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Value of Time in Highway Assignment

Overview

The Travel Model Two (TM2) highway assignment system uses value of time (VOT) parameters to convert monetary costs into time-equivalent units for generalized cost calculations. This enables the traffic assignment algorithm to find equilibrium paths that balance travel time, distance, and monetary costs (tolls and operating costs).

Value of Time Parameters

Primary Configuration

Default Value of Time: $18.93/hour (2010 dollars)

  • Source: Defined in tm2py.config.py
  • Configuration Parameter: highway.classes[].value_of_time
  • Units: US dollars per hour (2010 base year)
  • Application: Used across all highway assignment components

Supporting Parameters

Auto Operating Cost: 17.23 cents/mile (2010 dollars) - Configuration Parameter: highway.classes[].operating_cost_per_mile - Purpose: Vehicle operating cost for distance-based cost calculations

Conversion Factor: 0.6 - Purpose: Converts dollars per hour to minutes per cent - Formula: perception_factor = 0.6 / value_of_time

Implementation in Highway Assignment

In the MAZ-to-MAZ assignment (highway_maz.py):

vot = self.config.value_of_time  # $18.93/hour
op_cost = self.config.operating_cost_per_mile  # 17.23 cents/mile

# Link cost formula (in minutes):
link_cost = travel_time + (0.6 / vot) * (link_length * op_cost)

Components: - travel_time: Link travel time in minutes - (0.6 / vot): Conversion factor (≈ 0.0317 minutes/cent) - link_length * op_cost: Distance-based operating cost in cents

2. Traffic Assignment Perception Factor

In the EMME traffic assignment specification (highway_emme_spec.py):

perception_factor = 0.6 / self.class_config.value_of_time
# With default VOT: 0.6 / 18.93 = 0.0317 minutes/$0.01

Purpose: - Converts link costs (in cents) to time units for path building - Used in EMME’s SOLA traffic assignment algorithm - Ensures consistent generalized cost calculations

3. Drive Access Skim Generation

In transit drive access calculations (drive_access_skims.py):

value_of_time = 18.93  # $/hour
vot_factor = 0.6 / value_of_time  # minutes/cents conversion

# Generalized cost calculation:
total_cost = drive_time + walk_time + vot_factor * (operating_cost + toll_cost)

Class-Specific Configurations

Vehicle Class Differentiation

The system supports different VOT values for different vehicle classes:

Class Type Default VOT Description
Drive Alone (DA) $18.93/hour Single occupant vehicles
Shared Ride 2 (SR2) $18.93/hour Two-person carpools
Shared Ride 3+ (SR3) $18.93/hour Three+ person carpools
Trucks Configurable Commercial vehicles

Configuration Structure

[[highway.classes]]
name = "da"
description = "drive alone"
value_of_time = 18.93  # $ / hr
operating_cost_per_mile = 17.23  # cents / mile
mode_code = "d"
excluded_links = ["is_sr2", "is_sr3"]

Mathematical Framework

Generalized Cost Function

The highway assignment uses a generalized cost function that combines time and monetary costs:

GC = α₁ × Time + α₂ × Distance + α₃ × Tolls + α₄ × Operating_Cost

Where: - α₁ = 1.0 (time coefficient) - α₂ = (0.6 / VOT) × operating_cost_per_mile (distance coefficient) - α₃ = (0.6 / VOT) (toll coefficient) - α₄ = (0.6 / VOT) (operating cost coefficient)

Unit Consistency

Time Units: Minutes Distance Units: Miles (converted from feet in network) Cost Units: Cents (2010 dollars) VOT Units: Dollars per hour (2010 dollars)

Conversion Relationships: - 1 dollar = 100 cents - 1 hour = 60 minutes - Conversion factor = 60 minutes/hour ÷ 100 cents/dollar = 0.6

Equilibrium Assignment Process

Path Building

  1. Initialize: Calculate link costs using VOT-adjusted generalized cost
  2. Shortest Paths: Find minimum generalized cost paths for each O-D pair
  3. Load Traffic: Assign demand to shortest paths
  4. Update Costs: Recalculate link travel times based on volume-delay functions
  5. Iterate: Repeat until convergence

Convergence Criteria

The assignment reaches equilibrium when the difference in generalized costs between iterations falls below specified thresholds, ensuring that: - No traveler can unilaterally reduce their generalized cost by changing routes - The system reflects realistic trade-offs between time and money

Sensitivity and Validation

VOT Sensitivity

The highway assignment results are sensitive to VOT values: - Higher VOT: Greater willingness to pay tolls to save time - Lower VOT: More price-sensitive route choice, avoiding tolls - Impact: Affects traffic distribution on toll vs. free facilities

Calibration Considerations

Observed Behavior: VOT should reflect regional travel behavior patterns Income Distribution: May warrant income-stratified VOT values Facility Usage: Validation against observed toll facility usage patterns

Technical Implementation

Code Structure

tm2py/components/network/highway/
├── highway_assign.py      # Main assignment coordination
├── highway_maz.py         # MAZ-to-MAZ shortest paths  
├── highway_emme_spec.py   # EMME assignment specification
├── drive_access_skims.py  # Transit drive access costs
└── toll_choice.py         # Toll vs. non-toll choice

Key Classes and Methods

HighwayAssignmentConfig: Configuration data class for VOT parameters EmmeHighwayClassSpec: Generates EMME assignment specifications HighwayMAZSkims: Calculates MAZ-to-MAZ generalized costs

Last Updated: November 2025
Model Version: Travel Model Two v2.2
Authors: MTC Staff & GitHub Copilot