|
Digital
Library of the European Council for Modelling
and Simulation |
Title: |
Analysis Of Unreliable Multi-Server Queueing System
With Breakdowns Spread And Quarantine |
Authors: |
Alexander
Dudin, Sergei Dudin, Olga Dudinx, Konstantin Samouylov |
Published in: |
(2017).ECMS 2017 Proceedings
Edited by: Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás
Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics European Council for Modeling and Simulation. doi:10.7148/2017 ISBN:
978-0-9932440-4-9/ ISBN:
978-0-9932440-5-6 (CD) 31st European Conference on Modelling and
Simulation, Budapest, Hungary, May 23rd
– May 26th, 2017 |
Citation
format: |
Alexander
Dudin, Sergei Dudin, Olga Dudinx, Konstantin Samouylov (2017). Analysis Of
Unreliable Multi-Server Queueing System With Breakdowns Spread And Quarantine,
ECMS 2017 Proceedings Edited by: Zita Zoltay Paprika, Péter Horák, Kata
Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter
Rádics European Council for Modeling and Simulation. doi:
10.7148/2017-0680 |
DOI: |
https://doi.org/10.7148/2017-0680 |
Abstract: |
We
consider an unreliable multi-server queue in which the rate of servers’
breakdowns increases when the number of broken servers grows. To prevent
quick degradation of the system, it is proposed to switch to a quarantine
regime when the number of broken servers exceeds some threshold and to
maintain this regime until the number of broken servers becomes less than
another threshold. During the quarantine, service of customers is stopped, new breakdowns do not arrive while the broken
servers continue recovering. Under the fixed values of the thresholds, behavior of the system is described by the multi-dimensional
continuous time Markov chain. The steady state distribution of the
chain and the key performance measures of the system are computed as the
functions of the thresholds. Possibility of the optimal choice of the
thresholds providing the minimal value of an economical criterion is
numerically illustrated. |
Full
text: |