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Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks - - PowerPoint PPT Presentation

Jan 11, 2023 396 likes •804 views

Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks Pontus Ekberg & Wang Yi Uppsala University, Sweden ECRTS 2012 Mixed-criticality sporadic tasks D i : Relative deadline T i : Period L i : Criticality (lo or hi) Pontus

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Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks

Pontus Ekberg & Wang Yi

Uppsala University, Sweden

ECRTS 2012

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Mixed-criticality sporadic tasks

(Ci(lo) ⩽ Ci(hi)) Ci(lo): WCET at low-criticality Ci(hi): WCET at high-criticality Di: Relative deadline Ti: Period Li: Criticality (lo or hi) Task τi

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 2

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Mixed-criticality sporadic tasks

τ1 (L1 = lo): τ2 (L2 = hi): τ3 (L3 = hi):

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 3

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Mixed-criticality sporadic tasks

τ1 (L1 = lo): τ2 (L2 = hi): τ3 (L3 = hi):

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 4

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Mixed-criticality sporadic tasks

τ1 (L1 = lo): τ2 (L2 = hi): τ3 (L3 = hi):

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 5

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Schedulability analysis

A task set τ is schedulable if ∀ℓ ⩾ 0 : ∑

τi∈τ

dbf(τi, ℓ) ⩽ sbf(ℓ). Classic EDF analysis Low-criticality mode High-criticality mode Time

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 6

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Schedulability analysis

A task set τ is schedulable if both A and B hold: A : ∀ℓ ⩾ 0 : ∑

τi∈τ

dbflo(τi, ℓ) ⩽ sbflo(ℓ) B : ∀ℓ ⩾ 0 : ∑

τi∈hi(τ)

dbfhi(τi, ℓ) ⩽ sbfhi(ℓ) Mixed-criticality EDF analysis Low-criticality mode High-criticality mode Time

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 7

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Demand-bound functions

Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time Each τi behaves exactly like a standard sporadic task with WCET Ci(lo). Use dbfs from Baruah et al., 1990! Each

i behaves similar to a standard

sporadic task with WCET Ci hi .

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 8

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Demand-bound functions

Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time Each τi behaves exactly like a standard sporadic task with WCET Ci(lo). Use dbfs from Baruah et al., 1990! Each

i behaves similar to a standard

sporadic task with WCET Ci hi .

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 9

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Demand-bound functions

Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time Each τi behaves exactly like a standard sporadic task with WCET Ci(lo). Use dbfs from Baruah et al., 1990! Each τi behaves similar to a standard sporadic task with WCET Ci(hi).

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 10

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Demand-bound functions

Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time Each τi behaves exactly like a standard sporadic task with WCET Ci(lo). Use dbfs from Baruah et al., 1990! Each τi behaves similar to a standard sporadic task with WCET Ci(hi).

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 11

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Carry-over jobs

Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time To show A ∧ B, we show A ∧ (A → B). Restricting to the interesting cases

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 12

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Carry-over jobs

t t + Di Release of τi Absolute deadline Switch to high-criticality mode Remaining scheduling window Ci hi Ci lo … Time

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 13

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Carry-over jobs

t t + Di Release of τi Absolute deadline Switch to high-criticality mode Remaining scheduling window Ci hi Ci lo … Time

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 14

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Carry-over jobs

t t + Di Release of τi Absolute deadline Switch to high-criticality mode Remaining scheduling window Ci hi Ci lo … Time

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 15

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Carry-over jobs

t t + Di Release of τi Absolute deadline Switch to high-criticality mode Remaining scheduling window Ci(hi)−Ci(lo) … Time

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 16

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Adjusting the demand of carry-over jobs

t t + Di(lo) t + Di(hi) Release of τi Deadlines in low- and high-criticality mode … Time … Time Switch to high-criticality mode … Time Switch to high-criticality mode Remaining scheduling window

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 17

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Adjusting the demand of carry-over jobs

t t + Di(lo) t + Di(hi) Release of τi Deadlines in low- and high-criticality mode … Time … Time Switch to high-criticality mode … Time Switch to high-criticality mode Remaining scheduling window

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 18

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Adjusting the demand of carry-over jobs

t t + Di(lo) t + Di(hi) Release of τi Deadlines in low- and high-criticality mode … Time … Time Switch to high-criticality mode … Time Switch to high-criticality mode Remaining scheduling window

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 19

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Adjusting the demand of carry-over jobs

t t + Di(lo) t + Di(hi) Release of τi Deadlines in low- and high-criticality mode … Time … Time Switch to high-criticality mode … Time Switch to high-criticality mode Remaining scheduling window

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 20

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Adjusting the demand of carry-over jobs

t t + Di(lo) t + Di(hi) Release of τi Deadlines in low- and high-criticality mode … Time … Time Switch to high-criticality mode … Time Switch to high-criticality mode Remaining scheduling window

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 21

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Demand-bound functions for high-criticality mode

5 10 15 20 25 30 Time interval length (ℓ) 5 10 15 20 25 30 Demand dbf HI(τi, ℓ)

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 22

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Demand-bound functions for high-criticality mode

5 10 15 20 25 30 Time interval length (ℓ) 5 10 15 20 25 30 Demand dbf HI(τi, ℓ) dbf LO(τi, ℓ)

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 23

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The effect of the low-criticality relative deadline

If Di(lo) is decreased by δ ∈ Z, then dbflo(τi, ℓ) ❀ dbflo(τi, ℓ + δ) dbfhi(τi, ℓ) ❀ dbfhi(τi, ℓ − δ) Shifuing lemma

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 24

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The effect of the low-criticality relative deadline

5 10 15 20 25 30 Time interval length (ℓ) 5 10 15 20 25 30 Demand

δ δ

dbf HI(τi, ℓ) dbf LO(τi, ℓ) dbf HI(τi, ℓ), Di(LO) decreased by δ dbf LO(τi, ℓ), Di(LO) decreased by δ

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 25

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Shaping the demand of the task set

A task set τ is schedulable if both A and B hold: A : ∀ℓ ⩾ 0 : ∑

τi∈τ

dbflo(τi, ℓ) ⩽ sbflo(ℓ) B : ∀ℓ ⩾ 0 : ∑

τi∈hi(τ)

dbfhi(τi, ℓ) ⩽ sbfhi(ℓ) Mixed-criticality EDF analysis Is there a valid assignment of Di(lo)s to each high-criticality task τi such that both A and B hold? A constraint satisfaction problem

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 26

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Shaping the demand of the task set

10 20 30 40 50 60 70 80 90 100 Time interval length (ℓ) 10 20 30 40 50 60 70 80 90 100 Demand

dbf HI dbf LO

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 27

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Shaping the demand of the task set

10 20 30 40 50 60 70 80 90 100 Time interval length (ℓ) 10 20 30 40 50 60 70 80 90 100 Demand

dbf HI dbf LO

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 28

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Shaping the demand of the task set

10 20 30 40 50 60 70 80 90 100 Time interval length (ℓ) 10 20 30 40 50 60 70 80 90 100 Demand

dbf HI dbf LO

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 29

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Shaping the demand of the task set

10 20 30 40 50 60 70 80 90 100 Time interval length (ℓ) 10 20 30 40 50 60 70 80 90 100 Demand

dbf HI dbf LO

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 30

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Shaping the demand of the task set

10 20 30 40 50 60 70 80 90 100 Time interval length (ℓ) 10 20 30 40 50 60 70 80 90 100 Demand

dbf HI dbf LO

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 31

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Shaping the demand of the task set

10 20 30 40 50 60 70 80 90 100 Time interval length (ℓ) 10 20 30 40 50 60 70 80 90 100 Demand

dbf HI dbf LO

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 32

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Shaping the demand of the task set

10 20 30 40 50 60 70 80 90 100 Time interval length (ℓ) 10 20 30 40 50 60 70 80 90 100 Demand

dbf HI dbf LO

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 33

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Shaping the demand of the task set

10 20 30 40 50 60 70 80 90 100 Time interval length (ℓ) 10 20 30 40 50 60 70 80 90 100 Demand

dbf HI dbf LO

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 34

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Evaluation

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Average utilization 10 20 30 40 50 60 70 80 90 100 Acceptance ratio (%)

Our OCBP-prio AMC-max Vestal EDF-VD OCBP-load Naive

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 35

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Evaluation

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Probability of high-criticality 10 20 30 40 50 60 70 80 90 100 Weighted acceptance ratio (%)

Our OCBP-prio AMC-max Vestal EDF-VD OCBP-load Naive

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 36

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Evaluation

1 3 5 7 9 11 13 15 17 19 Maximum ratio of high- to low-criticality WCET 10 20 30 40 50 60 70 80 90 100 Weighted acceptance ratio (%)

Our OCBP-prio AMC-max Vestal EDF-VD OCBP-load Naive

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 37

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Conclusions

1 Demand-bound functions are useful also for mixed-criticality systems. 2 Tie particulars of mixed-criticality demand-bound functions allow

us to easily shape the demand to the supply of the platform.

3 Experiments indicate that this approach performs well.

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 38

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Qvestions?

Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 39