Approximate formulas of average distances associated with regions and their applications to location problems

This study is concerned with the problem of measuring average distances between two points in two different coplanar regions. The objectives are: (1) to derive the approximated average distances associated with circular regions and to check their accuracy; and (2) to apply these approximated distances to location problems. Results show that the simple approximate formulas are accurate and useful. The approximated average distances can be applied to the analyses of varied kinds of movement phenomena in cities.