Feasibility of on-line speed policies in real-time systems
Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed...
Ausführliche Beschreibung
Autor*in: |
Gaujal, Bruno [verfasserIn] Girault, Alain [verfasserIn] Plassart, Stéphan [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2020 |
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Schlagwörter: |
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Übergeordnetes Werk: |
Enthalten in: Real-time systems - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1989, 56(2020), 3 vom: 27. Apr., Seite 254-292 |
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Übergeordnetes Werk: |
volume:56 ; year:2020 ; number:3 ; day:27 ; month:04 ; pages:254-292 |
Links: |
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DOI / URN: |
10.1007/s11241-020-09347-y |
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Katalog-ID: |
SPR040369897 |
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520 | |a Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility. | ||
650 | 4 | |a Hard real-time systems |7 (dpeaa)DE-He213 | |
650 | 4 | |a Feasibility |7 (dpeaa)DE-He213 | |
650 | 4 | |a On-line speed policy |7 (dpeaa)DE-He213 | |
650 | 4 | |a Markov decision process |7 (dpeaa)DE-He213 | |
650 | 4 | |a Dynamic voltage |7 (dpeaa)DE-He213 | |
650 | 4 | |a Frequency scaling |7 (dpeaa)DE-He213 | |
700 | 1 | |a Girault, Alain |e verfasserin |4 aut | |
700 | 1 | |a Plassart, Stéphan |e verfasserin |4 aut | |
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773 | 1 | 8 | |g volume:56 |g year:2020 |g number:3 |g day:27 |g month:04 |g pages:254-292 |
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10.1007/s11241-020-09347-y doi (DE-627)SPR040369897 (SPR)s11241-020-09347-y-e DE-627 ger DE-627 rakwb eng 004 ASE 54.27 bkl Gaujal, Bruno verfasserin aut Feasibility of on-line speed policies in real-time systems 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility. Hard real-time systems (dpeaa)DE-He213 Feasibility (dpeaa)DE-He213 On-line speed policy (dpeaa)DE-He213 Markov decision process (dpeaa)DE-He213 Dynamic voltage (dpeaa)DE-He213 Frequency scaling (dpeaa)DE-He213 Girault, Alain verfasserin aut Plassart, Stéphan verfasserin aut Enthalten in Real-time systems Dordrecht [u.a.] : Springer Science + Business Media B.V, 1989 56(2020), 3 vom: 27. Apr., Seite 254-292 (DE-627)271351209 (DE-600)1480026-3 1573-1383 nnns volume:56 year:2020 number:3 day:27 month:04 pages:254-292 https://dx.doi.org/10.1007/s11241-020-09347-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.27 ASE AR 56 2020 3 27 04 254-292 |
spelling |
10.1007/s11241-020-09347-y doi (DE-627)SPR040369897 (SPR)s11241-020-09347-y-e DE-627 ger DE-627 rakwb eng 004 ASE 54.27 bkl Gaujal, Bruno verfasserin aut Feasibility of on-line speed policies in real-time systems 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility. Hard real-time systems (dpeaa)DE-He213 Feasibility (dpeaa)DE-He213 On-line speed policy (dpeaa)DE-He213 Markov decision process (dpeaa)DE-He213 Dynamic voltage (dpeaa)DE-He213 Frequency scaling (dpeaa)DE-He213 Girault, Alain verfasserin aut Plassart, Stéphan verfasserin aut Enthalten in Real-time systems Dordrecht [u.a.] : Springer Science + Business Media B.V, 1989 56(2020), 3 vom: 27. Apr., Seite 254-292 (DE-627)271351209 (DE-600)1480026-3 1573-1383 nnns volume:56 year:2020 number:3 day:27 month:04 pages:254-292 https://dx.doi.org/10.1007/s11241-020-09347-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.27 ASE AR 56 2020 3 27 04 254-292 |
allfields_unstemmed |
10.1007/s11241-020-09347-y doi (DE-627)SPR040369897 (SPR)s11241-020-09347-y-e DE-627 ger DE-627 rakwb eng 004 ASE 54.27 bkl Gaujal, Bruno verfasserin aut Feasibility of on-line speed policies in real-time systems 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility. Hard real-time systems (dpeaa)DE-He213 Feasibility (dpeaa)DE-He213 On-line speed policy (dpeaa)DE-He213 Markov decision process (dpeaa)DE-He213 Dynamic voltage (dpeaa)DE-He213 Frequency scaling (dpeaa)DE-He213 Girault, Alain verfasserin aut Plassart, Stéphan verfasserin aut Enthalten in Real-time systems Dordrecht [u.a.] : Springer Science + Business Media B.V, 1989 56(2020), 3 vom: 27. Apr., Seite 254-292 (DE-627)271351209 (DE-600)1480026-3 1573-1383 nnns volume:56 year:2020 number:3 day:27 month:04 pages:254-292 https://dx.doi.org/10.1007/s11241-020-09347-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.27 ASE AR 56 2020 3 27 04 254-292 |
allfieldsGer |
10.1007/s11241-020-09347-y doi (DE-627)SPR040369897 (SPR)s11241-020-09347-y-e DE-627 ger DE-627 rakwb eng 004 ASE 54.27 bkl Gaujal, Bruno verfasserin aut Feasibility of on-line speed policies in real-time systems 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility. Hard real-time systems (dpeaa)DE-He213 Feasibility (dpeaa)DE-He213 On-line speed policy (dpeaa)DE-He213 Markov decision process (dpeaa)DE-He213 Dynamic voltage (dpeaa)DE-He213 Frequency scaling (dpeaa)DE-He213 Girault, Alain verfasserin aut Plassart, Stéphan verfasserin aut Enthalten in Real-time systems Dordrecht [u.a.] : Springer Science + Business Media B.V, 1989 56(2020), 3 vom: 27. Apr., Seite 254-292 (DE-627)271351209 (DE-600)1480026-3 1573-1383 nnns volume:56 year:2020 number:3 day:27 month:04 pages:254-292 https://dx.doi.org/10.1007/s11241-020-09347-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.27 ASE AR 56 2020 3 27 04 254-292 |
allfieldsSound |
10.1007/s11241-020-09347-y doi (DE-627)SPR040369897 (SPR)s11241-020-09347-y-e DE-627 ger DE-627 rakwb eng 004 ASE 54.27 bkl Gaujal, Bruno verfasserin aut Feasibility of on-line speed policies in real-time systems 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility. Hard real-time systems (dpeaa)DE-He213 Feasibility (dpeaa)DE-He213 On-line speed policy (dpeaa)DE-He213 Markov decision process (dpeaa)DE-He213 Dynamic voltage (dpeaa)DE-He213 Frequency scaling (dpeaa)DE-He213 Girault, Alain verfasserin aut Plassart, Stéphan verfasserin aut Enthalten in Real-time systems Dordrecht [u.a.] : Springer Science + Business Media B.V, 1989 56(2020), 3 vom: 27. Apr., Seite 254-292 (DE-627)271351209 (DE-600)1480026-3 1573-1383 nnns volume:56 year:2020 number:3 day:27 month:04 pages:254-292 https://dx.doi.org/10.1007/s11241-020-09347-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.27 ASE AR 56 2020 3 27 04 254-292 |
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English |
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Enthalten in Real-time systems 56(2020), 3 vom: 27. Apr., Seite 254-292 volume:56 year:2020 number:3 day:27 month:04 pages:254-292 |
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Enthalten in Real-time systems 56(2020), 3 vom: 27. Apr., Seite 254-292 volume:56 year:2020 number:3 day:27 month:04 pages:254-292 |
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Hard real-time systems Feasibility On-line speed policy Markov decision process Dynamic voltage Frequency scaling |
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Gaujal, Bruno @@aut@@ Girault, Alain @@aut@@ Plassart, Stéphan @@aut@@ |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR040369897</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220111055615.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2020 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11241-020-09347-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR040369897</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s11241-020-09347-y-e</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">rakwb</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">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">54.27</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gaujal, Bruno</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Feasibility of on-line speed policies in real-time systems</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</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">Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hard real-time systems</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Feasibility</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">On-line speed policy</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Markov decision process</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dynamic voltage</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Frequency scaling</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Girault, Alain</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Plassart, Stéphan</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Real-time systems</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1989</subfield><subfield code="g">56(2020), 3 vom: 27. 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Gaujal, Bruno |
spellingShingle |
Gaujal, Bruno ddc 004 bkl 54.27 misc Hard real-time systems misc Feasibility misc On-line speed policy misc Markov decision process misc Dynamic voltage misc Frequency scaling Feasibility of on-line speed policies in real-time systems |
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004 ASE 54.27 bkl Feasibility of on-line speed policies in real-time systems Hard real-time systems (dpeaa)DE-He213 Feasibility (dpeaa)DE-He213 On-line speed policy (dpeaa)DE-He213 Markov decision process (dpeaa)DE-He213 Dynamic voltage (dpeaa)DE-He213 Frequency scaling (dpeaa)DE-He213 |
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ddc 004 bkl 54.27 misc Hard real-time systems misc Feasibility misc On-line speed policy misc Markov decision process misc Dynamic voltage misc Frequency scaling |
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ddc 004 bkl 54.27 misc Hard real-time systems misc Feasibility misc On-line speed policy misc Markov decision process misc Dynamic voltage misc Frequency scaling |
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feasibility of on-line speed policies in real-time systems |
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Feasibility of on-line speed policies in real-time systems |
abstract |
Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility. |
abstractGer |
Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility. |
abstract_unstemmed |
Abstract We consider a real-time system where a single processor with variable speed executes an infinite sequence of sporadic and independent jobs. We assume that job sizes and relative deadlines are bounded by C and %$\varDelta %$ respectively. Furthermore, %$S_{\max }%$ denotes the maximal speed of the processor. In such a real-time system, a speed selection policy dynamically chooses (i.e., on-line) the speed of the processor to execute the current, not yet finished, jobs. We say that an on-line speed policy is feasible if it is able to execute any sequence of jobs while meeting two constraints: the processor speed is always below %$S_{\max }%$ and no job misses its deadline. In this paper, we compare the feasibility region of four on-line speed selection policies in single-processor real-time systems, namely Optimal Available %${\text{(OA)}}%$ (Yao et al. in IEEE annual foundations of computer science, 1995), Average Rate %${\text{(AVR)}}%$ (Yao et al. 1995), %${\text{(BKP)}}%$ (Bansal in J ACM 54:1, 2007), and a Markovian Policy based on dynamic programming %${\text{(MP)}}%$ (Gaujal in Technical Report hal-01615835, Inria, 2017). We prove the following results:(OA)%$ {\text{(OA)}}%$ is feasible if and only if Smax≥C(hΔ-1+1)%$S_{\max } \ge C (h_{\varDelta -1}+1)%$, where hn%$h_n%$ is the n-th harmonic number (hn=∑i=1n1/i≈logn%$h_n = \sum _{i=1}^n 1/i \approx \log n%$).(AVR)%${\text{(AVR)}}%$ is feasible if and only if Smax≥ChΔ%$S_{\max } \ge C h_\varDelta %$.(BKP)%${\text{(BKP)}}%$ is feasible if and only if Smax≥eC%$S_{\max } \ge e C%$ (where e=exp(1)%$e = \exp (1)%$).(MP)%${\text{(MP)}}%$ is feasible if and only if Smax≥C%$S_{\max } \ge C%$. This is an optimal feasibility condition because when Smax<C%$S_{\max } < C%$ no policy can be feasible. This reinforces the interest of %${\text{(MP)}}%$ that is not only optimal for energy consumption (on average) but is also optimal regarding feasibility. |
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container_issue |
3 |
title_short |
Feasibility of on-line speed policies in real-time systems |
url |
https://dx.doi.org/10.1007/s11241-020-09347-y |
remote_bool |
true |
author2 |
Girault, Alain Plassart, Stéphan |
author2Str |
Girault, Alain Plassart, Stéphan |
ppnlink |
271351209 |
mediatype_str_mv |
c |
isOA_txt |
false |
hochschulschrift_bool |
false |
doi_str |
10.1007/s11241-020-09347-y |
up_date |
2024-07-03T15:33:12.955Z |
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|
score |
7.399701 |