[PPT] - Gang FTP scheduling of periodic and parallel rigid real-time tasks PowerPoint Presentation

SLIDE 1

Gang FTP scheduling of periodic and parallel rigid real-time tasks

Vandy Berten Jo¨ el Goossens

Universit´ e libre de Bruxelles

RTNS 2010

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 1 / 26

SLIDE 2

Table of contents I

1

Introduction Model Predictability Problem

2

Predictability

3

Schedulability test

4

Conclusions

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 3 / 26

SLIDE 4

Introduction

Our objectives: Explore the theory of parallel tasks, and Gang scheduling Provide schedulability tests for various kinds of Gang schedulers Why? Parallel tasks are coming on real-time/embedded systems (energy efficiency) Very few results in the literature

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 4 / 26

SLIDE 5

Introduction Model

Task model

d v r C D

n (rigid) parallel (v), periodic (T), constrained deadline (D ≤ T) tasks m identical processors

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 5 / 26

SLIDE 6

Introduction Model

Task model

Preemptive Migrations Rigid (not malleable/moldable)

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 6 / 26

SLIDE 7

Introduction Model

Gang FJP scheduler

1 2 3 4 5 6 1 2 3 4 5 6 4

Gang FJP scheduler

1

Pick the highest priority job

2

If it fits, start it now

3

Start again with the remaining jobs

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 7 / 26

SLIDE 8

Introduction Model

Schedulability test

Predictability

Schedulable for WCET ⇒ Schedulable

+ Feasibility interval [A, B]

Feasibility Interval

Schedulable in [A, B] ⇒ Schedulable forever

= Schedulability test

Schedulability test

Simulate the system in [A, B] with WCET

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 8 / 26

SLIDE 9

Introduction Predictability Problem

Deadline miss

5 6 4 4 5 6 4 1 2 3 1 2 3 3

⇒ Gang FJP not predictable!

One of the problems: priority inversion (slack introduces new preemptions)

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 9 / 26

SLIDE 10

Predictability

Table of contents I

1

Introduction

2

Predictability Possibilities Parallel Monotonic Idling FJP Scheduler Limited Gang FJP Scheduler Limited Slack Reclaiming

3

Schedulability test

4

Conclusions

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 10 / 26

SLIDE 11

Predictability Possibilities

Making the system predictable

We propose several solutions making the system predictable: Avoiding priority inversion Not using the slack Using the slack “smartly” Two ways of doing so: Constraint the task system Constraint the scheduler

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 11 / 26

SLIDE 12

Predictability Parallel Monotonic

Parallel monotonic

Parallel monotonic FJP assignment

Larger job ⇒ Lower priority → High priority to small jobs

1 2 3 4 5 6 4 6 1 2 5 3

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 12 / 26

SLIDE 13

Predictability Parallel Monotonic

Parallel monotonic

4 6 1 2 5 3 4 6 1 2 5 3

We avoid priority inversion!

Theorem

Parallel Monotonic systems are predictable

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 13 / 26

SLIDE 14

Predictability Idling FJP Scheduler

Idling FJP scheduler

Just don’t use the slack!

1 2 3 4 5 6 4 1 2 3 4 5 6 4

1

4

Still priority inversions, but same behavior as in the WCET case Not work conserving!

Theorem

Idling FJP schedulers are predictable

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 14 / 26

SLIDE 15

Predictability Limited Gang FJP Scheduler

Limited Gang FJP scheduler

1

Pick the highest priority job

2

If it fits, start it now

3

If it fitted in step 2, start again with the remaining jobs

1 2 3 5 6 4 1 2 3 5 6 4

We avoid priority inversion!

Theorem

Limited Gang FJP schedulers are predictable

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 15 / 26

SLIDE 16

Predictability Limited Gang FJP Scheduler

Limited Gang FJP scheduler

1 2 3 5 6 4

Limited Gang scheduler less efficient than “normal” Gang scheduler

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 16 / 26

SLIDE 17

Predictability Limited Slack Reclaiming

Limited slack reclaiming

Gang FJP scheduler with limited slack reclaiming

1

While there is no slack, behave as for Gang FJP scheduler

2

Use the slack to run ahead jobs narrower than the slack

5 1 2 3 4 5 6 4 1 2 3 4 5 6 4 4 6 5

Still priority inversions, but no “problematic preemptions”

Theorem

Gang schedulers with limited slack reclaiming are predictable

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 17 / 26

SLIDE 18

Schedulability test

Table of contents I

1

Introduction

2

Predictability

3

Schedulability test Periodicity Feasibility interval Exact Schedulability Test

4

Conclusions

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 18 / 26

SLIDE 19

Schedulability test Periodicity

Periodicity of Gang FTP

Theorem

(Whatever) Gang FTP schedulers are periodic (using WCET) : With a period P def = lcm{T1, . . . , Tn} Starting from Sn, where:

◮ S1

def

= O1;

◮ Si

def

= max

Oi, Oi +

Si−1 − Oi Ti

Ti
, ∀i ∈ {2, 3, . . . , n}.

⇒ Same as non-Gang systems! Going from sequential to parallel jobs did not change the periodicity

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 19 / 26

SLIDE 20

Schedulability test Periodicity

Periodicity

O2 O1 = S1 O3 O4 S2 S3 S4

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 20 / 26

SLIDE 21

Schedulability test Feasibility interval

Feasibility interval

Theorem

For any Gang FTP system (Parallel Monotonic, Idling scheduler, Limited Gang scheduler, Limited Slack reclaiming scheduler), we can use the following Feasibility interval: [0, Sn + P]

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 21 / 26

SLIDE 22

Schedulability test Exact Schedulability Test

Exact schedulability test

Predictability

OK for Parallel Monotonic, Idling-, Limited Gang- and Limited Slack reclaiming scheduler

+ Feasibility Interval

Feasibility interval

[0, Sn + P]

= Schedulability test

Schedulability test

Simulate the system in [0, Sn + P] with WCET

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 22 / 26

SLIDE 23

Conclusions

Table of contents I

1

Introduction

2

Predictability

3

Schedulability test

4

Conclusions Future work Questions

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 23 / 26

SLIDE 24

Conclusions

We strictly defined rigid, moldable and maleable reccurent tasks We provided (and proved) an exact schedulability test for several kinds of FTP Gang schedulers We studied the predictability of those schedulers

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 24 / 26

SLIDE 25

Conclusions Future work

Future work

Extends our results to moldable and maleable tasks Sufficient RM-schedulability test for sporadic Gang scheduling . . .

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 25 / 26

SLIDE 26

Conclusions Questions

Questions?

V. Berten, J. Goossens (ULB)

Gang FTP scheduling of real-time tasks RTNS 2010 26 / 26