Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Chernishova E. N., Lisovskaya E. Y. On a Total Resource Amounts at the System with Parallel Service and MMPP Arrivals. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 3, pp. 400-410. DOI: 10.18500/1816-9791-2020-20-3-400-410, EDN: PTIYON

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On a Total Resource Amounts at the System with Parallel Service and MMPP Arrivals

Chernishova Elizaveta N., Tomsk State University
Lisovskaya Ekaterina Yu., Tomsk State University

In this paper, we consider a resource system with an unlimited resources and servers number, with parallel customers servicing, arriving at the system according to the MMPP. Using a combination of multidimensional dynamic screening methods and asymptotic analysis, it is proved that the joint asymptotic probability distribution of the total resource amounts converges to a bi-dimensional Gaussian distribution under conditions of increasing intensity of MMPP. The parameters of the asymptotic probability distribution are found. A numerical analysis of the approximation accuracy is carried out.

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