The Expected Length of an Orderly Path

June 2020 | ,

Combining order statistics with probability theory, this research develops a closed form expression for the expected Euclidean distance between two consecutive points in the X direction on a Cartesian X-Y plane. This expectation has applications in Steiner tree problems, traveling salesman problems, drone delivery routing, and aircraft sorties.



  • Heather Lutz, Penn State University
  • Faizul Huq, Ohio University


Annals of Operations Research