Stationary characteristics of unreliable queueing system with a batch Markovian arrival process
Unreliable queuing systems are of considerable interest both in mathematical terms and for applications. Systems with stationary Poisson flows of customers and breakdowns and exponentially distributed service and repair times are mainly considered. This circumstance greatly simplifies the mathematic...
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| Format: | Article |
| Language: | Russian |
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National Academy of Sciences of Belarus, the United Institute of Informatics Problems
2019-09-01
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| Series: | Informatika |
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| Online Access: | https://inf.grid.by/jour/article/view/870 |
| _version_ | 1826546825317842944 |
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| author | V. I. Klimenok |
| author_facet | V. I. Klimenok |
| author_sort | V. I. Klimenok |
| collection | DOAJ |
| description | Unreliable queuing systems are of considerable interest both in mathematical terms and for applications. Systems with stationary Poisson flows of customers and breakdowns and exponentially distributed service and repair times are mainly considered. This circumstance greatly simplifies the mathematical analysis of the corresponding models but rarely occurs in real systems, especially in telecommunications networks. The purpose of this study is to analyze the stationary behavior of a multi-server unreliable queueing system with a batch Markovian arrival process, which takes into account the correlation and bursty nature of real traffic. The service and repair processes are described by phase type distributions which makes it possible to take into account not only the average service and repair times but also the variance of these times. As a result of the research, the operation of the system is described by a multi-dimensional Markov chain. The condition of ergodicity of this chain is presented in a simple algorithmic form. An algorithm for calculating the stationary distribution is proposed. Formulas for the key performance characteristics of the system are obtained in terms of the stationary distribution of the Markov chain describing the system dynamics. The results can be used to make expert decisions in analyzing the performance and design of various telecommunication networks. |
| first_indexed | 2024-04-10T02:14:30Z |
| format | Article |
| id | doaj.art-e0fc19e505d140338f9bcbc10b41727e |
| institution | Directory Open Access Journal |
| issn | 1816-0301 |
| language | Russian |
| last_indexed | 2025-03-14T05:39:55Z |
| publishDate | 2019-09-01 |
| publisher | National Academy of Sciences of Belarus, the United Institute of Informatics Problems |
| record_format | Article |
| series | Informatika |
| spelling | doaj.art-e0fc19e505d140338f9bcbc10b41727e2025-03-05T13:56:47ZrusNational Academy of Sciences of Belarus, the United Institute of Informatics ProblemsInformatika1816-03012019-09-011636978840Stationary characteristics of unreliable queueing system with a batch Markovian arrival processV. I. Klimenok0Belarusian State UniversityUnreliable queuing systems are of considerable interest both in mathematical terms and for applications. Systems with stationary Poisson flows of customers and breakdowns and exponentially distributed service and repair times are mainly considered. This circumstance greatly simplifies the mathematical analysis of the corresponding models but rarely occurs in real systems, especially in telecommunications networks. The purpose of this study is to analyze the stationary behavior of a multi-server unreliable queueing system with a batch Markovian arrival process, which takes into account the correlation and bursty nature of real traffic. The service and repair processes are described by phase type distributions which makes it possible to take into account not only the average service and repair times but also the variance of these times. As a result of the research, the operation of the system is described by a multi-dimensional Markov chain. The condition of ergodicity of this chain is presented in a simple algorithmic form. An algorithm for calculating the stationary distribution is proposed. Formulas for the key performance characteristics of the system are obtained in terms of the stationary distribution of the Markov chain describing the system dynamics. The results can be used to make expert decisions in analyzing the performance and design of various telecommunication networks.https://inf.grid.by/jour/article/view/870queuing systemunreliable serversbatch markovian arrival processphase type distributionstationary distributionperformance characteristics |
| spellingShingle | V. I. Klimenok Stationary characteristics of unreliable queueing system with a batch Markovian arrival process Informatika queuing system unreliable servers batch markovian arrival process phase type distribution stationary distribution performance characteristics |
| title | Stationary characteristics of unreliable queueing system with a batch Markovian arrival process |
| title_full | Stationary characteristics of unreliable queueing system with a batch Markovian arrival process |
| title_fullStr | Stationary characteristics of unreliable queueing system with a batch Markovian arrival process |
| title_full_unstemmed | Stationary characteristics of unreliable queueing system with a batch Markovian arrival process |
| title_short | Stationary characteristics of unreliable queueing system with a batch Markovian arrival process |
| title_sort | stationary characteristics of unreliable queueing system with a batch markovian arrival process |
| topic | queuing system unreliable servers batch markovian arrival process phase type distribution stationary distribution performance characteristics |
| url | https://inf.grid.by/jour/article/view/870 |
| work_keys_str_mv | AT viklimenok stationarycharacteristicsofunreliablequeueingsystemwithabatchmarkovianarrivalprocess |