Multimodal Bicriterion Highway Assignment for Toll Roads Jian Zhang Andres Rabinowicz Jonathan Brand

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Multi-modal Bi-criterion Highway Assignment for
Toll RoadsJian Zhang Andres RabinowiczJonathan
BrandonCaliper Corporation5-9-2007
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Traditional Traffic Assignment

• Assuming uniformity among users
• Access to network
• Link cost function (VDF)
• Value of time (VOT)
• Out-of-pocket cost

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Advantages of MMA(multi-modal assignment)

• Simulating user variety in
• Vehicle type (car,bus,light / heavy trucks, etc.)
• Occupancy(HOV,LOV)
• Driver characteristics (cost or time sensitive)
• Class-specific VOTs

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Advantages of MMA

• Simulating vehicle-type-specific network
  accessibility
• Lane usage (HOV, HOT)
• Height/Weight limits
• Toll charge
• Access to network status info.

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MMA Model Analysis

• Standardized volume
• vak total PCE on link a for type k
• ak PCE conversion factor for type k
• Cost function based on
• standardized volume
• cak cost for type k (e.g. toll payment)
• ßk VOT for type k

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T2 Traffic Assignment Model

• Developed by Robert Dial, features include
• VOT as a random variable in calculating link
  cost
• P path,a random VOT variable with known
  probability density
• Bi-criterion multiple path building
• Fast path calculation using Efficient Frontier
• One user class (K1)

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New MMA-T2 Model

• Combining MMA and T2
• Multiple user classes
• VOT of each user class as a random variable with
  its unique mean and distribution
• Bi-criterion multiple path building for each user
  type

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MMA-T2 Model Advantages

• Representing various user income levels
• Considering VOT variation within each user group
• Allowing more realistic simulation of user
  response to different highway toll policies.

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MMA-T2 Model Structure(variational inequality )
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MMA-T2 Model Solution
Model Solution Equilibrium Conditions
gpk travel cost on path p for type k uwk min.
travel cost between w-th OD pair for type k fpk
type k volume on path p
Note Only min.-cost paths have flow, which
satisfies multi-modal traffic assignment
equilibrium condition
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MMA-T2 Model Solution Algorithm
Step 0 Initialization do non-equilibrium T2
assignment for each user type Step 1 Renew link
times Step 2 Conduct non-equilibrium T2
assignment for each user type based on new link
times so as to get auxiliary link flows. Step
3 Compute step size and combine current and
auxiliary link flows (MSA) Step 4 Check
convergence. Stop if converged, otherwise go to
Step 1
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Example 1 Network
Capacity and Free-flow Speed
Free-flow Time and Cost
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Example 1 Users
VOT Probability Density
O-D Demand
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Example 1 Results
Class 2 Flows
Class 1 Flows
Class 3 Flows
Total Flows
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Example 2 Network
Mass. Highway Network (5627 links, 2025 nodes,
106 toll links)
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Example 2 User Demands
Classes Car, Light Truck, Heavy Truck of O-D
pairs 19,460 Total demand 416,426 (70, 23,
7)
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Example 2 Toll Scenarios
Original Toll Matrices
Toll Scenarios 1 original 2 original
2 3 original 3 4 original 4
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Example 2 User VOT DistributionScenarios
SD 5
SD 10
SD 15
Pearson Type III Distribution Means Car 20,
Light Truck 40, Heavy Truck 60 (/hr)
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Example 2 Result Toll Road Usages
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Example 2 Results Average Trip Time
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Observations

• When toll charge is high, MMA model tends to
  underestimate toll road usages than predicted by
  MMA-T2 model
• When toll charge is high, MMA model tends to
  overestimate average trip times than forecast by
  MMA-T2 model
• As user VOT distributions become wider, toll road
  usages increase and average trip times drop

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Conclusion

• MMA-T2 model has the advantages of both MMA and
  T2 (bi-criterion multi-path building,
  multi-user-class specifications, etc.)
• The new model is able to capture heterogeneous
  users response to toll charges for a more
  accurate evaluation of different toll scenarios

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Thanks!