THE NEWTON-KANTOROVICH METHOD FOR SOLVING THE GRAVITY MODEL IN TRAFFIC PLANNING

The commonly used gravity model with exponential distance function can be derived in several ways: 1) by an optimisation problem whose solution is the gravity formula, 2) by probabilistic arguments developed into the entropy maximising approach, 3) by application of information theory and statistical mechanics, 4) by use of utility functions to obtain a wide range of models including the gravity model. This paper discusses the use of entropy and its relation to the idea of accessibility. The usual procedure for solving the gravity model is to start with some initial set of values of the trip matrix and then proceed by successive normalisations of rows and columns. Convergence of this procedure has been proved. The above iterative procedure is however an approximate version of the Newton-Kantarovich method for solving systems of non-linear equations. This is demonstrated. Calibration procedures for the gravity model and their relation to the procedure employed are also discussed. /TRRL/

• Corporate Authors:

  Linkoeping University, Sweden

  Department of Mathematics
  S-58183 Linkoeping,   Sweden 
• Authors:
  • Erlander, S
• Publication Date: 1977

Media Info

• Features: References;
• Pagination: 18 p.

Subject/Index Terms

• TRT Terms: Accessibility; Calibration; Entropy (Communications); Exponential functions; Gravity models; Highway planning; Iterative methods; Optimization; Traffic; Travel
• Uncontrolled Terms: Optimum
• Old TRIS Terms: Traffic planning
• ITRD Terms: 9139: Accessibility; 6171: Calibration; 690: Gravity model; 6492: Iteration; 698: Journey
• Subject Areas: Highways; Operations and Traffic Management; I71: Traffic Theory;

Filing Info

• Accession Number: 00163990
• Record Type: Publication
• Source Agency: Swedish National Road and Transport Research Institute (VTI)
• Report/Paper Numbers: Lith-Mat-R-77-1 Monograph
• Files: ITRD, TRIS
• Created Date: Dec 27 1977 12:00AM