On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacity
A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating funct...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2020-03-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/10433 |
| _version_ | 1819158547204669440 |
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| author | Wojciech M. Kempa |
| author_facet | Wojciech M. Kempa |
| author_sort | Wojciech M. Kempa |
| collection | DOAJ |
| description | A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overflow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overflows is also given. Numerical examples are attached as well. |
| first_indexed | 2024-12-22T16:26:23Z |
| format | Article |
| id | doaj.art-17542099702a45b5829c9af6c552f097 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-22T16:26:23Z |
| publishDate | 2020-03-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-17542099702a45b5829c9af6c552f0972022-12-21T18:20:09ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102020-03-0125210.3846/mma.2020.10433On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacityWojciech M. Kempa0Silesian University of Technology, Faculty of Applied Mathematics, Kaszubska 23, 44-100 Gliwice, PolandA model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overflow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overflows is also given. Numerical examples are attached as well.https://journals.vgtu.lt/index.php/MMA/article/view/10433buffer overflowgeometric distributionproduction linequeueing modeltransient analysis |
| spellingShingle | Wojciech M. Kempa On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacity Mathematical Modelling and Analysis buffer overflow geometric distribution production line queueing model transient analysis |
| title | On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacity |
| title_full | On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacity |
| title_fullStr | On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacity |
| title_full_unstemmed | On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacity |
| title_short | On time-to-buffer overflow distribution in a single-machine discrete-time system with finite capacity |
| title_sort | on time to buffer overflow distribution in a single machine discrete time system with finite capacity |
| topic | buffer overflow geometric distribution production line queueing model transient analysis |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/10433 |
| work_keys_str_mv | AT wojciechmkempa ontimetobufferoverflowdistributioninasinglemachinediscretetimesystemwithfinitecapacity |