User equilibrium vs. System optimum: an analysis based on demand level breakpoints

The purpose of this study is to compare optimal network loadings related to network equilibria. The direct comparison of path flows or trajectory patterns is hard to achieve so here the authors propose a more aggregate approach based on the comparison of demand level breakpoints. A breakpoint occurs at a particular demand level when after this level, the pattern of the path flow loading is changed or the set of active alternatives with at least one assigned user is modified. For instance a breakpoint occurs when the authors start to assign the users to new paths, or when the flow of one path becomes zero. The authors examine the formation of the equilibrium both in the case of static and dynamic traffic assignment, in the following context: the structure of the demand is given, but the level of demand increases. The authors focus on discrete demand formulation and choices because most actual traffic simulators are either microscopic or mesoscopic. The equilibrium changes qualitatively when the demand is increasing, which results in breakpoints for the demand level at which the equilibrium solution changes significantly by the definition of breakpoints.This study analyzes the breakpoints for the solution of three popular equilibrium conditions: User equilibrium (UE), System optimum (SO) and Boundary Rational User Equilibrium (BRUE). First, the authors investigate breakpoints on a very simple and well-known network (Braess) in the static case in order to better define this concept. Second, breakpoints are investigated on a real network (Lyon, France) and travel times are calculated by microscopic traffic simulator. The ultimate goal is to find, at each level of demand, the critical set of users that can be made to change paths in order to move the system from demander side (UE and BRUE) to supplier side (SO). Users can be guided by the network controllers to change path, or the network controller can manage the price of paths or can ban some paths. The numerical results show that this approach can help identify such sets of users.

  • Supplemental Notes:
    • This paper was sponsored by TRB committee ADB30 Standing Committee on Transportation Network Modeling. Alternate title: User Equilibrium Versus System Optimum: An Analysis Based on Demand-Level Breakpoints
  • Authors:
    • Ameli, Mostafa
    • Lebacque, Jean-Patrick
    • Leclercq, Ludovic
  • Conference:
  • Date: 2018


  • English

Media Info

  • Media Type: Digital/other
  • Features: Figures; References;
  • Pagination: 5p

Subject/Index Terms

Filing Info

  • Accession Number: 01659930
  • Record Type: Publication
  • Report/Paper Numbers: 18-01806
  • Files: TRIS, TRB, ATRI
  • Created Date: Jan 8 2018 10:27AM