1 / 29

# Dorin MAXIM INRIA Nancy Grand Est - PowerPoint PPT Presentation

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Dorin MAXIM INRIA Nancy Grand Est' - arnold

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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

• n independent tasks with independent jobs

• a task τi is characterized by τi = (Ti, Ci, Di),

period

• probabilistic execution time

• 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

MIT

WCET

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

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

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

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

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

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

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

Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

T1,0 = 1

0 1 2 3 4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• 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

• 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

Rate Monotonic is NOT optimal for probabilistic systems:

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

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

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

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

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