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

Abstract

In this paper, we study the cooperation between two searchers start the searching process from the origin to meet a Brownian moving target on a real line. We find the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite. This is the first model which calculates the approximate value for the expected value of the first meeting time. An illustrative example has been given to demonstrate the applicability of this model. ARTICLE HISTORY

The searching algorithm for detecting a Markovian target based on maximizing the discounted effort reward search

“…Step 5. From equations (18) and (19), compute the values of Z ij , Z i(j+ ) , elsewhere go to step 8.…”

Existence of cooperative search technique to find a Brownian target

“…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]. We use n cooperative searchers to seek a Brownian target which moves in one of the n disjoint cylinders (real lines).…”

Minimizing the expected search time of finding the hidden object by maximizing the discount effort reward search

“…On the other hand, for a stochastically moving object, El-Hadidy and Abou-Gabal [5] and El-Hadidy and Alzulaibani [6,7] used a linear coordinated search technique to present a finite search plan which minimizes the first collision time expected value between one of the searchers and the stochastically moving object. Moreover, this technique is applied by using the Bayesian approach (see, e.g.…”

“…Earlier, many interesting methods to track the stochastically moving object have been presented by Dai et al [12] and Deilami et al [13]. Besides that, Mohamed et al [14,15], Mohamed and El-Hadidy [16], Mohamed and El-Hadidy [17], Beltagy and El-Hadidy [18], Abou-Gabal and El-Hadidy [19], Mohamed et al [20], Kassem and El-Hadidy [21], El-Hadidy and El-Bagoury [22], El-Hadidy [23][24][25][26][27][28][29][30][31], El-Hadidy and Alzulaibani [6,7], and El-Hadidy et al [32] provided many different mathematical treatments of this issue in both cases stochastically moving and hidden objects.…”