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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2017-01-01
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| Series: | MATEC Web of Conferences |
| Online Access: | https://doi.org/10.1051/matecconf/201711205005 |
| _version_ | 1818730744611078144 |
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| author | Kempa Wojciech M. Paprocka Iwona Grabowik Cezary Kalinowski Krzysztof Krenczyk Damian |
| author_facet | Kempa Wojciech M. Paprocka Iwona Grabowik Cezary Kalinowski Krzysztof Krenczyk Damian |
| author_sort | Kempa Wojciech M. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T23:06:39Z |
| format | Article |
| id | doaj.art-e5a551688c4746c6873341abd8be763a |
| institution | Directory Open Access Journal |
| issn | 2261-236X |
| language | English |
| last_indexed | 2024-12-17T23:06:39Z |
| publishDate | 2017-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | MATEC Web of Conferences |
| spelling | doaj.art-e5a551688c4746c6873341abd8be763a2022-12-21T21:29:14ZengEDP SciencesMATEC Web of Conferences2261-236X2017-01-011120500510.1051/matecconf/201711205005matecconf_imane2017_05005Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machineKempa Wojciech M.0Paprocka Iwona1Grabowik Cezary2Kalinowski Krzysztof3Krenczyk Damian4Silesian University of Technology, Faculty of Applied Mathematics, Institute of MathematicsSilesian University of Technology, Faculty of Mechanical Engineering, Institute of Engineering Processes Automation and Integrated Manufacturing SystemsSilesian University of Technology, Faculty of Mechanical Engineering, Institute of Engineering Processes Automation and Integrated Manufacturing SystemsSilesian University of Technology, Faculty of Mechanical Engineering, Institute of Engineering Processes Automation and Integrated Manufacturing SystemsSilesian University of Technology, Faculty of Mechanical Engineering, Institute of Engineering Processes Automation and Integrated Manufacturing SystemsOne 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.https://doi.org/10.1051/matecconf/201711205005 |
| spellingShingle | Kempa Wojciech M. Paprocka Iwona Grabowik Cezary Kalinowski Krzysztof Krenczyk Damian Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine MATEC Web of Conferences |
| title | Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine |
| title_full | Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine |
| title_fullStr | Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine |
| title_full_unstemmed | Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine |
| title_short | Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine |
| title_sort | distribution of time to buffer overflow in a finite buffer manufacturing model with unreliable machine |
| url | https://doi.org/10.1051/matecconf/201711205005 |
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