Nonlinear Pricing on Transportation Networks

Under nonlinear road pricing (or tolling), the price charged is not strictly proportional to the distance travelled inside a tolling area, the generalized travel cost is not link-wise additive, and finding a user equilibrium distribution is typically formulated as a complementarity problem. The latter is a difficult problem to solve in mathematical programming. In this paper, the authors use piecewise linear functions to determine tolls and show that finding a user equilibrium distribution with such functions can be formulated as a convex optimization problem that is based on path flows and solvable by traditional algorithms such as simplicial decomposition. For area-based and two-part pricing schemes, the tolling function consists of only one linear piece and finding a user equilibrium distribution reduces to a convex optimization problem formulated in terms of link flows and solvable by any software for linearly constrained convex programs. To find an optimal pricing scheme, e.g., one that maximizes the social benefit, the authors formulate the problem as a mathematical program with equilibrium constraints, an optimization problem that is generally non convex and difficult to solve. However, it is possible to use search algorithms to find an optimal scheme because the number of parameters in our piecewise linear function is few. To illustrate, the authors use a coordinate search algorithm to find an optimal two-part pricing scheme for a small network with randomly generated data.

• Record URL:
  http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B9853-52X1TRD-19-1&_cdi=59087&_user=10&_pii=S1877042811010780&_origin=browse&_zone=rslt_list_item&_coverDate=12%2F31%2F2011&_sk=999829999&wchp=dGLzVlb-zSkWW&md5=46b2a7c17d9e21fdce66eed99ba7d315&ie=/sdarticle.pdf
• 
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/18770428
• Supplemental Notes:
  • Abstract reprinted with permission from Elsevier.
• Authors:
  • Yin, Yafeng
  • Lawphongpanich, Siriphong
• Conference:
  • 19th International Symposium on Transportation and Traffic Theory
  • Location: Berkeley CA, United States
  • Date: 2011-7-18 to 2011-7-20
• Publication Date: 2011

Language

• English

Media Info

• Media Type: Web
• Features: Appendices; Figures; References; Tables;
• Pagination: pp 292-315
• Monograph Title: International Symposium on Transportation and Traffic Theory, 19th
• Serial:
  • Procedia - Social and Behavioral Sciences
  • Volume: 17
  • Publisher: Elsevier
  • ISSN: 1877-0428
  • Serial URL: http://www.sciencedirect.com/science/journal/18770428/53
• Publication flags:

  Open Access (libre)

Subject/Index Terms

• TRT Terms: Algorithms; Congestion pricing; Optimization; Programming (Mathematics); Road pricing; Social benefits; Traffic congestion; Traffic flow; Travel costs
• Uncontrolled Terms: Pricing schemes; Transportation networks; User equilibrium
• Subject Areas: Finance; Highways; Operations and Traffic Management; Planning and Forecasting; I72: Traffic and Transport Planning;

Filing Info

• Accession Number: 01345413
• Record Type: Publication
• Files: TRIS
• Created Date: Jul 21 2011 10:08AM