Searching for the Random Walking microorganism cells

El–Hadidy, Mohamed Abd Allah; Abou-Gabal, Hamdy M.

doi:10.1142/s1793524519500645

Cited by 18 publications

(8 citation statements)

References 28 publications

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“…They presented the existence of the optimal search plan which detects this person in minimum time. Also, El Hadidy 8–15 showed the importance of this theory in many real life applications. They presented new models for discovering lost targets (randomly located or moving) with maximum probability and the lowest possible cost.…”

Section: Introductionmentioning

confidence: 99%

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

El–Hadidy

2021

Math Methods in App Sciences

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This paper presents a novel model to detect the COVID‐19 infected person from a Markovian feedback persons in a limited department capacity. The persons arrive one by one to the department and the balking and the retention of reneged person approaches are considered. There exists one server presents the service to these persons according to first‐come, first‐served (FCFS) discipline. An efficient and novel algorithm is presented to get the exact value of the probability of n persons in the department at any time interval. This algorithm depends on the Laplace transform to solve a probabilistic dynamical system of differential equations. By considering the exponential detection function and if the probability of the infected person in the department is equal to the probability of each one, then this algorithm is useful to obtain the detection probability of the infected one. Under steady state, the detection probability of the infected person is described. The usefulness of this model is illustrated for different capacities by using a numerical example to describe the behavior of probabilities of the persons in the department, the detection probabilities of the infected person as functions in time, and the mean time to detection.

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Section: Introductionmentioning

confidence: 99%

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

El–Hadidy

2021

Math Methods in App Sciences

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“…This problem has an important application in our life. It might emerge in numerous true circumstances, for example, looking for a broken unit in a huge straight framework (electrical cables, phone lines and mining framework), searching for some data in a memory of PC tapes, etc., (see [4][5][6][7][8][9][10][11][12]. When the target is very important, we use the cooperative search technique.…”

Section: Introductionmentioning

confidence: 99%

Optimal Multi Zones Search Technique to Detect a Lost Target by Using K Sensors

El–Hadidy¹,

Abou-Gabal²,

Gabr³

2021

Stat., optim. inf. comput.

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This paper presents the discrete search technique on multi zones to detect a lost target by using sensors. The search region is divided into zones. These zones contain an equal number of states (cells) not necessarily identical. Each zone has a one sensor to detect the target. The target moves over the cells according to a random process. We consider the searching effort as a random variable with a known probability distribution. The detection function with the discounted reward function in a certain state and time interval are given. The optimal effort distribution that minimizes the probability of undetection is obtained after solving a discrete stochastic optimization problem. An algorithm is constructed to obtain the optimal solution as in the numerical application.

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“…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%

“…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).…”

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confidence: 99%

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

El–Hadidy

2020

Quality & Reliability Eng

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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.

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Searching for the Random Walking microorganism cells

Cited by 18 publications

References 28 publications

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

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

Optimal Multi Zones Search Technique to Detect a Lost Target by Using K Sensors

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

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