Search in Random Media with Lévy Flights

Erol Gelenbe, Omer H. Abdelrahman

Published 2013-05-15, updated 2013-07-15Version 2

We review some of our work regarding search which has been motivated by a variety of applications in engineering and technology, including traffic routing and security in communication networks, explosive mine detection and removal, tactical operations as well as emergency management. We develop the basic mathematical model representing N searchers that proceed independently, and which can be affected by destruction or loss, and time-outs. An approach based on Laplace transform is then developed for the case where the success of the search requires that k out of the N searchers be successful, and we estimate the amount of energy expended and the number of searchers that are required to conduct a successful search in time B, provided B is large. Finally, we present an iterative numerical solution approach that allows us to analyse the search time and the energy needed to find an object when the search space is non-homogeneous.