A mathematical model of urban spatial interaction based on the intervening-opportunities principle is discussed and its equilibria are studied. It is shown that, under natural assumptions, the number of equilibria is finite, and a mathematical criterion for distinguishing the equilibrium corresponding to reality is given.
Get full access to this article
View all access options for this article.
References
1.
FaddeevD KFaddeevaV N, 1963Computational Methods of Linear Algebra (Freeman, San Francisco)
2.
HeanueK EPyersC E, 1966“A comparative evaluation of trip distribution procedures”Highway
3.
Research Record11435
4.
KuratowskiK, 1972Introduction to Set Theory and Topology (Pergamon Press, Oxford)
5.
LathropG THamburgJ RYoungG F, 1965“Opportunity-accessibility model for allocating regional growth”Highway Research Record10254–66
6.
LemarechalC, 1975“An existence of Davidon methods to non-differentiable problems”Mathematical Programming Study395–109
7.
MillerA J, 1970“The intervening-opportunities model applied to residential land use in a uniform city”Transportation Research4145–149
8.
OrtegaJ MRheinboldtW C, 1970Iterative Solutions of Nonlinear Equations in Several Variables (Academic Press, New York)
9.
PyersC E, 1966“Evaluation of intervening opportunities trip distribution model”Highway Research Record11471–98
10.
RobertsA WVarbergD E, 1973Convex Functions (Academic Press, New York)
11.
RockafellarR T, 1970Convex Analysis (Princeton University Press, Princeton, NJ)
12.
RuiterE R, 1967“Improvements in understanding, calibrating and applying the opportunity model”Highway Research Record1651–5
13.
SaleniusA G, 1972“An intervening opportunities trip distribution model with competing tripmakers”Transportation Research6169–185
14.
SchneiderM, 1960“A formula for predicting travel between zones in an urban region” in Chicago Area Transportation Study, Final Report in Three Parts, Volume II, Data Projection Eds JonesG PDoggettL M, (City of Chicago, Cook County, Ill.; US Department of Commerce, Washington, DC) appendix, page 111
15.
SwerdloffC NStowersJ R, 1966“A test of some first generation residential land use models”Highway Research Record126.
16.
WolfeP, 1975“A method of conjugate subgradients for minimizing nondifferentiable functions”Mathematical Programming Study3145–173
17.
ZipserT, 1973“A simulation model of urban growth based on the model of the opportunity selection process”Geographia Polonica27119–132
18.
ZoutendijkG, 1960Methods of Feasible Directions: A Study in Linear and Non-linear Programming (Elsevier, Amsterdam)
