Distance Between Random Points in Two Rectangular Cities

ABSTRACT

The travel distance between two cities of rectangular shape is considered. Two uniformly distributed random points, one from each city, are taken. Their straight path travel distance is then measured. The explicit forms for the probability density function of this distance and its expected value are obtained. Numerical results of calculating the exact expected distance and the estimated distance as well as computer simulation are given for various cases. The integer moments of the distance are also discussed.

Keywords:

• Expected travel distance
• Rectangular cities
• Transformation of variables
• Uniformly distributed random points

Mathematics Subject Classification:

• 62E15
• 62H10
• 62P12
• 90C15
• 60E05
• 62H12

Acknowledgment

The author is grateful to a referee for the suggestion of plotting the graph in Fig. 3.