Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine

One of the most important characteristic of each queueing model is time to buffer overflow. In the paper the distribution of that time in a single-channel manufacturing system, modelled by a Markovian finite-buffer queue with machine breakdowns, is studied. By using the analytical approach based on...

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Veröffentlicht in:MATEC web of conferences Jg. 112; S. 5005
Hauptverfasser: Kempa, Wojciech M., Paprocka, Iwona, Grabowik, Cezary, Kalinowski, Krzysztof, Krenczyk, Damian
Format: Journal Article Tagungsbericht
Sprache:Englisch
Veröffentlicht: Les Ulis EDP Sciences 01.01.2017
Schlagworte:
Buffers
Cybersecurity
Linear algebra
Markov analysis
Markov chains
Queues
Queuing theory
ISSN:2261-236X, 2274-7214, 2261-236X
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Abstract One of the most important characteristic of each queueing model is time to buffer overflow. In the paper the distribution of that time in a single-channel manufacturing system, modelled by a Markovian finite-buffer queue with machine breakdowns, is studied. By using the analytical approach based on the idea of embedded Markov chain, total probability law and linear algebra, the formula for Laplace transform of the time to buffer overflow conditional distribution is found. Numerical illustration is presented.
AbstractList One of the most important characteristic of each queueing model is time to buffer overflow. In the paper the distribution of that time in a single-channel manufacturing system, modelled by a Markovian finite-buffer queue with machine breakdowns, is studied. By using the analytical approach based on the idea of embedded Markov chain, total probability law and linear algebra, the formula for Laplace transform of the time to buffer overflow conditional distribution is found. Numerical illustration is presented.
Author Grabowik, Cezary
Kalinowski, Krzysztof
Kempa, Wojciech M.
Paprocka, Iwona
Krenczyk, Damian
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  fullname: Kalinowski, Krzysztof
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  givenname: Damian
  surname: Krenczyk
  fullname: Krenczyk, Damian
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Cites_doi 10.1080/15326340701300746
10.1016/S0304-4149(00)00034-X
10.1016/0377-2217(95)00378-9
10.1007/s11134-011-9213-6
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Snippet One of the most important characteristic of each queueing model is time to buffer overflow. In the paper the distribution of that time in a single-channel...
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SubjectTerms Buffers
Cybersecurity
Linear algebra
Markov analysis
Markov chains
Queues
Queuing theory
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