Towards the Analysis of the Queuing System Operating in the Random Environment with Resource Allocation

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The mathematical model of the system, that consists of a storage device and several homogeneous servers and operates in a random environment, and provides incoming applications not only services, but also access to resources of the system, is being constructed. The random environment is represented by two independent Markov processes. The first of Markov processes controls the incoming flow of applications to the system and the size of resources required by each application. The incoming flow is a Poisson one, the rate of the flow and the amount of resources required for the application are determined by the state of the external Markov process. The service time for applications on servers is exponential distributed. The service rate and the maximum amount of system resources are determined by the state of the second external Markov process. When the application leaves the system, its resources are returned to the system. In the system under consideration, there may be failures in accepting incoming applications due to a lack of resources, as well as loss of the applications already accepted in the system, when the state of the external Markov process controlling the service and provision of resources changes. A random process describing the functioning of this system is constructed. The system of equations for the stationary probability distribution of the constructed random process is presented in scalar form. The main tasks for further research are formulated.

Sobre autores

Ivan Zaryadov

Peoples’ Friendship University of Russia (RUDN University); Institute of Informatics Problems, FRC CSC RAS

Autor responsável pela correspondência
Email: zaryadov-is@rudn.ru

Candidate of Physical and Mathematical Sciences, assistant professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University); Senior Researcher of Institute of Informatics Problems of Federal Research Center “Computer Science and Control” Russian Academy of Sciences

IPI FRC CSC RAS, 44-2 Vavilova Str., Moscow 119333, Russian Federation

Vladimir Tsurlukov

Peoples’ Friendship University of Russia (RUDN University)

Email: dober.vvt@gmail.com

master’s degree student of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)

6, Miklukho-Maklaya str., Moscow, 117198, Russian Federation

Cravid Carvalho

Peoples’ Friendship University of Russia (RUDN University)

Email: hilvianamat1@gmail.com

master’s degree student of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)

6, Miklukho-Maklaya str., Moscow, 117198, Russian Federation

Anna Zaytseva

Peoples’ Friendship University of Russia (RUDN University)

Email: anna-z96@mail.ru

master’s degree student of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)

6, Miklukho-Maklaya str., Moscow, 117198, Russian Federation

Tatiana Milovanova

Peoples’ Friendship University of Russia (RUDN University)

Email: milovanova-ta@rudn.ru

Candidate of Physical and Mathematical Sciences, lecturer of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)

6, Miklukho-Maklaya str., Moscow, 117198, Russian Federation

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