Method of Successive Weighted Averages and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem

It is well-known that comparing with the deterministic user equilibrium (UE) model, stochastic user equilibrium (SUE) is more appropriate to model the aggregate effect of travelers' route choice. However, SUE is not widely implemented for practical use in the traffic assignment software packages. One of the reasons is that the convergence of SUE is generally quite slow because of the use of the Method of Successive Averages (MSA), in which the auxiliary flow pattern generated at each iteration contributes equally to the final solution. Realizing that the auxiliary flow pattern is in fact approaching to the solution point when the iteration number is large, in this paper, we introduce the method of successive weighted averages (MSWA) that includes a new step size sequence giving higher weights to the auxiliary flow pattern from the later iterations. We further develop a self-regulated averaging method, in which the step sizes are varying, rather than fixed, based on the distance between intermediate solution and auxiliary point. The proposed step size sequences in both MSWA and self-regulated averaging method satisfy the Blum Theorem, which guarantees the convergence of SUE problem. Computation results demonstrate that the convergence speeds of MSWA and self-regulated averaging method are much faster than that of MSA and the speedup factors are in a manner of magnitude for the high accuracy solution points. The proposed methods are also applicable to the class of fixed-point problems, which have wide range applications in the area of transportation.

Language

  • English

Media Info

  • Media Type: CD-ROM
  • Features: Figures; References; Tables;
  • Pagination: 22p
  • Monograph Title: TRB 86th Annual Meeting Compendium of Papers CD-ROM

Subject/Index Terms

Filing Info

  • Accession Number: 01046484
  • Record Type: Publication
  • Report/Paper Numbers: 07-1573
  • Files: TRIS, TRB
  • Created Date: Feb 8 2007 6:13PM