In the process of optimising the partition of a field service region into territories it is necessary to estimate the expected distance between two random points in a territory. This paper considers territories with a fine rectangular street grid and no barriers to travel so that the distance between any two points is calculated using the Manhattan or rectilinear metric. If all that is known of the territory is its area, then the expected distance between two randomly chosen points can be estimated by assuming that the territory is square. It is demonstrated that this estimate is quite robust for fairly wide deviations in compactness and convexity. Finally, it is shown that these conventional descriptors of shape are not adequate predictors of differences in travel distances. (a) For the covering entry of this conference, please see ITRD abstract no. E211903.
Abstract