Multiplicative linear search for a brownian target motion

Abstract

a b s t r a c tThis paper investigates a search problem for a brownian target motion on one of n-intersected real lines in which any information of the target position is not available to the searchers all the time. We have n-searchers start searching for the target from the origin that is the intersection point of these lines. Each of the searchers moves continuously along his line in both directions of the starting point. 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 is finite. Also, we show the existence of the optimal search plan which minimizes the expected value of the first meeting time and find it.

Searching for a Target Whose Truncated Brownian Motion

“…They showed the existence of the optimal search plan which makes the expected value of the first meeting time between the searcher and target minimum. Mohamed et al [2] studied this problem for a Brownian target on one of n-intersected real lines.…”

Optimal Multiplicative Generalized Linear Search Plan for a Discrete Random Walker

“…El-Rayes et al [9] illustrated this problem when the target moves on the real line with a Brownian motion, and the searcher starts the search from the origin. Recently, Mohamed et al [10] discussed this problem for a Brownian target motion on one of -intersected real lines in which any information of the target position is not available to the searchers all the time. Mohamed et al formulate a search model and find the conditions under which the expected value of the first meeting time between one of the searchers and the target is finite.…”

M-states search problem for a lost target with multiple sensors

“…After several decades of development, search problems are still largely of the same form as in 1942: a single target is lost and the problem is to find it efficiently. Therefore, the study of search plans for a lost target that either stationary or which move according to a known random motion has a remarkable importance in our life, because it has various applications like searching for a faulty unit in large linear system such as electrical power lines, petrol or gas supply under ground, missing boats and submarines, mining systems and search for a randomly located goal at two separated regions (see, e.g., El-Rayes and Mohamed, 1998Mohamed, , 1986Oshumi, 1991;El-Rayes et al, 2003;Mohamed et al, 2009Mohamed et al, , 2011Alpern and Haward, 2000).…”