On an exact solution of the rate matrix of

In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Garimella, Rama Murthy [verfasserIn] Alexander, Rumyantsev [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Matrix polynomial equation Matrix-analytic method Explicit solution Energy efficiency

Übergeordnetes Werk:	Enthalten in: Journal of parallel and distributed computing - Amsterdam [u.a.] : Elsevier, 1984, 119, Seite 172-178
Übergeordnetes Werk:	volume:119 ; pages:172-178

DOI / URN:	10.1016/j.jpdc.2018.04.013

Katalog-ID:	ELV001675559

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520			\|a In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study.
650		4	\|a Matrix polynomial equation
650		4	\|a Matrix-analytic method
650		4	\|a Explicit solution
650		4	\|a Energy efficiency
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allfields	10.1016/j.jpdc.2018.04.013 doi (DE-627)ELV001675559 (ELSEVIER)S0743-7315(18)30282-X DE-627 ger DE-627 rda eng 004 DE-600 54.25 bkl 54.32 bkl Garimella, Rama Murthy verfasserin aut On an exact solution of the rate matrix of 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study. Matrix polynomial equation Matrix-analytic method Explicit solution Energy efficiency Alexander, Rumyantsev verfasserin (orcid)0000-0003-2364-5939 aut Enthalten in Journal of parallel and distributed computing Amsterdam [u.a.] : Elsevier, 1984 119, Seite 172-178 Online-Ressource (DE-627)267328222 (DE-600)1469781-6 (DE-576)104193921 nnns volume:119 pages:172-178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 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_4393 54.25 Parallele Datenverarbeitung 54.32 Rechnerkommunikation AR 119 172-178
spelling	10.1016/j.jpdc.2018.04.013 doi (DE-627)ELV001675559 (ELSEVIER)S0743-7315(18)30282-X DE-627 ger DE-627 rda eng 004 DE-600 54.25 bkl 54.32 bkl Garimella, Rama Murthy verfasserin aut On an exact solution of the rate matrix of 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study. Matrix polynomial equation Matrix-analytic method Explicit solution Energy efficiency Alexander, Rumyantsev verfasserin (orcid)0000-0003-2364-5939 aut Enthalten in Journal of parallel and distributed computing Amsterdam [u.a.] : Elsevier, 1984 119, Seite 172-178 Online-Ressource (DE-627)267328222 (DE-600)1469781-6 (DE-576)104193921 nnns volume:119 pages:172-178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 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_4393 54.25 Parallele Datenverarbeitung 54.32 Rechnerkommunikation AR 119 172-178
allfields_unstemmed	10.1016/j.jpdc.2018.04.013 doi (DE-627)ELV001675559 (ELSEVIER)S0743-7315(18)30282-X DE-627 ger DE-627 rda eng 004 DE-600 54.25 bkl 54.32 bkl Garimella, Rama Murthy verfasserin aut On an exact solution of the rate matrix of 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study. Matrix polynomial equation Matrix-analytic method Explicit solution Energy efficiency Alexander, Rumyantsev verfasserin (orcid)0000-0003-2364-5939 aut Enthalten in Journal of parallel and distributed computing Amsterdam [u.a.] : Elsevier, 1984 119, Seite 172-178 Online-Ressource (DE-627)267328222 (DE-600)1469781-6 (DE-576)104193921 nnns volume:119 pages:172-178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 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_4393 54.25 Parallele Datenverarbeitung 54.32 Rechnerkommunikation AR 119 172-178
allfieldsGer	10.1016/j.jpdc.2018.04.013 doi (DE-627)ELV001675559 (ELSEVIER)S0743-7315(18)30282-X DE-627 ger DE-627 rda eng 004 DE-600 54.25 bkl 54.32 bkl Garimella, Rama Murthy verfasserin aut On an exact solution of the rate matrix of 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study. Matrix polynomial equation Matrix-analytic method Explicit solution Energy efficiency Alexander, Rumyantsev verfasserin (orcid)0000-0003-2364-5939 aut Enthalten in Journal of parallel and distributed computing Amsterdam [u.a.] : Elsevier, 1984 119, Seite 172-178 Online-Ressource (DE-627)267328222 (DE-600)1469781-6 (DE-576)104193921 nnns volume:119 pages:172-178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 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_4393 54.25 Parallele Datenverarbeitung 54.32 Rechnerkommunikation AR 119 172-178
allfieldsSound	10.1016/j.jpdc.2018.04.013 doi (DE-627)ELV001675559 (ELSEVIER)S0743-7315(18)30282-X DE-627 ger DE-627 rda eng 004 DE-600 54.25 bkl 54.32 bkl Garimella, Rama Murthy verfasserin aut On an exact solution of the rate matrix of 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study. Matrix polynomial equation Matrix-analytic method Explicit solution Energy efficiency Alexander, Rumyantsev verfasserin (orcid)0000-0003-2364-5939 aut Enthalten in Journal of parallel and distributed computing Amsterdam [u.a.] : Elsevier, 1984 119, Seite 172-178 Online-Ressource (DE-627)267328222 (DE-600)1469781-6 (DE-576)104193921 nnns volume:119 pages:172-178 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 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_4393 54.25 Parallele Datenverarbeitung 54.32 Rechnerkommunikation AR 119 172-178
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author	Garimella, Rama Murthy
spellingShingle	Garimella, Rama Murthy ddc 004 bkl 54.25 bkl 54.32 misc Matrix polynomial equation misc Matrix-analytic method misc Explicit solution misc Energy efficiency On an exact solution of the rate matrix of
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topic_title	004 DE-600 54.25 bkl 54.32 bkl On an exact solution of the rate matrix of Matrix polynomial equation Matrix-analytic method Explicit solution Energy efficiency
topic	ddc 004 bkl 54.25 bkl 54.32 misc Matrix polynomial equation misc Matrix-analytic method misc Explicit solution misc Energy efficiency
topic_unstemmed	ddc 004 bkl 54.25 bkl 54.32 misc Matrix polynomial equation misc Matrix-analytic method misc Explicit solution misc Energy efficiency
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title	On an exact solution of the rate matrix of
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title_full	On an exact solution of the rate matrix of
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title_sort	on an exact solution of the rate matrix of
title_auth	On an exact solution of the rate matrix of
abstract	In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study.
abstractGer	In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study.
abstract_unstemmed	In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study.
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title_short	On an exact solution of the rate matrix of
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up_date	2024-07-06T22:11:29.574Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV001675559</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230524160912.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230428s2018 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.jpdc.2018.04.013</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV001675559</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0743-7315(18)30282-X</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">54.25</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">54.32</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Garimella, Rama Murthy</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On an exact solution of the rate matrix of</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</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">In this research paper we consider the matrix polynomial equation arising naturally in the equilibrium analysis of a structured G ∕ M ∕ 1 -type Markov process. We obtain an explicit expression for the unknown rate matrix R being 2 × 2 matrix. The method is based on symbolic solution of the determinantal polynomial equation. Using Cayley–Hamilton theorem, the matrix polynomial equation for the matrix R is reduced to the system of linear equations. Motivated by applications in Edge Computing by means of Internet of Things devices having tight constraints in energy consumption, we demonstrate the applicability of the method by a novel approach to energy efficiency of a single-server computing system. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrix polynomial equation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrix-analytic method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Explicit solution</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Energy efficiency</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Alexander, Rumyantsev</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-2364-5939</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of parallel and distributed 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