Traffic Assignment Part I

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Traffic Assignment Part I

• CE 573 Transportation Planning
• Lecture 17

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Objectives
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Network Loading

• The basic objective is to assign traffic in a
  reasonable fashion that approximates, on the
  aggregate scale, how traffic uses the
  transportation network.
• Assign traffic (vehicle trips) to the links
• Approximates traffic use of network
• Assumptions
• drivers information?perfectly informed
• driver response to information?perception of cost
• driver objectives?minimize cost
• Traffic assignment result?User Equilibrium
• no driver can reduce their travel costs from i to
  j by changing routes

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Basic Inputs to Traffic Assignment (network
loading)

• Trip matrix?convert from person trips to vehicle
  trips By trip purpose
• HBW 1.1 person trips/veh trip
• HBO 1.6 person trips/veh trip
• Network components
• Links
• centroid connectors
• nodes
• link travel costs
• Route selection criteria/rules
• Cost function
• Minimize cost

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Route Selection Criteria/Rules

• Routing concerns
• stochastic?difference in motorist perceptions
  (quality of information and sensitivities to
  costs)
• congested?capacity constrained
• Classification scheme for traffic assignment
  algorithms

Stochastic effects included? Stochastic effects included?
No Yes
Is capacity restraint included? No All-or-nothing Pure stochastic Dials, Burrells
Is capacity restraint included? Yes Wardrops Equilibrium Stochastic user equilibrium
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Basic Steps of Traffic Assignment Methods

• Identify routes
• stored in tree
• output from tree building algorithm
• Assign trip matrix
• to routes
• creates flows on links
• Check for convergence to user equilibrium

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Assigning the Trip Matrix to Routes

• Use Dijkstras algorithm to build the minimum
  cost path trees
• Have min cost path tree for all origins
• Lets use a link index to represent these path
  trees
• a ? index for each link
• i ? index for the origin zone
• j ? index for the destination zone
• Lets put all of the link indices () in matrix
  form, link choice matrix (P)
• One dimension is O-D pairs
• Another dimension is links
• Now cumulatively assign all of the O-D pair
  volumes to their respective shortest path links

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Dijkstras Algorithm, Link Indices, and
Creating P
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Dijkstras Algorithm, Link Indices, and
Creating P
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Dijkstras Algorithm, Link Indices, and
Creating P
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Assigning O-D Pair Volumes

• Cumulatively to their respective shortest path
  links
• This is called All-or-Nothing Assignment
• no representation of traffic effects on travel
  costs
• Only one path per O-D pair
• Just like our link choice matrix

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Assigning O-D Pair Volumes
A B C D E
A 0 100 500 200 400
B 600 0 100 300 200
C 100 300 0 100 800
D 400 1000 200 0 500
E 400 200 300 100 0
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Assigning O-D Pair Volumes

• Assume a vehicle occupancy of
• 1 person trips/veh trip

Links Links Links Links Links Links Links
1-2 2-3 1-4 2-4 2-5 3-5 4-5
Volume 0 0 0 0 0 0 0