Coordinated Search for a Random Walk Target Motion

Abstract

This paper presents the cooperation between two searchers at the origin to find a Random Walk moving target on the real line. No information is not available about the target’s position all the time. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, we show the existence of the optimal search strategy which minimizes this first meeting time. The effectiveness of this model is illustrated using a numerical example.

Existence of a finite multiplicative search plan with random distances and velocities to find a d-dimensional Brownian target

“…Now, the motion of S i on the line L i with a given initial density and the two PDFs for the distances and velocities is described by Equations (1) and (2) which can be solved analytically. Hence, we aim to find the frequency of velocity changes ς i (y i , h i ) and then substitute with result (2).…”

“…If the search space is a line, then the searcher aims to detect the target in the right or left part of the starting point, where the searcher can change its direction without losing any time. Most of the techniques that have been studied for the line deal with deterministic distances and velocities, see [1][2][3][4][5][6][7]. On the plane, Mohamed and El-Hadidy [8,9] and El-Hadidy [10] presented more interesting search strategies with deterministic distance and regular fixed velocity to find the two-dimensional randomly moving targets.…”

Existence of cooperative search technique to find a Brownian target

“…In recent works, El-Hadidy and Abou-Gabal [7] presented a coordinated search technique to find a random Walk target, which moves randomly on the real line. Rather than showing the existence of the optimal search strategy that minimizes this first interviewing time, El-Hadidy and Abou-Gabal [7] found the conditions that make E(τ) finite. El-Hadidy et al [8][9][10] also studied this technique on the plan and space when the target is hidden at any random point.…”

“…In this work, we use the technique which was presented in Reyniers [5,6] and El-Hadidy and Abou-Gabal [7] but without repeating the searching process on the searched parts of n disjoint real lines. This technique is the generalization of the technique which was used in El-Hadidy and Alzulaibani [27].…”

Cooperative search model for finding a brownian target on the real line

“…Recently, in the case of a Random Walk moving target on the line Abou-Gabal and El-Hadidy [19] introduced this technique and found the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite. In addition, they showed the existence of the optimal search strategy which minimizes this first meeting time.…”