Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time
Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amoun...
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| Autor*in: |
Moiseeva, S. P. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Automation and remote control - Pleiades Publishing, 1957, 83(2022), 8 vom: Aug., Seite 1213-1227 |
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| Übergeordnetes Werk: |
volume:83 ; year:2022 ; number:8 ; month:08 ; pages:1213-1227 |
| Links: |
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| DOI / URN: |
10.1134/S0005117922080057 |
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OLC2132057818 |
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| 520 | |a Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources. | ||
| 650 | 4 | |a infinite-server heterogeneous queuing system | |
| 650 | 4 | |a resource system | |
| 650 | 4 | |a parallel queuing | |
| 650 | 4 | |a Markov modulated Poisson flow | |
| 650 | 4 | |a asymptotic analysis | |
| 700 | 1 | |a Bushkova, T. V. |4 aut | |
| 700 | 1 | |a Pankratova, E. V. |4 aut | |
| 700 | 1 | |a Farkhadov, M. P. |4 aut | |
| 700 | 1 | |a Imomov, A. A. |4 aut | |
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10.1134/S0005117922080057 doi (DE-627)OLC2132057818 (DE-He213)S0005117922080057-p DE-627 ger DE-627 rakwb eng 000 620 VZ Moiseeva, S. P. verfasserin aut Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources. infinite-server heterogeneous queuing system resource system parallel queuing Markov modulated Poisson flow asymptotic analysis Bushkova, T. V. aut Pankratova, E. V. aut Farkhadov, M. P. aut Imomov, A. A. aut Enthalten in Automation and remote control Pleiades Publishing, 1957 83(2022), 8 vom: Aug., Seite 1213-1227 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:83 year:2022 number:8 month:08 pages:1213-1227 https://doi.org/10.1134/S0005117922080057 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 83 2022 8 08 1213-1227 |
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10.1134/S0005117922080057 doi (DE-627)OLC2132057818 (DE-He213)S0005117922080057-p DE-627 ger DE-627 rakwb eng 000 620 VZ Moiseeva, S. P. verfasserin aut Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources. infinite-server heterogeneous queuing system resource system parallel queuing Markov modulated Poisson flow asymptotic analysis Bushkova, T. V. aut Pankratova, E. V. aut Farkhadov, M. P. aut Imomov, A. A. aut Enthalten in Automation and remote control Pleiades Publishing, 1957 83(2022), 8 vom: Aug., Seite 1213-1227 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:83 year:2022 number:8 month:08 pages:1213-1227 https://doi.org/10.1134/S0005117922080057 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 83 2022 8 08 1213-1227 |
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10.1134/S0005117922080057 doi (DE-627)OLC2132057818 (DE-He213)S0005117922080057-p DE-627 ger DE-627 rakwb eng 000 620 VZ Moiseeva, S. P. verfasserin aut Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources. infinite-server heterogeneous queuing system resource system parallel queuing Markov modulated Poisson flow asymptotic analysis Bushkova, T. V. aut Pankratova, E. V. aut Farkhadov, M. P. aut Imomov, A. A. aut Enthalten in Automation and remote control Pleiades Publishing, 1957 83(2022), 8 vom: Aug., Seite 1213-1227 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:83 year:2022 number:8 month:08 pages:1213-1227 https://doi.org/10.1134/S0005117922080057 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 83 2022 8 08 1213-1227 |
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10.1134/S0005117922080057 doi (DE-627)OLC2132057818 (DE-He213)S0005117922080057-p DE-627 ger DE-627 rakwb eng 000 620 VZ Moiseeva, S. P. verfasserin aut Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources. infinite-server heterogeneous queuing system resource system parallel queuing Markov modulated Poisson flow asymptotic analysis Bushkova, T. V. aut Pankratova, E. V. aut Farkhadov, M. P. aut Imomov, A. A. aut Enthalten in Automation and remote control Pleiades Publishing, 1957 83(2022), 8 vom: Aug., Seite 1213-1227 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:83 year:2022 number:8 month:08 pages:1213-1227 https://doi.org/10.1134/S0005117922080057 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 83 2022 8 08 1213-1227 |
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10.1134/S0005117922080057 doi (DE-627)OLC2132057818 (DE-He213)S0005117922080057-p DE-627 ger DE-627 rakwb eng 000 620 VZ Moiseeva, S. P. verfasserin aut Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources. infinite-server heterogeneous queuing system resource system parallel queuing Markov modulated Poisson flow asymptotic analysis Bushkova, T. V. aut Pankratova, E. V. aut Farkhadov, M. P. aut Imomov, A. A. aut Enthalten in Automation and remote control Pleiades Publishing, 1957 83(2022), 8 vom: Aug., Seite 1213-1227 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:83 year:2022 number:8 month:08 pages:1213-1227 https://doi.org/10.1134/S0005117922080057 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 83 2022 8 08 1213-1227 |
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Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time |
| abstract |
Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources. © Pleiades Publishing, Ltd. 2022 |
| abstractGer |
Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources. © Pleiades Publishing, Ltd. 2022 |
| abstract_unstemmed |
Abstract We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources. © Pleiades Publishing, Ltd. 2022 |
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| title_short |
Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time |
| url |
https://doi.org/10.1134/S0005117922080057 |
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| author2 |
Bushkova, T. V. Pankratova, E. V. Farkhadov, M. P. Imomov, A. A. |
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Bushkova, T. V. Pankratova, E. V. Farkhadov, M. P. Imomov, A. A. |
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129603481 |
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| doi_str |
10.1134/S0005117922080057 |
| up_date |
2024-07-04T11:41:02.051Z |
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