Optimal Spatial Interaction and the Gravity Model

✍ Scribed by Sven Erlander (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1980
• Tongue: English
• Leaves: 105
• Series: Lecture Notes in Economics and Mathematical Systems 173
• Edition: 1
• Category: Library

✦ Synopsis

This book has grown out of a desire to explore the possibilities of using optimizing models in transportation planning. This approach has been followed throughout. Models which combine descriptive and optimizing elements are not treated. The gravity model is here studied as the solution to an optimizing model. In spite of this approach, much of the material shoula be of general interest. Algorithms are not discussed. The author has benefited from discussions with many colleagues. M. Florian suggested the term "interacti vi ty". N. F. Stewart and P. Smeds gave many valu­ able comments on a first draft. M. Beckmann made me think once more about the final chapters. R. Grubbstrem and K. Jornsten helped clarifYing some things in the same chapters. Remaining insufficiencies are due to the author. Gun Mannervik typed with great patience. Linkoping in October 1979 Sven Erlander ABSTRACT The book proposes extended use of optimizing models in transportation plann­ ing. An entropy constrained linear program for the trip distribution problem is formulated and shown to have the ordinarJ doubly constrained gravity model as its solution. Entropy is here used as a measure of interactivity, which is constrained to be at a prescribed level. In this way the variation present in the reference trip matrix is preserved. (The properties of entropy as a dispersion measure are shortly discussed. ) The detailed mathematics of the optimal solutions as well as of sensitivity and duality are given.

✦ Table of Contents

Front Matter....Pages N2-vii
The Transportation Planning Process....Pages 1-13
Front Matter....Pages 15-15
Entropy as a Measure of Dispersion....Pages 17-23
Some Comments Upon Entropy Maximizing....Pages 25-26
Front Matter....Pages 27-27
A Model for the Constraints....Pages 29-31
The Objective Function and Our Minimization Problem....Pages 33-34
The Gravity Model as the Optimal Solution of the Entropy Constrained Aggregate Linear Program....Pages 35-53
Sensitivity and the Dual Program....Pages 55-63
Interactivity and Entropy....Pages 65-67
Benefit Measures and the Gravity Model....Pages 69-70
Front Matter....Pages 71-71
Modal Split....Pages 73-76
Assignment to the Network....Pages 77-78
Front Matter....Pages 79-79
An Utility Approach to the Original Trip Distribution Problem....Pages 81-90
Entropy Constrained Aggregate Linear Program....Pages 91-95
Back Matter....Pages 97-113

✦ Subjects

Regional/Spatial Science