External Zones in Trip Distribution Models: Characterization and Solvability

The problem of incorporating zones outside the study area in a spacial interaction or trip distribution model is analyzed in this paper. The framework for the analysis is based on the maximum likelihood formulation of the problem, whose equivalence to the entropy maximization model was established i...

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Bibliographic Details
Published in:Transportation science 1984-08, Vol.18 (3), p.253-266
Main Authors: Dinkel, John J, Wong, Danny
Format: Article
Language:English
Subjects:
Applied sciences
Entropy
Exact sciences and technology
Ground, air and sea transportation, marine construction
Lagrange multipliers
Mathematical independent variables
Modeling
Optimal solutions
Parametric models
Solvability
Total costs
Transportation planning, management and economics
Travel expenses
Trip distribution
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Summary:The problem of incorporating zones outside the study area in a spacial interaction or trip distribution model is analyzed in this paper. The framework for the analysis is based on the maximum likelihood formulation of the problem, whose equivalence to the entropy maximization model was established in general by Wong (Wong, D. S. 1981. Maximum likelihood, entropy maximization, and the geometric programming approaches to the calibration of trip distribution models. Trans. Res. 15B 329–343.). We shall deal with two cases—when the number of incoming (or outgoing) trips to the study area is restricted, and when it is unrestricted. Based on this approach, we present a unified numerical solution methodology for these classes of problems. The sensitivity of the model with respect to changes in certain restrictive parameters will be examined. As a result, we characterize the solution space for certain values of the parameters under consideration. A numerical example is used to illustrate our presentation.
ISSN:0041-1655
1526-5447
DOI:10.1287/trsc.18.3.253