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Content available remote Investigation of queueing network with unreliable systems and large number of messages
Matalytski M., Statkevich S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 1
85-97
EN
The Markov network with unreliable queueing systems and a large number of messages is investigated. The service channels of systems are exposed to random failure, besides the time of the proper functionality and the time of reconstruction of each channel of system has the exponential distribution with distinctive parameters. The system of difference-differential equations of Kolmogorov for the states probabilities is compiled. The partial differential equation for the probability density function of the vector of states is deduced. The systems of ordinary differential equations for an average number of messages and serviceable channels of network systems are received.
2
Content available remote About simulation modeling of HM-queueing network with unreliable systems
Matalytski M., Statkevich S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 2
85-92
EN
The Markov network with unreliable queueing systems and incomes are considered. Analytical results on research of exponential networks in a case when incomes of transitions between network states depend on time are reduce. The algorithm of simulation modeling of HM-queueing networks based on the 0-moments. This method allows one to find incomes of networks when the service time of messages, serviceable work time of channels and restoration time of failure channels has any distribution. Results of simulation modeling are compared to analytical results. High accuracy of the developed algorithm is shown.
3
Content available remote Time-dependent state probabilities of queueing network with unreliable systems in transient regime
Matalytski M., Statkevich S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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Vol. 10, nr 1
175-187
EN
The method of a multidimensional generating function for finding timedependent state probabilities of a open queuing network with unreliable systems is studied. Assuming that the network functions in the condition of heavy loading, the flow parameters of messages, servicing, duration of serviceable working and duration of restoration of channels are time-dependent. Such networks can serve as models of the functioning of the Local Area Network (LAN). Expressions for network state probabilities at any moment of time are obtained. An example for finding network state probabilities with a central system is considered.
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