Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Chernishova E. N., Lisovskaya E. Y. On a Total Resource Amounts at the System with Parallel Service and MMPP Arrivals. Izv. Sarat. Univ. Math. Mech. Inform., 2020, vol. 20, iss. 3, pp. 400-410. DOI: 10.18500/1816-9791-2020-20-3-400-410

Published online: 
31.08.2020
Full text:
(downloads: 262)
Language: 
Russian
Heading: 
Article type: 
Article
UDC: 
519.21
DOI: 
10.18500/1816-9791-2020-20-3-400-410

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

Autors: 
Chernishova Elizaveta N., Tomsk State University
Lisovskaya Ekaterina Yu., Tomsk State University
Abstract: 

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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Received: 
07.06.2019