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Towards optimal priority assignments for real-time tasks with probabilistic arrivals and probabilistic execution times. Dorin MAXIM INRIA Nancy Grand Est. Model of the Probabilistic Real-Time System. n independent tasks with independent jobs - PowerPoint PPT Presentation
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Towards optimal priority assignments for real-time
tasks with probabilistic arrivals and probabilistic
execution times
Dorin MAXIM
INRIA Nancy Grand Est
RTSOPS, PISA, ITALY 10/07/2012
RTSOPS, PISA, ITALY 10/07/2012 2/7
Model of the Probabilistic Real-Time System
• n independent tasks with independent jobs
• a task τi is characterized by τi = (Ti, Ci, Di),
period• probabilistic execution time
deadline (constrained)
• single processor, synchronous, preemptive, fixed priorities
The goal: Assigning priorities to tasks so that each task meets certain conditions referring to its timing failures.
Probabilistic Period Probabilistic ET
MIT WCET
RTSOPS, PISA, ITALY 10/07/2012 3/7
Example
RTSOPS, PISA, ITALY 10/07/2012 4/7
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4
T1,0 = 1
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4
T1,0 = 1
T2,0 = 2
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4
T1,0 = 1
T2,0 = 2
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
Probability of occurrence = 0.42
0 1 2 3 4
T1,0 = 1
T2,0 = 2
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Example
Task-set τ = {τ1, τ2} with:
τ1=; τ2=
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T2,0 = 4
RTSOPS, PISA, ITALY 10/07/2012 4/7
Probability of occurrence =
3.24 * 10-6
Open problems
RTSOPS, PISA, ITALY 10/07/2012 5/7
Open problems
1. Algorithm for computing the response time distribution of different jobs of the given tasks.
RTSOPS, PISA, ITALY 10/07/2012 5/7
Open problems
1. Algorithm for computing the response time distribution of different jobs of the given tasks.
2. Priority assignment so that each task meets certain conditions referring to its timing failures.
RTSOPS, PISA, ITALY 10/07/2012 5/7
Open problems
1. Algorithm for computing the response time distribution of different jobs of the given tasks.
2. Priority assignment so that each task meets certain conditions referring to its timing failures.
3. Study interval.
RTSOPS, PISA, ITALY 10/07/2012 5/7
Intuitions and counter-intuitions
Rate Monotonic is NOT optimal for probabilistic systems:
RTSOPS, PISA, ITALY 10/07/2012 6/7
Intuitions and counter-intuitions
Rate Monotonic is NOT optimal for probabilistic systems:
RM does not take into account the probabilistic character of the tasks
RTSOPS, PISA, ITALY 10/07/2012 6/7
Intuitions and counter-intuitions
Rate Monotonic is NOT optimal for probabilistic systems:
RM does not take into account the probabilistic character of the tasks
RM considers tasks periods, which here are random variables that may not be comparable
RTSOPS, PISA, ITALY 10/07/2012 6/7
Intuitions and counter-intuitions
Rate Monotonic is NOT optimal for probabilistic systems:
RM does not take into account the probabilistic character of the tasks
RM considers tasks periods, which here are random variables that may not be comparable
RM was proved not optimal for tasks with deterministic arrivals and probabilistic executions times
RTSOPS, PISA, ITALY 10/07/2012 6/7
Thank you!
RTSOPS, PISA, ITALY 10/07/2012 7/7
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