Analysis of queueing model with processor sharing discipline and customers impatience

Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival an...
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Autor*in:	Dudin, A. N. [verfasserIn] Dudin, S. A. [verfasserIn] Dudina, O. S. [verfasserIn] Samouylov, K. E. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Übergeordnetes Werk:	Enthalten in: Operations research perspectives - Amsterdam [u.a.] : Elsevier, 2014, 5(2018), Seite 245-255
Übergeordnetes Werk:	volume:5 ; year:2018 ; pages:245-255

Links:	Volltext Volltext Link aufrufen Terms of use

DOI / URN:	10.1016/j.orp.2018.08.003

Katalog-ID:	1047037963

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Indexfelder

author_variant	a n d an and s a d sa sad o s d os osd k e s ke kes
matchkey_str	article:22147160:2018----::nlssfuuigoewtpoesrhrndsilna
hierarchy_sort_str	2018
publishDate	2018
allfields	10.1016/j.orp.2018.08.003 doi 10419/246353 hdl (DE-627)1047037963 (DE-599)GBV1047037963 DE-627 ger DE-627 rda eng Dudin, A. N. verfasserin aut Analysis of queueing model with processor sharing discipline and customers impatience A.N. Dudin, S.A. Dudin, O.S. Dudina, K.E. Samouylov 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed. Dudin, S. A. verfasserin aut Dudina, O. S. verfasserin aut Samouylov, K. E. verfasserin aut Enthalten in Operations research perspectives Amsterdam [u.a.] : Elsevier, 2014 5(2018), Seite 245-255 Online-Ressource (DE-627)826105165 (DE-600)2821932-6 (DE-576)433076496 2214-7160 nnns volume:5 year:2018 pages:245-255 https://doi.org/10.1016/j.orp.2018.08.003 Resolving-System kostenfrei Volltext https://www.sciencedirect.com/science/article/pii/S2214716018301313/pdfft?md5=b3c1e8340883ecd7fb1011c321865ea1&pid=1-s2.0-S2214716018301313-main.pdf Verlag kostenfrei Volltext http://hdl.handle.net/10419/246353 Resolving-System kostenfrei http://creativecommons.org/licenses/by-nc-nd/4.0/ Verlag Terms of use 46 GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 5 2018 245-255 26 01 0206 1841280593 x1k 21-01-19 26 00 DE-206 56 Processor sharing 26 00 DE-206 56 Admission control 26 00 DE-206 56 Markovian arrival process 26 00 DE-206 56 Impatience
spelling	10.1016/j.orp.2018.08.003 doi 10419/246353 hdl (DE-627)1047037963 (DE-599)GBV1047037963 DE-627 ger DE-627 rda eng Dudin, A. N. verfasserin aut Analysis of queueing model with processor sharing discipline and customers impatience A.N. Dudin, S.A. Dudin, O.S. Dudina, K.E. Samouylov 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed. Dudin, S. A. verfasserin aut Dudina, O. S. verfasserin aut Samouylov, K. E. verfasserin aut Enthalten in Operations research perspectives Amsterdam [u.a.] : Elsevier, 2014 5(2018), Seite 245-255 Online-Ressource (DE-627)826105165 (DE-600)2821932-6 (DE-576)433076496 2214-7160 nnns volume:5 year:2018 pages:245-255 https://doi.org/10.1016/j.orp.2018.08.003 Resolving-System kostenfrei Volltext https://www.sciencedirect.com/science/article/pii/S2214716018301313/pdfft?md5=b3c1e8340883ecd7fb1011c321865ea1&pid=1-s2.0-S2214716018301313-main.pdf Verlag kostenfrei Volltext http://hdl.handle.net/10419/246353 Resolving-System kostenfrei http://creativecommons.org/licenses/by-nc-nd/4.0/ Verlag Terms of use 46 GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 5 2018 245-255 26 01 0206 1841280593 x1k 21-01-19 26 00 DE-206 56 Processor sharing 26 00 DE-206 56 Admission control 26 00 DE-206 56 Markovian arrival process 26 00 DE-206 56 Impatience
allfields_unstemmed	10.1016/j.orp.2018.08.003 doi 10419/246353 hdl (DE-627)1047037963 (DE-599)GBV1047037963 DE-627 ger DE-627 rda eng Dudin, A. N. verfasserin aut Analysis of queueing model with processor sharing discipline and customers impatience A.N. Dudin, S.A. Dudin, O.S. Dudina, K.E. Samouylov 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed. Dudin, S. A. verfasserin aut Dudina, O. S. verfasserin aut Samouylov, K. E. verfasserin aut Enthalten in Operations research perspectives Amsterdam [u.a.] : Elsevier, 2014 5(2018), Seite 245-255 Online-Ressource (DE-627)826105165 (DE-600)2821932-6 (DE-576)433076496 2214-7160 nnns volume:5 year:2018 pages:245-255 https://doi.org/10.1016/j.orp.2018.08.003 Resolving-System kostenfrei Volltext https://www.sciencedirect.com/science/article/pii/S2214716018301313/pdfft?md5=b3c1e8340883ecd7fb1011c321865ea1&pid=1-s2.0-S2214716018301313-main.pdf Verlag kostenfrei Volltext http://hdl.handle.net/10419/246353 Resolving-System kostenfrei http://creativecommons.org/licenses/by-nc-nd/4.0/ Verlag Terms of use 46 GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 5 2018 245-255 26 01 0206 1841280593 x1k 21-01-19 26 00 DE-206 56 Processor sharing 26 00 DE-206 56 Admission control 26 00 DE-206 56 Markovian arrival process 26 00 DE-206 56 Impatience
allfieldsGer	10.1016/j.orp.2018.08.003 doi 10419/246353 hdl (DE-627)1047037963 (DE-599)GBV1047037963 DE-627 ger DE-627 rda eng Dudin, A. N. verfasserin aut Analysis of queueing model with processor sharing discipline and customers impatience A.N. Dudin, S.A. Dudin, O.S. Dudina, K.E. Samouylov 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed. Dudin, S. A. verfasserin aut Dudina, O. S. verfasserin aut Samouylov, K. E. verfasserin aut Enthalten in Operations research perspectives Amsterdam [u.a.] : Elsevier, 2014 5(2018), Seite 245-255 Online-Ressource (DE-627)826105165 (DE-600)2821932-6 (DE-576)433076496 2214-7160 nnns volume:5 year:2018 pages:245-255 https://doi.org/10.1016/j.orp.2018.08.003 Resolving-System kostenfrei Volltext https://www.sciencedirect.com/science/article/pii/S2214716018301313/pdfft?md5=b3c1e8340883ecd7fb1011c321865ea1&pid=1-s2.0-S2214716018301313-main.pdf Verlag kostenfrei Volltext http://hdl.handle.net/10419/246353 Resolving-System kostenfrei http://creativecommons.org/licenses/by-nc-nd/4.0/ Verlag Terms of use 46 GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 5 2018 245-255 26 01 0206 1841280593 x1k 21-01-19 26 00 DE-206 56 Processor sharing 26 00 DE-206 56 Admission control 26 00 DE-206 56 Markovian arrival process 26 00 DE-206 56 Impatience
allfieldsSound	10.1016/j.orp.2018.08.003 doi 10419/246353 hdl (DE-627)1047037963 (DE-599)GBV1047037963 DE-627 ger DE-627 rda eng Dudin, A. N. verfasserin aut Analysis of queueing model with processor sharing discipline and customers impatience A.N. Dudin, S.A. Dudin, O.S. Dudina, K.E. Samouylov 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed. Dudin, S. A. verfasserin aut Dudina, O. S. verfasserin aut Samouylov, K. E. verfasserin aut Enthalten in Operations research perspectives Amsterdam [u.a.] : Elsevier, 2014 5(2018), Seite 245-255 Online-Ressource (DE-627)826105165 (DE-600)2821932-6 (DE-576)433076496 2214-7160 nnns volume:5 year:2018 pages:245-255 https://doi.org/10.1016/j.orp.2018.08.003 Resolving-System kostenfrei Volltext https://www.sciencedirect.com/science/article/pii/S2214716018301313/pdfft?md5=b3c1e8340883ecd7fb1011c321865ea1&pid=1-s2.0-S2214716018301313-main.pdf Verlag kostenfrei Volltext http://hdl.handle.net/10419/246353 Resolving-System kostenfrei http://creativecommons.org/licenses/by-nc-nd/4.0/ Verlag Terms of use 46 GBV_USEFLAG_U GBV_ILN_26 ISIL_DE-206 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 5 2018 245-255 26 01 0206 1841280593 x1k 21-01-19 26 00 DE-206 56 Processor sharing 26 00 DE-206 56 Admission control 26 00 DE-206 56 Markovian arrival process 26 00 DE-206 56 Impatience
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author	Dudin, A. N.
spellingShingle	Dudin, A. N. 26 Processor sharing 26 Admission control 26 Markovian arrival process 26 Impatience Analysis of queueing model with processor sharing discipline and customers impatience
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topic_title	26 00 DE-206 56 Processor sharing 26 00 DE-206 56 Admission control 26 00 DE-206 56 Markovian arrival process 26 00 DE-206 56 Impatience Analysis of queueing model with processor sharing discipline and customers impatience A.N. Dudin, S.A. Dudin, O.S. Dudina, K.E. Samouylov
topic	26 Processor sharing 26 Admission control 26 Markovian arrival process 26 Impatience
topic_unstemmed	26 Processor sharing 26 Admission control 26 Markovian arrival process 26 Impatience
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title	Analysis of queueing model with processor sharing discipline and customers impatience
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title_full	Analysis of queueing model with processor sharing discipline and customers impatience A.N. Dudin, S.A. Dudin, O.S. Dudina, K.E. Samouylov
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title_sort	analysis of queueing model with processor sharing discipline and customers impatience
title_auth	Analysis of queueing model with processor sharing discipline and customers impatience
abstract	Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed.
abstractGer	Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed.
abstract_unstemmed	Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed.
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title_short	Analysis of queueing model with processor sharing discipline and customers impatience
url	https://doi.org/10.1016/j.orp.2018.08.003 https://www.sciencedirect.com/science/article/pii/S2214716018301313/pdfft?md5=b3c1e8340883ecd7fb1011c321865ea1&pid=1-s2.0-S2214716018301313-main.pdf http://hdl.handle.net/10419/246353 http://creativecommons.org/licenses/by-nc-nd/4.0/
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up_date	2024-07-04T15:37:07.728Z
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N.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Analysis of queueing model with processor sharing discipline and customers impatience</subfield><subfield code="c">A.N. Dudin, S.A. Dudin, O.S. Dudina, K.E. Samouylov</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Dudin, S. A.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Dudina, O. S.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Samouylov, K. 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