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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Published in:MATEC web of conferences Vol. 112; p. 5005
Main Authors: Kempa, Wojciech M., Paprocka, Iwona, Grabowik, Cezary, Kalinowski, Krzysztof, Krenczyk, Damian
Format: Journal Article Conference Proceeding
Language:English
Published: Les Ulis EDP Sciences 01.01.2017
Subjects:
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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  givenname: Damian
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  fullname: Krenczyk, Damian
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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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