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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

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slide1

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

model of the probabilistic real time system
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.

RTSOPS, PISA, ITALY 10/07/2012 2/7

probabilistic period probabilistic et
Probabilistic Period Probabilistic ET

MIT

WCET

RTSOPS, PISA, ITALY 10/07/2012 3/7

slide4

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide5

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide6

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide7

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T1,0 = 1

0 1 2 3 4

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide8

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T1,0 = 1

T2,0 = 2

0 1 2 3 4

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide9

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T1,0 = 1

T2,0 = 2

0 1 2 3 4

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide10

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T1,0 = 1

Probability of occurrence = 0.42

T2,0 = 2

0 1 2 3 4

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide11

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide12

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide13

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide14

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide15

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide16

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide17

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide18

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide19

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide20

Example

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

Probability of occurrence =

3.24 * 10-6

T2,0 = 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

RTSOPS, PISA, ITALY 10/07/2012 4/7

slide21

Open problems

RTSOPS, PISA, ITALY 10/07/2012 5/7

slide22

Open problems

  • Algorithm for computing the response time distribution of different jobs of the given tasks.

RTSOPS, PISA, ITALY 10/07/2012 5/7

slide23

Open problems

  • Algorithm for computing the response time distribution of different jobs of the given tasks.
  • Priority assignment so that each task meets certain conditions referring to its timing failures.

RTSOPS, PISA, ITALY 10/07/2012 5/7

slide24

Open problems

  • Algorithm for computing the response time distribution of different jobs of the given tasks.
  • Priority assignment so that each task meets certain conditions referring to its timing failures.
  • Study interval.

RTSOPS, PISA, ITALY 10/07/2012 5/7

slide25

Intuitions and counter-intuitions

Rate Monotonic is NOT optimal for probabilistic systems:

RTSOPS, PISA, ITALY 10/07/2012 6/7

slide26

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

slide27

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

slide28

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

slide29

Thank you!

RTSOPS, PISA, ITALY 10/07/2012 7/7

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