Optimal number and length of point-like and line-like facilities of grid and random patterns

This paper presents an analytical model for determining the number of point-like facilities and the length of line-like facilities. The proportions of area covered within a distance from the first and second nearest facilities are derived for grid and random patterns. The analytical expressions for the proportions of covered area demonstrate how the coverage distance, the number (length) of facilities, and the pattern of facilities affect the level of coverage. The number (length) of facilities required to achieve a certain level of coverage is then obtained. The level of coverage is represented as the combination of the coverage distance and the proportion of covered area. The model that incorporates any level of coverage and the secondary coverage helps planners with their location decisions.