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Statements

Subject Item
n2:RIV%2F61989100%3A27230%2F11%3A86079203%21RIV14-MSM-27230___
rdf:type
skos:Concept n16:Vysledek
dcterms:description
In the paper we introduce a mathematical model of a finite multi-server Markov queueing system M/M/n/m with servers which are subject to breakdowns. We assume that broken server is being repaired by a single repairman, where the number of repairmen is less than the number of the system servers. The system is modelled as a two-dimensional Markov process presented by a state transition diagram and a finite system of linear equations that describes the behaviour of the system in steady state. The steady state probabilities are obtained by numerical solving by means of Matlab. On the basis of the steady state probabilities we can compute several performance measures. The mathematical model is supported by a coloured Petri net model in order to validate the analytical outcomes. Further we present a cost function which can serve as an optimization criterion for the optimization of the studied system parameters. In the paper we introduce a mathematical model of a finite multi-server Markov queueing system M/M/n/m with servers which are subject to breakdowns. We assume that broken server is being repaired by a single repairman, where the number of repairmen is less than the number of the system servers. The system is modelled as a two-dimensional Markov process presented by a state transition diagram and a finite system of linear equations that describes the behaviour of the system in steady state. The steady state probabilities are obtained by numerical solving by means of Matlab. On the basis of the steady state probabilities we can compute several performance measures. The mathematical model is supported by a coloured Petri net model in order to validate the analytical outcomes. Further we present a cost function which can serve as an optimization criterion for the optimization of the studied system parameters.
dcterms:title
Cost Analysis of Finite Multi-server Markov Queueing System Subject to Breakdowns Cost Analysis of Finite Multi-server Markov Queueing System Subject to Breakdowns
skos:prefLabel
Cost Analysis of Finite Multi-server Markov Queueing System Subject to Breakdowns Cost Analysis of Finite Multi-server Markov Queueing System Subject to Breakdowns
skos:notation
RIV/61989100:27230/11:86079203!RIV14-MSM-27230___
n16:predkladatel
n21:orjk%3A27230
n3:aktivita
n20:S
n3:aktivity
S
n3:dodaniDat
n5:2014
n3:domaciTvurceVysledku
n11:6860273 n11:7604335
n3:druhVysledku
n17:D
n3:duvernostUdaju
n8:S
n3:entitaPredkladatele
n6:predkladatel
n3:idSjednocenehoVysledku
192091
n3:idVysledku
RIV/61989100:27230/11:86079203
n3:jazykVysledku
n14:eng
n3:klicovaSlova
Unreliable M/M/n/m, cost analysis, coloured Petri net
n3:klicoveSlovo
n7:coloured%20Petri%20net n7:cost%20analysis n7:Unreliable%20M%2FM%2Fn%2Fm
n3:kontrolniKodProRIV
[A5338275CF95]
n3:mistoKonaniAkce
Janská Dolina
n3:mistoVydani
Praha
n3:nazevZdroje
29th International Conference Mathematical Methods in Economics 2011 Proceedings
n3:obor
n19:BB
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:rokUplatneniVysledku
n5:2011
n3:tvurceVysledku
Dorda, Michal Teichmann, Dušan
n3:typAkce
n4:WRD
n3:wos
000309074600022
n3:zahajeniAkce
2011-09-06+02:00
s:numberOfPages
6
n10:hasPublisher
Professional Publishing
n18:isbn
978-80-7431-059-1
n15:organizacniJednotka
27230