Probit-Based Time-Dependent Stochastic User Equilibrium: Reformulation and Solution Algorithm

This paper presents a theoretically sound time-dependent stochastic user equilibrium (TDSUE) traffic assignment model and its simulation-based solution algorithm within a probit-based path choice decision framework. The TDSUE problem, which aims to find time-dependent SUE path flows, is typically considered as a fixed point problem; it is reformulated as an equivalent gap function-based nonlinear optimization problem, and then solved by a column generation-based solution framework which embeds (i) a simulation-based dynamic network loading model to capture traffic dynamics and determine experienced time-dependent path travel disutilities and temporal and spatial path correlations for a given path flow pattern; (ii) a projected gradient-based descent direction method to solve the restricted SUE problem defined by a subset of feasible paths; and (iii) a time-dependent least-cost path algorithm to generate paths to augment the feasible path set. This nonlinear optimization reformulation provides a wide spectrum of opportunities to use nonlinear programming (NLP) solution procedures to solve the (probit-based) SUE problem in the dynamic context. In this study, a projected gradient-based descent direction method (PGDDM) considering time-varying, cross-path marginal cost effects is developed to solve the NLP reformulation. Within the same solution framework, an averaging method, which can be viewed as an approximate descent direction method without considering the cross path marginal cost effect, is also proposed for solving large-scale problems. A set of numerical experiments are conducted to investigate the convergence and solution quality of the solution algorithm.

• Corporate Authors:

  Transportation Research Board

  500 Fifth Street, NW
  Washington, DC  United States  20001
• Authors:
  • Zhang, Kuilin
  • Mahmassani, Hani S
  • Lu, Chung-Cheng
• Conference:
  • Transportation Research Board 88th Annual Meeting
  • Location: Washington DC, United States
  • Date: 2009-1-11 to 2009-1-15
• Date: 2009

Language

• English

Media Info

• Media Type: DVD
• Features: Figures; References; Tables;
• Pagination: 28p
• Monograph Title: TRB 88th Annual Meeting Compendium of Papers DVD

Subject/Index Terms

• TRT Terms: Choice models; Nonlinear programming; Probits; Stochastic programming; Time dependence; Traffic assignment; Travel surveys
• Uncontrolled Terms: User equilibrium
• Subject Areas: Highways; Planning and Forecasting; I72: Traffic and Transport Planning;

Filing Info

• Accession Number: 01127290
• Record Type: Publication
• Report/Paper Numbers: 09-3407
• Files: TRIS, TRB
• Created Date: Apr 28 2009 8:10AM