Mixed Criticality Systems with Weakly-Hard Constraints

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1 Mixed Criticality Systems with Weakly-Hard Costraits Oliver Gettigs Uiversity of York Sophie Quito INRIA Greoble Rob Davis Uiversity of York

Mixed Criticality Systems Mixed Criticality Criticality is the required level of assurace agaist failure Mixed Criticality Systems cotai applicatios of at least two criticality levels Examples:

2 Mixed Criticality Systems Mixed Criticality Criticality is the required level of assurace agaist failure Mixed Criticality Systems cotai applicatios of at least two criticality levels Examples: Aerospace Flight Cotrol Systems v. Surveillace Motivatio for MCS Automotive Electric Power Steerig v. Cruise Cotrol Drive by Size, Weight ad Power (SWaP) ad cost requiremets Applicatios with differet criticalities (safety critical, missio critical etc.) o the same HW platform This research: Dual-Criticality - Applicatios of HI ad LO criticality 2

3 Mixed Criticality Systems Key requiremets Separatio must esure that LO-criticality applicatios caot impige o those of HI-criticality Sharig wat to allow LO- ad HI-criticality applicatios to use the same resources for efficiecy Real-Time behaviour Cocept of a criticality mode (LO or HI) LO ad HI-criticality applicatios must meet their time costraits i LO-criticality mode Oly HI-criticality applicatios eed meet their time costraits i HIcriticality mode (?) Iitial Research (Vestal 2007) Idea of differet LO- ad HI-criticality WCET estimates for the same code Certificatio authority requires pessimistic approach to C "# System desigers take a more realistic approach to C $% 3

4 System Model Uiprocessor, fixed priority pre-emptive schedulig Sporadic task sets where a task, τ ( = (T (, D (, C (, L ( ) T ( - Task period or miimum iter-arrival time D ( - Relative deadlie C / ( - WCET of τ ( at criticality level l L ( - Desigated criticality level for τ ( hp(i) - Set of higher priority tasks (tha τ ( ) hphi(i) - Set of higher priority, HI criticality tasks hplo(i) - Set of higher priority, LO criticality tasks 4

5 Recap: Adaptive Mixed Criticality AMC schedulig scheme If a HI-criticality task executes for its C $% without sigallig completio the o further jobs of LO-criticality tasks are started 1 ad the system eters HI-criticality mode This frees up processor badwidth to esure that HI-criticality tasks ca meet their deadlies i HI-criticality mode But, it has the drawback that LO-criticality fuctioality is completely abadoed 1 Ay partially executed job of each LO-criticality task may complete 5

6 Recap: Adaptive Mixed Criticality HI criticality task τ i LO Mode y HI Mode After Criticality chage, τ ( assumed to execute up to C ( "# 0 t C i LO C i HI Job released Deadlie Met τ i Executig LO Mode y HI Mode LO criticality task τ k 0 t LO C k τ k Preempted τ k Executig No more releases of τ 7 after criticality chage 6

7 Recap: AMC-rtb Aalysis LO-criticality mode R ( $% = C ( $% + ; R ( $% < >?(() T < C < $% HI-criticality mode R ( "# = C ( "# + ; R ( "# < hphi(() T < C < "# Iterferece from higher priority LO-criticality tasks oly up to R LO Mode chage trasitio R ( = C "# ( + ; R ( "# C T < < < hphi(() + ; R ( $% 7 hplo(() T 7 C 7 $% 7

8 Recap: AMC-max Aalysis AMC-rtb aalysis assumes (pessimistically) that all jobs of HIcriticality tasks execute with their C "# values AMC-max removes this pessimism LO Mode y HI Mode τ i 0 t C i LO C i HI Job released Deadlie Met τ i Executig Calculates umber of releases after criticality chage up to t M i, y, t = mi t + y + D ( T (, t T ( 8

9 Recap: AMC-max Aalysis AMC-max Criticality Mode Chage (LO HI) at time y R M ( = C "# ( + ; y + 1 C T $% 7 + ; M j, y, R M ( C "# < + R M ( 7 7 hplo(() < hphi (() T < M j, y, R ( M C < $% Values of y that eed to be assessed are bouded by 0 ad R $%. Values of y at which respose time may chage correspod to releases of higher priority, LO-criticality tasks: R ( = max R ( M y where y kt< j hplo i y R ( $% k N 9

10 AMC Abadomet Problem Abadoig all LO-criticality jobs Is ot acceptable i may real systems May lead to loss of importat fuctioality as LO-criticality tasks are still critical (ot o-critical) This work: Aims to address the abadomet problem by combiig AMC with a existig cocept called Weakly-Hard Provides a guarateed miimum quality of service for LO-criticality tasks i HI-criticality mode graceful degradatio 10

11 AMC-Weakly Hard Weakly Hard Model Proposed i 2001 by Guillem Berat et al. Guaratees that (m s ) out of ay m deadlies are met via (somewhat complex) offlie aalysis AMC-Weakly Hard Combies a simple iterpretatio of the weakly-hard cocept with existig AMC policy ad schedulability aalysis Allows s out of m LO-criticality jobs to be skipped i HI-criticality mode to reduce the load o the system Still provides a level of service to LO-criticality applicatios, sice (m s ) out of m deadlies are met Gives system desiger flexibility to provide graceful degradatio for LO-criticality applicatios 11

12 AMC-Weakly Hard Skips a umber of cosecutive jobs i a cycle LO Mode Criticality Mode Chage HI Mode LO criticality task τ k t Job released Deadlie Met τ k Executig τ k Job Skipped After criticality mode chage: Skip s jobs i ext m releases Repeat this cycle idefiitely i HI-criticality mode Number of skipped jobs is strictly bouded (m s ) out of m deadlies met 12

13 AMCrtb-WH Aalysis =3 =2 =1 τ k t m k T k τ k Executig Job released τ k Job Skipped Deadlie Met \ ] t ; t m 7 T 7 T 7 m 7 T 7 ^_` C 7 τ ( = T (, D (, C (, L (, s (, m ( m is legth of a cycle s is umber of skipped jobs i a cycle is idex of a skipped job 13

14 AMCrtb-WH Aalysis LO Criticality Mode R ( $% = C ( $% + < hp(() HI Criticality Mode b c de f g C < $% Worst case assumes skips are at the ed of each cycle R ( "# = C ( $ c + ; R ( "# < hphi(() T < C < "# + ; R ( "# ; R ( "# m 7 T 7 T 7 m 7 T 7 7 hplo ( \ ] ^_` h C 7 $% 14

15 AMCrtb-WH Aalysis Criticality Mode Chage (LO HI) LO Mode R i LO HI Mode Skips starts o first release after mode chage τ k t x k m k T k m k T k τ k Executig Job released τ k Job Skipped Deadlie Met First release of job after Criticality Mode Chage x 7 = R ( $% T 7 T 7 15

16 AMCrtb-WH Aalysis Criticality Mode Chage (LO HI) : HI Criticality Tasks R ( = C ( "# + ; R ( < hphi (() T < C < "# + ; R ( ; R ( m 7 T 7 x 7 T 7 m 7 T 7 7 hplo ( j ] ^_\ ] h C 7 $% Criticality Mode Chage (LO HI) : LO Criticality Tasks Assumes skips are at the start of each cycle R ( = C ( $% + ; R ( < hphi(() T < C < "# + ; R ( 7 hplo(() T 7 C 7 $% No skippig assumed for higher priority LOcriticality task. 16

17 AMCmax-WH Aalysis AMCrtb-WH criticality mode chage aalysis is pessimistic AND Aalysig HI-criticality: Assumes all HI-criticality jobs up to R execute with their C "# values Aalysig LO-criticality: Assumes o skippig of LO-criticality jobs up to R. AMCmax-WH aalysis remove these sources of pessimism by takig ito accout the poits at which a criticality mode chage could occur Aalysis for LO- ad HI-criticality modes is same as AMCrtb-WH 17

18 AMCmax-WH Aalysis Criticality Mode Chage (LO HI) at time y y LO Mode HI Mode τ k t z k m k T k m k T k τ k Executig Job released τ k Job Skipped Deadlie Met First release of job after Criticality Mode Chage z 7 = M f ] T 7 18

19 AMCmax-WH Aalysis Criticality Mode Chage (LO HI) : All Tasks Jobs of LO-criticality task k skipped after the criticality mode chage at time y M R M R ( = C $ ( ( + ; ( ; R M ( m 7 T 7 z 7 T 7 m 7 T 7 7 hplo ( j ] ^_\ ] h C 7 $% + ; M j, y, R M ( C "# < + R M ( < hphi (() T < M j, y, R ( M C < $% Jobs of HI-criticality task k oly take C HI values after the criticality mode chage at time y R M ( = max R ( M where y kt < j hplo i y R $% ( k N For HI-criticality tasks, y checked for values up to R $% For LO-criticality tasks y is icreased util R coverges below the curret value of y 19

20 Evaluatio Compared existig policies: UB-H&L - Composite upper-boud o schedulability AMC-max Baruah et al [3] AMC-rtb - Baruah et al. [3] SMC SMC-NO with budget eforced executio for LO-criticality tasks [3] SMC-NO - Vestal s origial aalysis [29] AMCmax-WH - Weakly-Hard versio of AMC-max AMCrtb-WH - Weakly-Hard versio of AMC-rtb FPPS Fixed priority preemptive schedulig with ru-time moitorig to prevet LO-criticality tasks overruig CrMPO Criticality Mootoic Priority Orderig. Tasks ordered by criticality the by DMPO withi the two partitios 20

21 Evaluatio Taskset geeratio: Uiformly distributed utilisatio values geerated with UUifast T radomly assiged from a Log uiform distributio betwee 10 ad 1000 C $% ( = U ( /T ( Criticality Factor (CF) C "# ( = C $% ( CF Criticality Probability (CP) - probability that a task will be HI-criticality Notes about graphs Plotted agaist LO-criticality utilisatio Solid lies represet policies that guaratee some LO-criticality task deadlies are met i HI-criticality mode. Dashed lies represet polices that de-schedule or permit deadlie misses of LO-criticality tasks i HI criticality mode. 21

22 1: Percetage of Schedulable Tasksets AMC-WH domiates CrMPO ad FPPS s = 1 m = 2 CP = 0.5 CF = 2.0 D = T 20 Tasks AMC-WH domiated by AMC 22

23 Weighted Schedulability Weighted Schedulability Eables overall comparisos whe varyig a specific parameter (ot just utilisatio) Combies results form of a set of equally spaced utilisatio levels W φ p = U τ S ~ τ, P U(τ) Collapses all data o a success ratio plot for a give method, ito a sigle poit o a weighted schedulability graph Weighted schedulability is effectively a weighted versio of the area uder a success ratio curve biased towards schedulig higher utilisatio message sets 23

24 2: Varyig the Criticality Mix Less pessimistic aalysis of LOcriticality tasks i HI-criticality mode with AMCmax-WH v. AMCrtb-WH s = 1 m = 2 CP = 0.05 to 0.95 CF = 2.0 D = T 20 Tasks 24

25 3: Varyig the Number of Skips (fixed cycle) s = 0 => FPPS s = m => AMC s = 0 to 10 m = 10 CP = 0.5 CF = 2.0 D = T 20 Tasks 25

26 Summary ad Coclusios AMC-WH Combies AMC protocol, with a simple iterpretatio of Weakly Hard costraits Provides guarateed miimum Quality of Service (QoS) for LO-criticality tasks HI-criticality mode, meet (m - s) out of m deadlies Performace scales betwee AMC ad FPPS Schedulability tests developed based o AMC-rtb ad AMC-max. Scope for future work: Permit weakly-hard behaviour i ay criticality mode, where each task is assiged a set of weakly hard costraits per criticality level Ivestigate recovery to LO-criticality mode 26

27 Questios? 27

Rank Modulation with Multiplicity

Rank Modulation with Multiplicity Rak Modulatio with Multiplicity Axiao (Adrew) Jiag Computer Sciece ad Eg. Dept. Texas A&M Uiversity College Statio, TX 778 ajiag@cse.tamu.edu Abstract Rak modulatio is a scheme that uses the relative order