Existence of cooperative search technique to find a Brownian target

Math Methods in App Sciences

2021

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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.

Section: Introductionmentioning

confidence: 99%

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

Math Methods in App Sciences

2021

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“…This theory has a remarkable importance in our real life where it is used to detect the lost targets (randomly located or moved) with the maximum probability and minimum cost. In an earlier work, many types of search plans have been derived on these line by Beck et al, [1][2][3] El-Hadidy et al, [4][5][6][7][8][9][10][11][12] Balkhi, 13 and Reyniers. 14,15 Many studies have presented different search techniques on the plan and space, such as El-Hadidy et al.…”

Section: Introductionmentioning

confidence: 99%

Detection of an appropriate pharmaceutical company to get a suitable vaccine against COVID‐19 with minimum cost under the quality control process

Quality & Reliability Eng

Alfreedi

2021

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Some international pharmaceutical companies have succeeded in producing vaccines against COVID-19. Countries all over the world have aimed to obtain these vaccines with minimum cost. We consider a set of K-independent Markovian waiting lists. Each list contains a set of countries, where each one of them has an exponential service time and a Poisson arrival process. These companies differ in some characteristics such as the vaccine production cost and the speed of the required quantity delivery. We present a new detection model that helps in providing an appropriate decision to choose a suitable company. Moreover, the concept of balking and the retention of reneged countries is taken into consideration under the quality control process of each waiting list. Under steady state, we face an interesting and difficult discrete stochastic optimization problem. Its solution gives an optimal distribution of the searching effort, which is bounded by a known probability distribution. A simulation study has been derived to get the minimum value of the paid cost random values. The highest service rate, the total expected profit of each queuing system, and the optimum performance measures, which depend on this cost, have been obtained to show the effectiveness of this model.

“…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).…”

mentioning

confidence: 99%

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

Quality & Reliability Eng

2020

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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.