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Highway Skimming and Assignment

The traffic assignment for the SANDAG model is a 15-class assignment with generalized cost on links and BPR-type volume-delay functions which include capacities on links and at intersection approaches. The assignment is run using the fast-converging Second-Order Linear Approximation (SOLA) method in Emme to a relative gap of 5×10⁻⁴. The per-link fixed costs include toll values and operating costs which vary by class of demand (see Table x for the complete list of classes). Assignment matrices and resulting network flows are always in PCE.

Table 1. List of traffic demand classes and key class parameter values

Name Mode VOT ($0.01/min) PCE Cost Attribute
SOV_NT_L s 8.81 @cost_auto
SOV_TR_L S 8.81 @cost_auto
HOV2_L H 8.81 @cost_hov2
HOV3_L I 8.81 @cost_hov3
SOV_NT_M s 18 @cost_auto
SOV_TR_M S 18 @cost_auto
HOV2_M H 18 @cost_hov2
HOV3_M I 18 @cost_hov3
SOV_NT_H s 85 @cost_auto
SOV_TR_H S 85 @cost_auto
HOV2_H H 85 @cost_hov2
HOV3_H I 85 @cost_hov3
TRK_L T 67 1.3 @cost_lgt_truck
TRK_M M 68 1.5 @cost_med_truck
TRK_H V 89 2.5 @cost_hvy_truck

Volume-delay Functions

The volume-delay functions are specified as open-ended algebraic expressions supporting standard functions. The VDF functions for SANDAG are a modified BPR of the form:

\[ T = T_0 \cdot \left(1 + \alpha_1 \left(\frac{\text{FLOW} + \text{PRELOAD}}{\text{CAPACITY}}\right)^{\beta_1} \right) + \frac{\text{CYCLE}}{2} (1 - \text{GC})^2 \cdot \left(1 + \alpha_2 \left(\frac{\text{FLOW} + \text{PRELOAD}}{\text{INT_CAPACITY}}\right)^{\beta_2} \right) \]

Where:

  • T0 is the free-flow travel time along the link in minutes
  • ALPHA1, BETA1, ALPHA2, and BETA2 are BPR calibration terms
  • FLOW is the assigned flow from the traffic demand in PCEs
  • PRELOAD is the background volume from transit vehicles in PCEs
  • CAPACITY is the link mid-block capacity
  • INT_CAPACITY is the total intersection approach capacity in PCEs
  • CYCLE is the signal cycle length in minutes
  • GC is the green-to-cycle length for the link approach

Attributes:

  • Attribute keyword for FLOW: volau
  • Attribute for PRELOAD: volad
    • This is calculated from the transit itineraries, their frequency, and the length of the period and is also stored in link data 2 (ul2)
  • T0: link data 1 (ul1)
  • CAPACITY: link data 2 (ul3)
  • GC: @green_to_cycle, cross-referenced by el1
  • INT_CAPACITY: @capacity_inter, cross-referenced by el3
  • CYCLE: 1.25, 1.5, 2.0, or 2.5
  • ALPHA1: always 0.8
  • BETA1: 5.5 or 4
  • ALPHA2: 6.0 or 4.5
  • BETA2: always 2

With these global parameters, there are 7 total volume-delay functions:

  • fd10 for freeways and links which do not end at an intersection:
\[ \text{ul1} \cdot \left(1.0 + 0.24 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{ul3}}\right)^{5.5} \right) \]
  • fd20 for local collector and lower intersection and stop-controlled approaches:
\[ \text{ul1} \cdot \left(1.0 + 0.8 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{ul3}}\right)^4 \right) + \frac{1.25}{2} \cdot (1 - \text{el1})^2 \cdot \left(1 + 4.5 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{el3}}\right)^2 \right) \]
  • fd21 for collector intersection approaches:
\[ \text{ul1} \cdot \left(1.0 + 0.8 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{ul3}}\right)^4 \right) + \frac{1.5}{2} \cdot (1 - \text{el1})^2 \cdot \left(1.0 + 4.5 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{el3}}\right)^2 \right) \]
  • fd22 for major arterial and major or prime arterial intersection approaches:
\[ \text{ul1} \cdot \left(1.0 + 0.8 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{ul3}}\right)^4 \right) + \frac{2.0}{2} \cdot (1 - \text{el1})^2 \cdot \left(1.0 + 4.5 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{el3}}\right)^2 \right) \]
  • fd23 for primary arterial intersection approaches:
\[ \text{ul1} \cdot \left(1.0 + 0.8 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{ul3}}\right)^4 \right) + \frac{2.5}{2} \cdot (1 - \text{el1})^2 \cdot \left(1.0 + 4.5 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{el3}}\right)^2 \right) \]
  • fd24 for metered ramps:
\[ \text{ul1} \cdot \left(1.0 + 0.8 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{ul3}}\right)^4 \right) + \frac{2.5}{2} \cdot (1 - \text{el1})^2 \cdot \left(1.0 + 6.0 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{el3}}\right)^2 \right) \]
  • fd25 for freeway node approach (AM and PM only):
\[ \text{ul1} \cdot \left(1.0 + 0.6 \cdot \left(\frac{\text{volau} + \text{volad}}{\text{ul3}}\right)^4 \right) \]

Traffic Skims and Results

The traffic skims are calculated by fixing the flows and running a second zero-iteration assignment, which computes the O-D skim values using path analyses. The total generalized cost, travel time, and distance are computed for all classes, as well as the toll cost, HOV facility distance, and managed lane distance for the applicable classes. The fixed flows are the MSA averaged flows for iterations after the first global iteration.

Note that the assigned flows for trucks are in PCE values unless otherwise specified. This includes any select type results.