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

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 Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 2 Task τ i C i ( lo ) : WCET at low-criticality ( C i ( lo ) ⩽ C i ( hi ) ) C i ( hi ) : WCET at high-criticality

Mixed-criticality sporadic tasks Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 3 τ 1 ( L 1 = lo): τ 2 ( L 2 = hi): τ 3 ( L 3 = hi):

Mixed-criticality sporadic tasks Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 4 τ 1 ( L 1 = lo): τ 2 ( L 2 = hi): τ 3 ( L 3 = hi):

Mixed-criticality sporadic tasks Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 5 τ 1 ( L 1 = lo): τ 2 ( L 2 = hi): τ 3 ( L 3 = hi):

Classic EDF analysis Schedulability analysis Low-criticality mode High-criticality mode Time Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 6 A task set τ is schedulable if ∑ ∀ ℓ ⩾ 0 : dbf ( τ i , ℓ ) ⩽ sbf ( ℓ ) . τ i ∈ τ

Schedulability analysis Mixed-criticality EDF analysis Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks Pontus Ekberg Time High-criticality mode Low-criticality mode 7 A task set τ is schedulable if both A and B hold: ∑ A : ∀ ℓ ⩾ 0 : dbf lo ( τ i , ℓ ) ⩽ sbf lo ( ℓ ) τ i ∈ τ ∑ B : ∀ ℓ ⩾ 0 : dbf hi ( τ i , ℓ ) ⩽ sbf hi ( ℓ ) τ i ∈ hi ( τ )

i behaves similar to a standard sporadic task with WCET C i hi . Demand-bound functions Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time Use dbf s from Baruah et al., 1990! Each Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 8 Each τ i behaves exactly like a standard sporadic task with WCET C i ( lo ) .

i behaves similar to a standard sporadic task with WCET C i hi . Demand-bound functions Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time Use dbf s from Baruah et al., 1990! Each Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 9 Each τ i behaves exactly like a standard sporadic task with WCET C i ( lo ) .

Demand-bound functions Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time Use dbf s from Baruah et al., 1990! Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 10 Each τ i behaves similar to a standard sporadic task with WCET C i ( hi ) . Each τ i behaves exactly like a standard sporadic task with WCET C i ( lo ) .

Demand-bound functions Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time Use dbf s from Baruah et al., 1990! Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 11 Each τ i behaves similar to a standard sporadic task with WCET C i ( hi ) . Each τ i behaves exactly like a standard sporadic task with WCET C i ( lo ) .

Carry-over jobs Half-fjnished jobs are carried over to high-criticality mode. Low-criticality mode High-criticality mode Time Restricting to the interesting cases Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 12 To show A ∧ B , we show A ∧ ( A → B ) .

C i hi C i lo Carry-over jobs t Absolute deadline Switch to high-criticality mode Remaining scheduling window … Time Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 13 t + D i Release of τ i

C i hi C i lo Carry-over jobs t Absolute deadline Switch to high-criticality mode Remaining scheduling window … Time Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 14 t + D i Release of τ i

C i hi C i lo Carry-over jobs t Absolute deadline Switch to high-criticality mode Remaining scheduling window … Time Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 15 t + D i Release of τ i

Carry-over jobs t Absolute deadline Switch to high-criticality mode Remaining scheduling window … Time Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 16 C i ( hi ) − C i ( lo ) t + D i Release of τ i

Switch to high-criticality mode Switch to high-criticality mode Adjusting the demand of carry-over jobs Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks Pontus Ekberg Remaining scheduling window Time … Time t … Time … Deadlines in low- and high-criticality mode 17 t + D i ( lo ) t + D i ( hi ) Release of τ i

Switch to high-criticality mode Adjusting the demand of carry-over jobs Switch to high-criticality mode Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks Pontus Ekberg Remaining scheduling window Time … Time t … Time … Deadlines in low- and high-criticality mode 18 t + D i ( lo ) t + D i ( hi ) Release of τ i

Switch to high-criticality mode Adjusting the demand of carry-over jobs Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks Pontus Ekberg Remaining scheduling window Switch to high-criticality mode Time … Time t … Time … Deadlines in low- and high-criticality mode 19 t + D i ( lo ) t + D i ( hi ) Release of τ i

Switch to high-criticality mode Adjusting the demand of carry-over jobs Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks Pontus Ekberg Remaining scheduling window Switch to high-criticality mode Time … Time t … Time … Deadlines in low- and high-criticality mode 20 t + D i ( lo ) t + D i ( hi ) Release of τ i

Switch to high-criticality mode Adjusting the demand of carry-over jobs Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks Pontus Ekberg Remaining scheduling window Switch to high-criticality mode Time … Time t … Time … Deadlines in low- and high-criticality mode 21 t + D i ( lo ) t + D i ( hi ) Release of τ i

Demand-bound functions for high-criticality mode Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 22 30 dbf HI ( τ i , ℓ ) 25 20 Demand 15 10 5 0 0 5 10 15 20 25 30 Time interval length ( ℓ )

Demand-bound functions for high-criticality mode Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 23 30 dbf HI ( τ i , ℓ ) dbf LO ( τ i , ℓ ) 25 20 Demand 15 10 5 0 0 5 10 15 20 25 30 Time interval length ( ℓ )

Shifuing lemma The effect of the low-criticality relative deadline Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 24 If D i ( lo ) is decreased by δ ∈ Z , then dbf lo ( τ i , ℓ ) dbf lo ( τ i , ℓ + δ ) ❀ dbf hi ( τ i , ℓ ) dbf hi ( τ i , ℓ − δ ) ❀

The effect of the low-criticality relative deadline Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 25 30 dbf HI ( τ i , ℓ ) dbf LO ( τ i , ℓ ) 25 dbf HI ( τ i , ℓ ) , D i ( LO ) decreased by δ dbf LO ( τ i , ℓ ) , D i ( LO ) decreased by δ 20 Demand 15 10 δ δ 5 0 0 5 10 15 20 25 30 Time interval length ( ℓ )

Shaping the demand of the task set Mixed-criticality EDF analysis Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks Pontus Ekberg A constraint satisfaction problem 26 A task set τ is schedulable if both A and B hold: ∑ A : ∀ ℓ ⩾ 0 : dbf lo ( τ i , ℓ ) ⩽ sbf lo ( ℓ ) τ i ∈ τ ∑ B : ∀ ℓ ⩾ 0 : dbf hi ( τ i , ℓ ) ⩽ sbf hi ( ℓ ) τ i ∈ hi ( τ ) Is there a valid assignment of D i ( lo ) s to each high-criticality task τ i such that both A and B hold?

Shaping the demand of the task set Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 27 100 � dbf HI 90 � dbf LO 80 70 60 Demand 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Time interval length ( ℓ )

Shaping the demand of the task set Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 28 100 � dbf HI 90 � dbf LO 80 70 60 Demand 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Time interval length ( ℓ )

Shaping the demand of the task set Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 29 100 � dbf HI 90 � dbf LO 80 70 60 Demand 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Time interval length ( ℓ )

Shaping the demand of the task set Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 30 100 � dbf HI 90 � dbf LO 80 70 60 Demand 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Time interval length ( ℓ )

Shaping the demand of the task set Pontus Ekberg Bounding and Shaping the Demand of Mixed-Criticality Sporadic Tasks 31 100 � dbf HI 90 � dbf LO 80 70 60 Demand 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Time interval length ( ℓ )