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

Abstract

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.

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

“…shows the amount of the searching effort (see El-Hadidy 30 ). Thus, one can consider the function ( ) = ∑ = 1 ∑ =1 ( ) , as a cost function of detection where 0 ≤ ( ) ≤…”

“…( ) ≤ such that ∑ =1 ( ) ≤ and be a random variable having a known probability distribution. As in El-Hadidy, 30 we can get the probability of detection for the suitable company under the quality control process by…”

“…Therefore, we assume that the country moves according to the Markov process under favorable conditions to choose the suitable company. If the service is done, then the conditional probability of detecting the suitable company , will be where shows the amount of the searching effort (see El‐Hadidy 30 ). Thus, one can consider the function as a cost function of detection where such that and X be a random variable having a known probability distribution.…”

“…There exists another benefit of this model helps countries to take an appropriate economic decision in any economic field. Here, we use the same model which was recently used in El‐Hadidy, 30 but with quality control for each queue through the presence of an inspector. If any defect happened, then this inspector will return the country to the waiting list again.…”

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

“…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.…”