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Queueing models can be used for making decisions about the resources required to provide high quality service. In this paper, a finite capacity single server queueing model with bulk arrivals is studied in IoT-based edge computing systems. The transient analysis of the model is carried out and the transient analytical solution to the system is derived with a group of recursive coefficients by using the ordinary differential equations (ODEs) technique. From which the steady-state probabilities are solved. Then, some performance metrics of interest are derived along with numerical results. Although the paper is initiated from the IoT based edge computing platform, the proposed system modeling and analysis method can be extended to more general situations such as telecommunication, manufacturing, transportation, and many other areas that are closely related to people’s daily lives.

The question of determination of stationary probabilities of the states of the queuing system with an unreliable device, vacation and prophylaxis describing functioning of both basic and auxiliary material stream of the logistic system is considered in the article.В статье рассмотрен вопрос определения стационарных вероятностей состояний системы массового обслуживания с ненадежным прибором, переналадкой и профилактикой, описывающей функционирование как основного, так и вспомогательного материального потока логистической системы.

We will consider the management of stormwater storage in a system of two connected dams. It is assumed that we have stochastic input of stormwater to the first dam and that there is regular demand from the second dam. We wish to choose a control policy from a simple class of control policies that releases an optimal flow of water from the first dam to the second dam. The cost of each policy is determined by the expected volume of water lost through overflow.

Refereed/Peer-reviewed

El secuestro es considerado un delito de lesa humanidad, las estadísticas en Colombia en cuanto a este fenómeno son de las más altas del mundo, infortunadamente es una de las principales fuentes de financiamiento de los grupos insurgentes y de la delincuencia común. En este trabajo se plantea el fenómeno como un proceso de Markov continuo, tomando como base estadísticas disponibles desde el año 1996 a 2006 y se realizan un análisis de ellas a la luz de esta herramienta matemática. Kidnapping is considered a crime against humanity; the statistics in Colombia about this phenomenon are the highest in the world, unfortunately one of the main sources of financing insurgent groups and common criminals. This paper presents the phenomenon as a continuous Markov process, based on available statistics from 1996 to 2006 and performed an analysis of them using this mathematical tool.