Title: On the existence of a finite linear search plan with random distances and velocities for a one-dimensional Brownian target

Authors: Mohamed Abd Allah El-Hadidy

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

Abstract: In this paper, we consider a linear search model that takes into consideration the velocities and the distances which the searcher do them are independent random variables with known probability density functions (PDFs). The searcher moves continuously along the line in both directions of the starting point (origin of line). We use the Fourier-Laplace representation to give an analytical expression for the density of the random distance in the model. Also, we get the conditions that make the expected value of the first meeting time between the searcher and the target is finite.

Keywords: linear search problem; finite search plan; one-dimensional Brownian motion; Fourier-Laplace transform.

DOI: 10.1504/IJOR.2020.105369

International Journal of Operational Research, 2020 Vol.37 No.2, pp.245 - 258

Accepted: 16 Mar 2017
Published online: 20 Feb 2020 *

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