An off-line multiprocessor real-time scheduling algorithm to reduce static energy consumption

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1 An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion Firs Workshop on Highly-Reliable Power-Efficien Embedded Designs Shenzhen, China Vincen Legou, Mahieu Jan, Lauren Paue CEA LIST February 24, 2013

2 Inroducion Conex: embedded hard real-ime sysems (e.g. auomoive,... ) Hard real-ime: ime consrains canno be violaed Reducing energy consumpion has several advanages: Increase he auonomy of baery-powered sysems Provide energy efficien or green soluions Targe muliprocessor sysems Uniprocessor are now superseded by muliprocessor sysems Almos no muliprocessor soluion exiss o reduce consumpion Objecive Schedule muliprocessor real-ime sysems o reduce consumpion An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

3 Modeling he consumpion of processors Focusing on saic consumpion Dynamic and saic consumpion (P = P dynamic + P saic ) P saic = consan (leakage curren) Saic consumpion now dominaes dynamic consumpion Technology evolves: higher densiy, smaller supply volage 2 sofware soluions o reduce consumpion Dynamic consumpion: Dynamic Volage & Frequency Scaling Saic consumpion: Dynamic Power Managemen An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

4 DPM: Dynamic Power Managemen Reduce saic consumpion by using he low-power saes of processors In a low-power sae: Processor inacive and energy consumpion reduced Transiion delay δ required o ge back o he acive sae Several low-power saes available The lower he consumpion, he higher he ransiion delay Break-Even Time (BET): smalles idle period for which acivaing a low-power sae saves more energy han leing he processor idle δ τ BET idle τ low-power sae BET Objecive: acivae he mos efficien low-power saes wihou increasing he number of preempions and migraions An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

5 DPM muliprocessor scheduling algorihms The objecive being o creae large idle periods Pariioned scheduling (no migraion) Use uniprocessor DPM soluions on each processor Canno merge idle periods from differen processors Global scheduling (migraions allowed) Minimize he number of processors [Bhai09] Non-opimal scheduling algorihm Exising DPM scheduling algorihms are no suiable Schedule decisions should be aken according o he workload Insead, hey use ask characerisics (e.g. earlies deadline) WCET 1 2 Period 2 3 c 1 c An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

6 Approach Solve he problem off-line. Several advanages: Compue a schedule in a hyperperiod Wihou aking scheduling decisions for each ask individually Bu for he ask se as a whole in a hyperperiod Use linear programming o express consrains and objecives: Real-ime consrain: no deadline miss Consumpion objecive: large idle periods Ensure a maximal consumpion in he wors case scenario Compuaion using he Wors Case Execuion Time (WCET) Larger idle periods means minimizing he number of idle periods LPDPM: Linear Programming DPM An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

7 Task model m processors, n asks (WCET C, period T ), hyperperiod H Global uilizaion U = n C i i=1 T i (m 1 < U < m) Division in inervals, for example : WCET Period Jobs Objecive o compue all weighs of all asks on all inervals w j,k weigh of job j on inerval k I 1 I 2 I 3 I 4 w 1,1 w 2,2 w 2,3 w 3,4 w 7,1 w 7,2 w 8,3 w 8, An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

8 Iniial linear sysem Se of consrains o keep he schedulabiliy [Lemerre08]: I k : lengh of inerval k J k : se of jobs in inerval k E j : se of inervals where j is presen k, j J k w j,k m k, j, 0 w j,k 1 j, k E j w j,k I k = j.c U m inside each inerval 0 u 1 for each ask inside each inerval All jobs are fully execued I 1 I 2 I 3 I 4 c 1 c An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

9 Add an addiional idle ask τ Accouns for he ime where processors are supposed o be idle Uilizaion of τ = m U, period = H As a consequence: global uilizaion U = m Only one processor can be idle simulaneously w k weigh of τ on inerval k Objecive: reduce he number of preempions of τ Inerval w k I 1 I 2 I 3 I 4 c 1 c An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

10 Add an addiional idle ask τ Accouns for he ime where processors are supposed o be idle Uilizaion of τ = m U, period = H As a consequence: global uilizaion U = m Only one processor can be idle simulaneously w k weigh of τ on inerval k Objecive: reduce he number of preempions of τ Inerval w k I 1 I 2 I 3 I 4 c 1 c 2 τ' τ' τ' τ' An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

11 Reducing he number of preempions of τ (1) Add a firs objecive funcion in he linear sysem Avoid inervals where 0 < w k < 1 Because a preempion occurs Promoe full inervals (w k = 1) and empy inervals (w k = 0) Inerval w k I 1 I 2 I 3 I 4 c 1 c 2 τ' τ' τ' τ' An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

12 Reducing he number of preempions of τ (1) Add a firs objecive funcion in he linear sysem Avoid inervals where 0 < w k < 1 Because a preempion occurs Promoe full inervals (w k = 1) and empy inervals (w k = 0) Inerval w k I 1 I 2 I 3 I 4 c 1 c 2 τ' τ' τ' An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

13 Reducing he number of preempions of τ (2) Add a second objecive funcion in he linear sysem Avoid preempions beween inervals Group full inervals and group empy inervals Inerval w k I 1 I 2 I 3 I 4 c 1 c 2 τ' τ' τ' An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

14 Reducing he number of preempions of τ (2) Add a second objecive funcion in he linear sysem Avoid preempions beween inervals Group full inervals and group empy inervals Inerval w k I 1 I 2 I 3 I 4 c 1 c 2 τ' τ' τ' τ' An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

15 On-line schedule inside inervals Using he weighs compued off-line using he linear program Schedule impacs idle periods only when 0 < w k < 1 Soluion: schedule τ a he beginning or a he end he inerval During he execuion of τ, acivae he deepes low-power sae Processor says idle if he idle period is no large enough I 1 I 2 I 3 I 4 c 1 c 2 τ' τ' τ' τ' An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

16 On-line schedule inside inervals Using he weighs compued off-line using he linear program Schedule impacs idle periods only when 0 < w k < 1 Soluion: schedule τ a he beginning or a he end he inerval During he execuion of τ, acivae he deepes low-power sae Processor says idle if he idle period is no large enough I 1 I 2 I 3 I 4 c 1 c 2 τ' τ' τ' τ' An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

17 Experimenal evaluaion In a simulaor, schedule random ask ses wih LPDPM and wo exising opimal muliprocessor schedulers RUN & U-EDF No oher DPM opimal muliprocessor scheduling algorihm RUN & U-EDF: schedulers reducing he number of preempions 4 processors, 10 asks 2000 ask ses for each global uilizaion beween 3.05 and 3.95 Objecive: evaluae he number and he lengh of he idle periods as well as he number of preempions An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

18 Mean number of idle periods Beween 2 and 5 imes less idle periods for LPDPM 70 RUN U-EDF 60 LPDPM Global uilizaion An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

19 Idle period lenghs Using all idle periods generaed by all ask ses RUN & U-EDF: smaller idle periods, wih a lengh always < 120 LPDPM: larger idle periods, can be wice as large 10 7 RUN U-EDF LPDPM Idle period Lengh An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

20 Mean oal number of preempions Fewer preempions han U-EDF Less han 1.4 more preempions han RUN RUN U-EDF LPDPM Global uilizaion An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

21 Conclusion and perspecives Conribuion: LPDPM, an off-line opimal muliprocessor real-ime scheduling algorihm reducing saic consumpion LPDPM generaes less and larger idle periods such ha deeper low-power saes can be acivaed. The oal number of preempions does no increase. Global consumpion simulaion using he low-power saes of he STM32L board (Corex-M3): LPDPM is up o 8% more energy efficien han exising opimal scheduling algorihms Perspecives When asks do no use heir WCET, schedule inervals o furher exend he exising idle periods Temperaure: impac on he energy consumpion An off-line muliprocessor real-ime scheduling algorihm o reduce saic energy consumpion February 24, / 17

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