Resource System with Losses in a Random Environment

Valeriy Naumov and Konstantin Samouylov
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Valeriy Naumov: Service Innovation Research Institute, Annankatu 8 A, 00120 Helsinki, Finland
Konstantin Samouylov: Applied Informatics and Probability Department, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, 117198 Moscow, Russia

Mathematics, 2021, vol. 9, issue 21, 1-10

Abstract: The article deals with queueing systems with random resource requirements modeled as bivariate Markov jump processes. One of the process components describes the service system with limited resources. Another component represents a random environment that submits multi-class requests for resources to the service system. If the resource request is lost, then the state of the service system does not change. The change in the state of the environment interacting with the service system depends on whether the resource request has been lost. Thus, unlike in known models, the service system provides feedback to the environment in response to resource requests. By analyzing the properties of the system of integral equations for the stationary distribution of the corresponding random process, we obtain the conditions for the stationary distribution to have a product form. These conditions are expressed in the form of three systems of nonlinear equations. Several special cases are explained in detail.

Keywords: product form; loss system; resource requirement; random environment; Marked Markovian Arrival Process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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