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1

A multi-source fluid queue based stochastic model of the probabilistic offloading strategy in a MEC system with multiple mobile devices and a single MEC server

Zheng Huan, Jin Shunfu

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 1

125--138

EN

Mobile edge computing (MEC) is one of the key technologies to achieve high bandwidth, low latency and reliable service in fifth generation (5G) networks. In order to better evaluate the performance of the probabilistic offloading strategy in a MEC system, we give a modeling method to capture the stochastic behavior of tasks based on a multi-source fluid queue. Considering multiple mobile devices (MDs) in a MEC system, we build a multi-source fluid queue to model the tasks offloaded to the MEC server. We give an approach to analyze the fluid queue driven by multiple independent heterogeneous finite-state birth-and-death processes (BDPs) and present the cumulative distribution function (CDF) of the edge buffer content. Then, we evaluate the performance measures in terms of the utilization of the MEC server, the expected edge buffer content and the average response time of a task. Finally, we provide numerical results with some analysis to illustrate the feasibility of the stochastic model built in this paper.

2

Diffusion approximation of the network with limited number of same type customers and time dependent service parameters

Matalytski M., Kopats D.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 2

77--84

EN

The article presents research of an open queueing network (QN) with the same types of customers, in which the total number of customers is limited. Service parameters are dependent on time, and the route of customers is determined by an arbitrary stochastic transition probability matrix, which is also dependent on time. Service times of customers in each line of the system is exponentially distributed. Customers are selected on the service according to FIFO discipline. It is assumed that the number of customers in one of the systems is determined by the process of birth and death. It generates and destroys customers with certain service times of rates. The network state is described by the random vector, which is a Markov random process. The purpose of the research is an asymptotic analysis of its process with a big number of customers, obtaining a system of differential equations (DE) to find the mean relative number of customers in the network systems at any time. A specific model example was calculated using the computer. The results can be used for modelling processes of customer service in the insurance companies, banks, logistics companies and other organizations.

3

Prognozowanie stanu systemu w markowskim modelu procesu rezerwowania obiektów technicznych

Woropay M., Landowski B., Perczyński D.

Biuletyn Wojskowej Akademii Technicznej

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2004

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Vol. 53, nr 5

95-106

PL

W niniejszym artykule przedstawiono sposób oceny (prognozowania) zachowania się podsystemu rezerwowego przy założeniu, że modelem procesu rezerwowania jest jednorodny proces Markowa (proces urodzin i śmierci). Przedstawiony w artykule sposób wyznaczania prawdopodobieństw znajdowania się obiektów technicznych w danej chwili czasu w podsystemie rezerwowym umożliwia wyznaczenie niezbędnej liczby obiektów rezerwowych dla przyjętego kryterium ryzyka wyczerpania się rezerwy. Całość rozważań zilustrowano na przykładzie systemu eksploatacji autobusów komunikacji miejskiej.

EN

The unique manner of estimating (including the prognosis) the behaviour of the reserve subsystem is shown in the paper. There is an assumption, that the model of the reserve process can be designed and described with the homogeneous Markov's one (so called the birth and death process). The way of evaluating values of finding probabilities the technical objects in the reserve subsystem (at the moment of time t) is shown. A forementioned way of evaluation enables of computing indispen sable quantity of the technical objects for every assumed reserve run low risk criterion. All considerations have been illustrated and exemplified with the urban bus transport maintenance system.