Towards optimal priority assignments for real-time tasks with probabilistic arrivals and probabilistic execution times Dorin MAXIM INRIA Nancy Grand Est.

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


Example


Task-set τ = {τ1, τ2} with:

τ1=;

τ2=

Example


τ1=;

τ2=


Example


τ1=;

τ2=


Example


τ1=;

τ2=

0 1 2 3 4

T1,0 = 1


Example


τ1=;

τ2=

0 1 2 3 4

T1,0 = 1

T2,0 = 2


Example


τ1=;

τ2=

0 1 2 3 4

T1,0 = 1

T2,0 = 2


Example


τ1=;

τ2=

Probability of occurrence = 0.42

0 1 2 3 4

T1,0 = 1

T2,0 = 2


Example


τ1=;

τ2=

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

T2,0 = 4


Example


τ1=;

τ2=

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

T2,0 = 4


Example


τ1=;

τ2=

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

T2,0 = 4


Example


τ1=;

τ2=

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

T2,0 = 4


Example


τ1=;

τ2=

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

T2,0 = 4


Example


τ1=;

τ2=

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

T2,0 = 4


Example


τ1=;

τ2=

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

T2,0 = 4


Example


τ1=;

τ2=

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

T2,0 = 4


Example


τ1=;

τ2=

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

T2,0 = 4


Example


τ1=;

τ2=

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

T2,0 = 4


Probability of occurrence =

3.24 * 10-6

Open problems


Open problems

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


Open problems


2. Priority assignment so that each task meets certain conditions referring to its timing failures.


Open problems


2. Priority assignment so that each task meets certain conditions referring to its timing failures.

3. Study interval.


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 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


Thank you!


Towards optimal priority assignments for real-time tasks with probabilistic arrivals and probabilistic execution times Dorin MAXIM INRIA Nancy Grand Est.

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