Traffic Assignment Part III

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Traffic Assignment Part III

• CE 573 Transportation Planning
• Lecture 19

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Objectives

• Updating link costs
• Finding a search direction
• Measuring proximity to user equilibrium

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Updating Link Costs

• Traffic assignment assign trips to links
• Gives volume on links
• Link costs are a function of volume
• Input link volumes into link cost functions
• Output is the updated link costs

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Updating Link Costs (Example)
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Updating Link Costs (Example)

• Using equations of this form for link cost for
  each link (travel time)
• Where
• ta link travel cost per unit distance on link a,
• toa free flow travel time per unit distance on
  link a,
• Va flow on link a,
• Qpa practical capacity of link a, and
• a and ß calibration parameters for link cost
  (a1.0 and ß3).
• Given the volume estimated from All-Or-Nothing
  (AON) assignment (last class example)
• Update the link costs

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Updating Link Costs (Example)
Links Links Links Links Links Links Links
Link 1-2 2-3 1-4 2-4 2-5 3-5 4-5
Link Volume 2700 1000 0 3100 0 1400 2100
Directional Volume (50/50) 1350 500 0 1550 0 700 1050
to 5 10 15 9 16 12 6
a 1 1 1 1 1 1 1
ß 3 3 3 3 3 3 3
Qp 1000 1000 1000 1000 1000 1000 1000
t (updated link cost) 17.3 11.3 15.0 42.5 16.0 16.1 12.9
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Update Minimum Cost Path Trees (Origin A)
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Update Minimum Cost Path Trees (Origin B)
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Update Minimum Cost Path Trees (Origin C)
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Update Minimum Cost Path Trees (Origin D)
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Update Minimum Cost Path Trees (Origin E)
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Update P-Matrix and Compare to Previous Matrix

• Which links are, and are not, used?
• If you were to assign traffic with the updated
  trees, would it be the same as it was before?
• Which traffic assignment is correct?
• Should you combine the two traffic assignments
  (before and after the update)? If so then how?

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Congestion Restrained Traffic Assignment
Algorithms

• Incremental Assignment
• Method of Successive Averages
• Frank-Wolfe Algorithm