Distribution of the Angle between Directions of the First and Second Nearest Facilities

Abstract

This paper examines the angle between the directions of the first and second nearest facilities. An application of the angle can be found in location analysis of refuges where the direction of facilities is important. The angle represents the service level of facility location when customers are serviced by the first and second nearest facilities. The distribution of the angle is derived for regular and random patterns of facilities. The distribution shows how the angle is distributed in a study region, and is useful for location models using the direction of facilities. The distribution of the angle for actual facility location is also calculated.