Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

For citation:

Tananko I. E., Fokina N. P. An Analysis Method of Open Queueing Networks with a Degradable Structure and Instantaneous Repair Times of Systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 2, pp. 266-276. DOI: 10.18500/1816-9791-2020-20-2-266-276, EDN: SRPQIC

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
01.06.2020
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Language: 
Russian
Heading: 
Computer Sciences
Article type: 
Article
UDC: 
519.872
DOI: 
10.18500/1816-9791-2020-20-2-266-276
EDN: 
SRPQIC

An Analysis Method of Open Queueing Networks with a Degradable Structure and Instantaneous Repair Times of Systems

Autors: 
Tananko Igor' Evstaf'evich, Saratov State University
Fokina Nadezhda Petrovna, Saratov State University
Abstract: 

An unreliable open queueing network with Poisson arrivals is considered. For each queueing system the service and failures times are exponentially distributed random variables. The failures of systems lead to changes in the structure of the network and corresponding changes in the performance measures of the queueing network. It is assumed that the times between changes in the network structure are sufficient for the steady-state regime. The main measure of the quality for the network at each structure constancy interval is the average response time. Repairs of all queueing systems occur immediately when the average response time becomes greater than the threshold value. This article presents a method of the network analysis using continuous time Markov chains. It is shown that the steady-state probability distribution of the unreliable queueing network has a product form solution. Expressions for the stationary performance measures of queueing systems and the network including the average of system repair time intervals are obtained. A numerical example to investigate the dependence of the performance measures on some network parameters is demonstrated.

Key words: 
queueing networks
Markov chains
unreliable queueing systems
degradable structure of queueing network
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Received: 
23.11.2018
Accepted: 
05.04.2019
Published: 
01.06.2020
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