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

Abstract

We present the existence of a finite search plan to find Brownian target on the d-space by using d-searchers. Each searcher moves continuously in both directions of the origin (starting point) of the line (field of its search) with random distances and velocities. We express theses distances and velocities with independent random variables with known probability density functions (PDFs). We present more analysis about the density of the random distances in our model by using Fourier-Laplace representation. This analysis will provide us with the conditions that make the expected value of the first meeting time between the target and one of the searchers finite.

Developing a detection model for a COVID‐19 infected person based on a probabilistic dynamical system

“…This plan will minimize the expected value of the first meeting time between the searcher and the target. Previous works 20–32 presented more useful search models in many real life situations to detect the lost target with minimum cost and maximum probability. Recently, El‐Hadidy and Alfreedi 33 used a novel search model to discover an appropriate pharmaceutical company to get a suitable vaccine against COVID‐19 with minimum cost under the quality control policy.…”

Quality control for a detected an appropriate queue from K‐independent M/M/C/N queueing models

“…This problem is similar to the previous one which was solved by El‐Hadidy et al 3–5 They gave the optimal distribution of an, effort which maximizes the probability of detecting the target. In recent years, the detection (searching) process for the lost targets (stationary or mobile or randomly moving targets) has been studied extensively in many variations, mostly by El‐Hadidy et al 6–22 The main aim of this studies is to detect the lost target with maximum probability and minimum cost (time).…”

“…process for the lost targets (stationary or mobile or randomly moving targets) has been studied extensively in many variations, mostly by El-Hadidy et al [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] The main aim of this studies is to detect the lost target with maximum probability and minimum cost (time).…”

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.…”