Performance characteristics of the fork-join queuing system
Objectives. The problem of investigating a fork-join queuing system is considered. It is required to build the process of the system functioning, to find the condition for the existence of a stationary distribution, and propose algorithms for calculating the stationary distribution and the main stat...
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| Format: | Article |
| Language: | Russian |
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National Academy of Sciences of Belarus, the United Institute of Informatics Problems
2023-09-01
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| Series: | Informatika |
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| Online Access: | https://inf.grid.by/jour/article/view/1254 |
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| _version_ | 1832543435209310208 |
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| author | V. I. Klimenok |
| author_facet | V. I. Klimenok |
| author_sort | V. I. Klimenok |
| collection | DOAJ |
| description | Objectives. The problem of investigating a fork-join queuing system is considered. It is required to build the process of the system functioning, to find the condition for the existence of a stationary distribution, and propose algorithms for calculating the stationary distribution and the main stationary performance characteristics. The special interest of the study is to obtain the lower and upper bounds of the mean sojourn time of a customer in the system.Methods. Methods of probability theory, queuing theory and matrix theory are used.Results. The functioning of the system is described in terms of a multidimensional Markov chain. A constructive condition for the existence of a stationary distribution is found, and algorithms for calculating the stationary distribution and stationary performance characteristics of the system are proposed. Analytical expressions are obtained for the lower and upper bounds of the mean sojourn time of customers in the system.Conclusion. The functioning of the fork-join queuing system with a stationary Poisson flow has been studied. Each of the arriving customers forks into two tasks that go to two subsystems, each of which consists of a server and a buffer. We assume that the buffer to one of the servers is unlimited, and to the second server has a finite volume. Service times have, generally speaking, different phase distributions (PH-Phase type distributions). For this system, a condition for the existence of a stationary distribution is obtained, algorithms for calculating the stationary distribution and a number of stationary performance measures of the system are proposed. Analytical expressions for the lower and upper bounds of the mean sojourn time of a customer in the system from the moment it enters the system to the moment of synchronization, which is a critical performance indicator of the fork-join queues, are obtained. The results of the study can be used for modeling various computer and communication systems, in particular, systems that perform parallel computing, customer processing in distributed databases, and parallel disk access. |
| format | Article |
| id | doaj-art-8ac08296a85c4839bc797840c39e3cd4 |
| institution | Kabale University |
| issn | 1816-0301 |
| language | Russian |
| publishDate | 2023-09-01 |
| publisher | National Academy of Sciences of Belarus, the United Institute of Informatics Problems |
| record_format | Article |
| series | Informatika |
| spelling | doaj-art-8ac08296a85c4839bc797840c39e3cd42025-02-03T11:40:30ZrusNational Academy of Sciences of Belarus, the United Institute of Informatics ProblemsInformatika1816-03012023-09-01203506010.37661/1816-0301-2023-20-3-50-601041Performance characteristics of the fork-join queuing systemV. I. Klimenok0Belarusian State UniversityObjectives. The problem of investigating a fork-join queuing system is considered. It is required to build the process of the system functioning, to find the condition for the existence of a stationary distribution, and propose algorithms for calculating the stationary distribution and the main stationary performance characteristics. The special interest of the study is to obtain the lower and upper bounds of the mean sojourn time of a customer in the system.Methods. Methods of probability theory, queuing theory and matrix theory are used.Results. The functioning of the system is described in terms of a multidimensional Markov chain. A constructive condition for the existence of a stationary distribution is found, and algorithms for calculating the stationary distribution and stationary performance characteristics of the system are proposed. Analytical expressions are obtained for the lower and upper bounds of the mean sojourn time of customers in the system.Conclusion. The functioning of the fork-join queuing system with a stationary Poisson flow has been studied. Each of the arriving customers forks into two tasks that go to two subsystems, each of which consists of a server and a buffer. We assume that the buffer to one of the servers is unlimited, and to the second server has a finite volume. Service times have, generally speaking, different phase distributions (PH-Phase type distributions). For this system, a condition for the existence of a stationary distribution is obtained, algorithms for calculating the stationary distribution and a number of stationary performance measures of the system are proposed. Analytical expressions for the lower and upper bounds of the mean sojourn time of a customer in the system from the moment it enters the system to the moment of synchronization, which is a critical performance indicator of the fork-join queues, are obtained. The results of the study can be used for modeling various computer and communication systems, in particular, systems that perform parallel computing, customer processing in distributed databases, and parallel disk access.https://inf.grid.by/jour/article/view/1254fork-join queuing systemstationary poisson flowphase-type distribution of service timesstationary performance measuresbounds for the mean sojourn time |
| spellingShingle | V. I. Klimenok Performance characteristics of the fork-join queuing system Informatika fork-join queuing system stationary poisson flow phase-type distribution of service times stationary performance measures bounds for the mean sojourn time |
| title | Performance characteristics of the fork-join queuing system |
| title_full | Performance characteristics of the fork-join queuing system |
| title_fullStr | Performance characteristics of the fork-join queuing system |
| title_full_unstemmed | Performance characteristics of the fork-join queuing system |
| title_short | Performance characteristics of the fork-join queuing system |
| title_sort | performance characteristics of the fork join queuing system |
| topic | fork-join queuing system stationary poisson flow phase-type distribution of service times stationary performance measures bounds for the mean sojourn time |
| url | https://inf.grid.by/jour/article/view/1254 |
| work_keys_str_mv | AT viklimenok performancecharacteristicsoftheforkjoinqueuingsystem |