The implications of using a gravity model to determine territory in a circular domain

This paper uses a gravity model to determinate the territory of two facilities on a two-dimensional plane and aims to discover its new implications. The recursive process is installed to the model in such a way that the future scale of a facility reflects the present amount of territory. And the facilities can be located in a two-dimensional circular domain so that the hinterland effect is incorporated. As a result, firstly, an ordinary tendency—the so-called weak-to-the-wall phenomenon—is observed. The smaller the distance-decay parameter, the more frequently this monopolization occurs. On the other hand, peculiar variations in the model’s behavior are also found with changes in parameter values. A reversal of the facility scale, the coexistence of two facilities even with a small distance-decay parameter, and other novel phenomena also occur with some cases of facility locations and initial scale conditions. <br> <b>Keywords:</b> gravity model, territory, distance-decay parameter, facility location