Coronavirus disease 2019 is the most crucial issue of all countries worldwide as it poses a threat and risk to people in many aspects such as health and economy.Since each country's development level, economy, and infrastructure differ, countries' struggle against COVID-19 varies. Therefore, understanding the COVID-19 risk levels of countries can be crucial in determining possible strategies to take specific measures for those at the highest risk. Also, determining the risk level of countries can be more critical than estimates, such as the number of cases and deaths, as the level of risk alone can be an informative indicator for all such issues. Unlike most studies, this study concentrates on evaluating and estimating the COVID-19 risk level of countries. This study proposes two families of multivariate exponential estimators using two auxiliary attributes. Theoretically, the mean square error (MSE) equations of all proposed exponential estimators are obtained and compared with existing estimators. Some exceptional cases of the multivariate exponential estimators are regarded and compared with MSE values of proposed multivariate exponential estimators. As a result, the multivariate exponential estimators provide more efficient results than all other estimators. These theoretical findings are supported by a numerical illustration using real dataset. K E Y W O R D SCOVID-19 risk, exponential estimator, mean square error, risk assessment, two auxiliary attributes INTRODUCTIONThe World Health Organization (WHO) declared on March 11, 2020, that coronavirus disease 2019 (COVID-19) could be considered a pandemic. 1Since then, COVID-19 has caused a global crisis affecting people's health, well-being and lifestyle, and the world economy. As of January 16, 2021, there have been 92,506,811 confirmed COVID-19 cases and 2,001,773 reported deaths globally. 2 However, the number of cases and deaths varies from country to country. The main reason for this may be that each country differs in population density, cultural habits, health services, protective measures, and infrastructure. 3Management and control of COVID-19 depend primarily on the health system of a country. 4 A robust health system plays a determining role in countries' preparedness and responses to pandemics. 5 In addition, socioeconomic factors are crucial in the spread of COVID-19. [6][7][8][9] Such parameters, health system, and socioeconomic vulnerability affect the risk level of countries. It is usual for COVID-19 to spread brutally in the least developed and most vulnerable countries (countries with the highest risk). 10 In this regard, evaluating and determining the COVID-19 risk level of countries can be crucial as it is an informative indicator for most issues, including the number of COVID-19 cases and mortality rates.
A stochastic model consisting of two heterogeneous channels and having no waiting room in front of each is considered. A customer who has completed his service in channel 1 while channel 2 is busy blocks channel 1 with probability or leaves the system with 1− probability. This model was analysed: expected number of customer and loss probability of customer are calculated and optimal ordering of channels minimizing parameters has been found. Additionally, this model was simulated; furthermore, simulated and exact results of loss probabilities of customers were given in the tables. Hindawi Publishing Corporation
Abstract:In this study a two stage queueing model is analyzed. At first stage there is a single server having exponential service time with parameter and no waiting is allowed in front of this server. There are two parallel phase-type servers at second stage and these parallel servers have exponential service time with parameter . Arrivals to this system is Poisson with parameter . An arriving customer to this system has service if the server at first stage is available or leaves the system if the server is busy where the first loss occurs. After having service in first stage the customer proceeds to the second stage, if both of the phase-type parallel servers in second stage are available the customer chooses one of these servers with probability 0.50 or leaves the system if any of these servers in second stage is busy so the second loss occurs. A customer who has service at both stages leaves the system. The number of customers in this model is represented by a 3-diamensional Markov chain and Kolmogorov differential equations are obtained. After that mean number of customers and mean waiting time in the system is obtained by limit probabilities. We have shown that the customer numbers at first and second stages are dependent to each other. The numerical analysis of obtained performance measures are shown by a numeric example. Finally the graphs of loss probabilities and measure of performances given for some values of arrival rate and the service parameters.
The aim of this paper is to analyze a tandem queueing model with two stages. The arrivals to the first stage are Poisson stream and the service time at this stage is exponential. There is no waiting room at first stage. The service time is hyperexponential and no waiting is allowed at second stage. The transition probabilities and loss probabilities of this model are obtained. In addition, the loss probability at second stage is optimized. Performance measures and the variance of the numbers of customers of this tandem queueing model are found. It is seen that the numbers of customers in first stage and second stage are dependent. Finally we have simulated this queueing model. For different values of parameters, exact values, simulated values, and optimal values of obtained performance measures of this model are numerically shown in tables and graphs.
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