Transcript Analyzing the Effects of Tolls and Operating Costs on
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 + 142 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
min
s
.
t
.
v a
a
0
v a s a
dx
i
j r
ij ar x ij r
r v a
x ij r
0
T ij x ij r
0
Generalized Cost Function Dummy variable for all links a in the network Number of vehicles from i to j
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 (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) No Solution converged?
Terminate Yes
Crux of Equilibrium: VDF function
• Bureau of Public Records Function
i t
1
i
x i C i
i
Capacity Free Flow Time
Crux of Equilibrium: VDF function
• Conical Volume Delay Function
f
(
x
) 2
where
2 1 2 2 1 2 ,
x x c
2
V C
2
and
1 1
c x
A Generalized Cost Delay Function
gc OD m
i
A m OD
VOT m
.
VDF
t a
,
Value of Time for mode m c a
,
PCE m x a
,..
FT a m
m m
M OD MT m i 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 ?
Key Variables
• Value of Time • Operating Costs • Volume Delay Curves – Travel Time Savings (Urban vs. Rural)
Toll Corridor
Toll Corridor
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 10-12 cents per minute ($7.2 per hour) for rural interstate travel in 2005 dollars
Variations in Value of Time for Auto $18 $16 $14 $12 $10 $8 $6 $4 $2 $0 Auto Austin DFW El Paso TTI per Auto TTI per Person $20 $15 $10 $5 $0 Austin HBW HBS HBSCH HBO WBO OBO
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
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 $0.40
$0.35
$0.30
$0.25
$0.20
$0.15
$0.10
$0.05
$0.00
All Urban Rural Combination Passenger Car Cash Rate per Mile 5-axle vehicle Cash Rate per Mile
Nationwide Toll Facilities Averages (USA - 75 Facilities)
Toll Sensitivity Curve (12 runs)
UE BPR
Sensitivities to Toll
Percentage of the total length of the corridor which has traffic more than 1000 vehicles for the considered toll rate
UE Assessment
• Fixed point equilibrium cut off • The same generalized cost function for all links (toll or non toll) • Perfect perception of time and costs along each route by all drivers.
Stochastic User Equilibrium
• No perfect information about network characteristics • Different travel costs perception • Eliminates “zero volume” roads • Implemented in TransCAD (utilizes Method of Successive Averages) • Requires large number of iterations and hence a longer run time
Stochastic User Equilibrium
• Utility Maximization.
• Random error term added to the utility to mimic differences in perceived costs and imperfect information.
U i l V i l
i l Randomly distributed error
i
I Deterministic Utility E
i
0
All influencing factors
Stochastic User Equilibrium
P i
• Estimate probability Pr
U i
U k
,
k
I
i
I
0
P i i I
1
P i
1
i
I
1 • Multinomial Logit, Multinomial Probit etc.
Stochastic User Equilibrium (8 runs)
Stochastic User Equilibrium % length of corridor > 1000 volume
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0.01
0.02
0.03
0.04
0.08
0.12
0.16
Toll ($ per mile)
0.2
0.24
0.28
0.32
0.36
UE Toll SUE Toll
50,000 45,000 40,000 35,000 30,000 25,000 20,000 15,000 10,000 5,000 0 0
Conical Volume Delay Function (12 runs) Comparison of different runs
0.05
0.1
0.15
0.2
Toll ($ per mile)
0.25
0.3
0.35
0.4
UE BPR SUE UE CONICAL
Conical Volume Delay Function % length of corridor with V>1000
100% 90% 80% 70% 60%
% of length
50% 40% 30% 20% 10% 0% 0.01
0.02
0.03
0.04
0.08
0.12
Toll ($ per mile)
0.16
0.2
0.24
0.28
0.32
0.36
UE BPR SUE BPR UE CONICAL
Operating Cost Analysis
Operating Cost Analysis Operating Cost
124,000,000 123,500,000 123,000,000
VMT
122,500,000 122,000,000 121,500,000 121,000,000 120,500,000 0.04
0.08
0.12
0.16
0.2
0.24
Operating Cost ($ per mile)
0.28
0.32
0.36
Operating Cost Analysis Variation across functional class
6.0% 4.0% 2.0% 0.0% -2.0% -4.0% -6.0% 0.04
0.08
0.12
0.16
0.2
0.24
Operating Cost ($ per mile)
0.28
0.32
0.36
IH SH US Local FM
% change in VMT
IH US SH FM Local
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 http://www.wilbursmith.com