Title: Searching for a d-dimensional Brownian target with multiple sensors

Authors: Mohamed Abd Allah El-Hadidy

Addresses: Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

Abstract: We consider a search problem for a d-dimensional Brownian target that moves randomly on d-space. We have n-searchers moving with a linear paths in d-dimension to search for the target. Each of the searchers moves continuously along its line in both directions of the starting point (origin of its line). The purpose of this paper is to formulate a search model and find the condition under which the expected value of the first meeting time between one of the searchers and the target finite. Also, we show the existence of the optimal search plan that minimises the expected value of the first meeting time.

Keywords: disjoint real lines; finite search plan; d-dimensional Brownian motion; digonal matrix; optimal search plan; multiple sensors.

DOI: 10.1504/IJMOR.2016.078822

International Journal of Mathematics in Operational Research, 2016 Vol.9 No.3, pp.279 - 301

Received: 27 Oct 2014
Accepted: 15 Nov 2014
Published online: 03 Sep 2016 *

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