Approximate network loading and dual-time-scale dynamic user equilibrium

In this paper the authors present a dual-time-scale formulation of dynamic user equilibrium (DUE) with demand evolution. The authors' formulation belongs to the problem class that Pang and Stewart (2008) refer to as differential variational inequalities. It combines the within-day time scale for which route and departure time choices fluctuate in continuous time with the day-to-day time scale for which demand evolves in discrete time steps. The authors' formulation is consistent with the often told story that drivers adjust their travel demands at the end of every day based on their congestion experience during one or more previous days. The authors show that analysis of the within-day assignment model is tremendously simplified by expressing dynamic user equilibrium as a differential variational inequality. The authors also show there is a class of day-to-day demand growth models that allow the dual-time-scale formulation to be decomposed by time-stepping to yield a sequence of continuous time, single-day, dynamic user equilibrium problems. To solve the single-day DUE problems arising during time-stepping, it is necessary to repeatedly solve a dynamic network loading problem. The authors observe that the network loading phase of DUE computation generally constitutes a differential algebraic equation (DAE) system, and the authors show that the DAE system for network loading based on the link delay model (LDM) of Friesz et al. (1993) may be approximated by a system of ordinary differential equations (ODEs). That system of ODEs, as the authors demonstrate, may be efficiently solved using traditional numerical methods for such problems. To compute an actual dynamic user equilibrium, the authors introduce a continuous time fixed-point algorithm and prove its convergence for effective path delay operators that allow a limited type of nonmonotone path delay. The authors show that their DUE algorithm is compatible with network loading based on the LDM and the cell transmission model (CTM) due to Daganzo (1995). The authors provide a numerical example based on the much studied Sioux Falls network.

• Record URL:
  http://www.sciencedirect.com/science/article/B6V99-50JGV1D-1/2/4461465cdb79a929833b9a02f1b6917f
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/01912615
• Supplemental Notes:
  • Abstract reprinted with permission from Elsevier.
• Authors:
  • Friesz, Terry L
  • Kim, Taeil
  • Kwon, Changhyun
  • Rigdon, Matthew A
• Publication Date: 2011-1

Language

• English

Media Info

• Media Type: Print
• Features: Appendices; Bibliography; Figures; References; Tables;
• Pagination: pp 176-207
• Serial:
  • Transportation Research Part B: Methodological
  • Volume: 45
  • Issue Number: 1
  • Publisher: Elsevier
  • ISSN: 0191-2615
  • Serial URL: http://www.sciencedirect.com/science/journal/01912615

Subject/Index Terms

• TRT Terms: Algorithms; Days; Departure time; Differential equations; Dynamic models; Route choice; Time studies; Travel demand
• Uncontrolled Terms: Dynamic network loading; Dynamic user equilibrium; Time scale
• Subject Areas: Highways; Operations and Traffic Management; Planning and Forecasting;

Filing Info

• Accession Number: 01323875
• Record Type: Publication
• Files: TRIS, ATRI
• Created Date: Dec 28 2010 1:30PM