. . . . . . "Unreliable M/M/n/m, cost analysis, coloured Petri net"@en . "Professional Publishing" . . "2"^^ . "Cost Analysis of Finite Multi-server Markov Queueing System Subject to Breakdowns"@en . "Praha" . "Cost Analysis of Finite Multi-server Markov Queueing System Subject to Breakdowns" . "2"^^ . "6"^^ . . "Cost Analysis of Finite Multi-server Markov Queueing System Subject to Breakdowns" . . "27230" . "2011-09-06+02:00"^^ . "S" . . "192091" . . "RIV/61989100:27230/11:86079203!RIV14-MSM-27230___" . . "Cost Analysis of Finite Multi-server Markov Queueing System Subject to Breakdowns"@en . "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."@en . "978-80-7431-059-1" . . . "Dorda, Michal" . "000309074600022" . "Jansk\u00E1 Dolina" . "Teichmann, Du\u0161an" . "[A5338275CF95]" . "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." . . "29th International Conference Mathematical Methods in Economics 2011 Proceedings" . "RIV/61989100:27230/11:86079203" . . .