Title: Generalised linear search plan for a D-dimensional random walk target

Authors: Mohamed Abd Allah El-Hadidy

Addresses: Mathematics and Statistics Department, College of Science, Taibah University, Yanbu, Saudi Arabia; Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Abstract: In this paper, we present a mathematical search model that studies the generalised linear search plan for detecting a d-dimensional random walk target. The target will meet one of the searchers where each searcher starts its motion from any point rather than the origin on n-disjoint real lines in ℝⁿ. Rather than, finding the conditions that show the finiteness of this search plan, we study the existence of the optimal search plan that minimises the expected value of the first meeting time between one of the searchers and the target.

Keywords: linear search method; d-dimensional random walk; finite search plan; optimal search plan; semi continuous mapping.

DOI: 10.1504/IJMOR.2019.101622

International Journal of Mathematics in Operational Research, 2019 Vol.15 No.2, pp.211 - 241

Received: 18 Aug 2017
Accepted: 16 Apr 2018
Published online: 16 Aug 2019 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article