Existence of finite parbolic spiral search plan for a Brownian target

Journal of Taibah University for Science

Alzulaibani

2019

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.

“…respectively. Consequently, from (5) and (10) one can get the expected value of the searching times to search h i1 , h i2 by…”

Section: Example 31mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Journal of Taibah University for Science

Alzulaibani

2019

“…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).…”

Section: Introductionmentioning

confidence: 99%

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

Quality & Reliability Eng

2020

In this paper, we consider a system of K‐independent Markovian queues such that each one of them has a Poisson arrival process and exponential service time. We assume that every server has some characteristics such as the speed of the service performance or the service cost. To find an appropriate queue, which meets customer needs for the service performance, we present a new approach that gives a suitable decision to choose an appropriate queue from our system. This allows the customer to deal with minimum cost and faster server under steady state. We solve an interesting discrete stochastic optimization problem where the paid cost by the customer is bounded by a Gaussian distribution. Using these hypotheses, we perform a simulation study by generating the paid cost random values and choosing the minimum value between them. This minimum cost gives the highest service rate, which is used to obtain the optimum values of the system effectiveness measures.

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Journal of Taibah University for Science

Alfreedi

2020

A new search technique is developed to locate the hidden target (object) in one of the Ndisjoint regions that are not identical. The lost object follows a bivariate distribution. Minimizing the search effort with discount reward has been applied instead of reducing the expected search time. Moreover, the minimum number of searchers is determined in order to minimize the total expected cost. Assuming the object's position has a Circular Normal distribution, the Kuhn-Tucker necessary conditions are implemented to get the optimum search plan.