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Traffic Assignment Part I

Traffic Assignment Part I. CE 573 Transportation Planning Lecture 16. Objectives. Define traffic assignment assumptions Mathematically define relationship between OD trips and network Load traffic onto the network. Network Loading.

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Traffic Assignment Part I

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  1. Traffic Assignment Part I CE 573 Transportation Planning Lecture 16

  2. Objectives • Define traffic assignment assumptions • Mathematically define relationship between OD trips and network • Load traffic onto the network Michael Dixon

  3. 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: • driver’s 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 Michael Dixon

  4. Zone A Zone B Michael Dixon

  5. 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 Michael Dixon

  6. 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 Michael Dixon

  7. 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 Michael Dixon

  8. Assigning the Trip Matrix to Routes • Use Dijkstra’s algorithm to build the minimum cost path trees • Have min cost path tree for all origins • Let’s 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 • Let’s 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 Michael Dixon

  9. Dijkstra’s Algorithm, Link Indices, and Creating P Michael Dixon

  10. Dijkstra’s Algorithm, Link Indices, and Creating P Michael Dixon

  11. Dijkstra’s Algorithm, Link Indices, and Creating P Michael Dixon

  12. 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 Michael Dixon

  13. Assigning O-D Pair Volumes Michael Dixon

  14. Assigning O-D Pair Volumes • Assume a vehicle occupancy of • 1 person trips/veh trip Michael Dixon

  15. Link Travel Costs • Until now, constant link costs. • Link costs should be f(traffic volume). • Need a link cost function. • BPR function Michael Dixon

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