The total benefit of facility users under a certain configuration of facilities in a network space when the choice behavior of the facility users follows an origin-constrained spatial interaction model

Abstract

This paper derives an analytical expression of the total benefit of facility users under the following conditions: (i) the behavior of facility users follows an origin-constrained spatial interaction model, and (ii) the distribution of facility users in a network space is represented by polynomials. We first represent the total benefit of facility users in a network as a definite integral. We then demonstrate that a part of integrand in the definite integral, which is the natural log of the accessibility, can be represented by the infinite series of exponential functions and that the analytical expression of the total benefit is derived based on the infinite series.