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

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.

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

SALIENT FEATURES

288 COUNTIES COVERED (Including some outside Texas)

4600 Zones External Stations, 323,350 square miles more than 35 million population

106,000 miles of network, 54,500 links with over 1 billion VMT

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

Four Step Model Freight Trip Generation using regression equations developed based on Reebie and WEFA Freight Trip Distribution: ATOM2 Mode Choice: Logit

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

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)

User Equilibrium Equation Dummy variable Number of vehicles from i to j Generalized Cost Function

Implementation Compute shortest paths for every O-D minimizing GC (Sol curr ) Assign all O-D trips to shortest path (Sol temp ) Sol curr = (1-λ) Sol curr + λ Sol temp, λ chosen to minimize new objective function (Frank-Wolfe algorithm) Solution converged? Compute GC for each link using seed values (Free flow times) Compute GC for each link with new solution No Terminate Yes

Crux of Equilibrium: VDF function Bureau of Public Records Function Free Flow Time Capacity

Crux of Equilibrium: VDF function Conical Volume Delay Function

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

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 ?

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

Toll Corridor

A high speed (>=80 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)

Value of Time for Auto Urban versus Intercity Markets Income / Wage Rate Distribution Rural / Purpose Segmentation and Distribution Average cents per minute ($7.2 per hour) for rural interstate travel in 2005 dollars

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

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 $ $ 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

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

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

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

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

Typical Toll Rates Ranges Nationwide Toll Facilities Averages (USA - 75 Facilities) 2004 Cash Toll Rates per mile

Toll Sensitivity Curve (12 runs) UE BPR

Sensitivities to Toll Percentage of the total length of the corridor which has traffic more than 1000 vehicles for the considered toll rate

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.

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

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

Stochastic User Equilibrium Estimate probability Multinomial Logit, Multinomial Probit etc.

Stochastic User Equilibrium (8 runs)

Stochastic User Equilibrium

Conical Volume Delay Function (12 runs)

Conical Volume Delay Function

Operating Cost Analysis

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.

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.

QUESTIONS / COMMENTS WILBUR SMITH ASSOCIATES