue
  estimation.

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SUMMARY

• A single Generalized Cost function alone may not
  be adequate to capture the differences in the
  elasticity associated with tolls and travel
  times.
• Volume delay functions (reflecting adequate delay
  in urban vs rural areas) and GC function should
  be carefully considered and analyzed on a case by
  case basis.

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QUESTIONS / COMMENTS

• WILBUR SMITH ASSOCIATES
• http//www.wilbursmith.com