Spatial-interaction-model-based estimation of the demand for a facility when the distribution of facility users in a network space is represented by polynomials

Abstract

This paper derives an analytical expression of the estimation of the demand for a facility under the following conditions: (i) the behavior of facility users follow an origin-constrained spatial interaction model, and (ii) the distribution of facility users in a network space is represented by polynomials. We demonstrate that a part of integrand in the definite integral representing the estimation for a facility can be represented by the infinite series of exponential functions and that the analytical expression of the demand is derived based on the infinite series. We then conclude with suggestions for a future study.