Advertisement

A New General Equilibrium Model

  • Yanling Xiang
  • Michael J. Smith
  • Miles Logie
Chapter
  • 508 Downloads
Part of the Applied Optimization book series (APOP, volume 64)

Abstract

In this paper we present a new general equilibrium model appropriate for multimodal networks. A solution of the model gives the equilibrium distribution of travellers and vehicles over a transportation network. The model is expressed in terms of inverse cost-flow functions; and delays are explicitly modelled. The paper outlines an equilibration algorithm and convergence results for a small network are provided. The equilibrium model has been designed in such a way that optimisation procedures may naturally be added to the equilibration algorithm.

Key words

Equilibrium assignment multicopy network bottleneck delay monotone cost functions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Beckmann, M., C. B. McGuire, and C. B. Winsten: 1956, Studies in the Economics of Transportation. Yale University Press.Google Scholar
  2. [2]
    Cairns, S., C. Hass-Klau, and P. Goodwin: 1998, Traffic Impact of Highway Capacity Reductions: Assessment of the Evidence. Landor Publishing.Google Scholar
  3. [3]
    Charnes, A. and W. W. Cooper: 1961, ‘Multicopy Traffic Network Models’. In: Herman R. (ed.): Proceedings of the Symposium on the Theory of Traffic Flow,. held at the General Motors Research Laboratories, Elsevier, Amsterdam.Google Scholar
  4. [4]
    Kimber, R. M. and E. M. Hollis: 1979, ‘Traffic Queues and Delays at Road Junctions’. Technical Report LR909, TRRL Laboratory, UK.Google Scholar
  5. [5]
    Logie, M., B. G. Heydecker, and M. J. Smith: 1998, ‘Generalised Equilibrium Modelling: An Integrated Framework for Transport Planning’. In: European Transport Forum.Google Scholar
  6. [6]
    MVA Limited: 1998, Traffic Impact of Highway Capacity Reductions: Report on Modelling. Landor Publishing.Google Scholar
  7. [7]
    Payne, H. J. and W. A. Thompson: 1975, ‘Traffic Assignment on Transportation Networks with Capacity Constraints and Queueing’. Paper presented at the 47th National ORSA/TIMS North American Meeting.Google Scholar
  8. [8]
    SACTRA: 1994, ‘Trunk Roads and the Generation of Traffic’. Technical report, Department of Transport, UK.Google Scholar
  9. [9]
    Smith, M. J.: 1979, ‘The Marginal Cost Taxation of a Transportation Network’. Transportation Research, B13, 237–242.Google Scholar
  10. [10]
    Smith, M. J.: 1984, ‘A Descent Method for Solving Monotone Variational Inequalities and Monotone Complementarity Problems’. Journal of Optimisation Theory and Applications 44, 485–496.zbMATHGoogle Scholar
  11. [11]
    Smith, M. J., Y. Xiang, R. Yarrow, and M. O. Ghali: 1998, ‘Bilevel and other Modelling Approaches to Urban Traffic Management and Control’. In: Marcotte P. and Nguyen. S (eds.): Equilibrium and Advanced Transportation Modelling. pp. 283–325.Google Scholar
  12. [12]
    Smith, M. J., Battye, A., A. Clune, and Y. Xiang: 2000, ‘Cone Fields and the Cone Projection Method of Designing Signal Settings and Prices for Transportation Networks’. In: Proceedings of the 6th Meeting of the EURO Working Group on Transportation, Gothenburg.Google Scholar
  13. [13]
    Wardrop, J. G.: 1952, ‘Some Theoretical Aspects of Road Traffic Research’. In: Proceedings, Institute of Civil Engineers II, 1, pp. 235–278.Google Scholar
  14. [14]
    Xiang, Y. and M. J. Smith: 1998, ‘A General Equilibrium Model, Solution Algorithms and Convergence Results’. Paper presented at the First International Transportation Symposium, Newcastle.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Yanling Xiang
  • Michael J. Smith
    • 1
  • Miles Logie
    • 2
  1. 1.York Network Control Group Mathematics DepartmentYork UniversityYorkUK
  2. 2.MVA HouseMVA LimitedWokingUK

Personalised recommendations