Fixed-Priority Multiprocessor Scheduling with Liu & Laylands - - PowerPoint PPT Presentation

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Fixed-Priority Multiprocessor Scheduling with Liu & Laylands - - PowerPoint PPT Presentation

Aug 08, 2023 268 likes •936 views

Fixed-Priority Multiprocessor Scheduling with Liu & Laylands Utilization Bound Nan Guan , Martin Stigge, Wang Yi Uppsala University, Sweden Outline Problem Previous Results Our New Result Scheduling of Multi-task System

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Fixed-Priority Multiprocessor Scheduling with Liu & Layland’s Utilization Bound

Nan Guan, Martin Stigge, Wang Yi

Uppsala University, Sweden

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Outline

Problem Previous Results Our New Result

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SLIDE 3

Scheduling of Multi-task System

multi-rate real-time task system each task

ri

1

ri

2

ri

3

ri

4

Ti Ti Ji

1

Ji

2

Ji

3

Ti Ci Ci Ci

Utilization:

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Liu and Layland’s Utilization Bound

Liu and Layland’s utilization bound for single-processor scheduling [ Liu1973]

(the 19th most cited paper in computer science)

  • : the number of tasks,
  • ptimal
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Multiprocessor Scheduling

Significantly more difficult

  • Bin-packing problem
  • Hard to identify the worst-case scenario
  • Suffer from timing anomalies
  • May lead to arbitrarily low utilization
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Open Problem

find a multiprocessor scheduling algorithm that can achieve Liu and Layland’s utilization bound

number of processors

?

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SLIDE 7

Multiprocessor Scheduling

5 2 1 6 8 4 new task waiting queue

cpu 1 cpu 2 cpu 3 Global Scheduling cpu 1 cpu 2 cpu 3 5 1 2 8 6 3 9 7 4 cpu 1 cpu 2 cpu 3 2 5 2 1 2 2 3 6 7 4 2 3 Partitioned Scheduling Partitioned Scheduling w ith Task Splitting

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Best Known Results

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Best Known Results

Lehoczky et al. CMU ECRTS 2009

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Best Known Results

Our New Result

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Lehoczky’s Algorithm [ ECRTS’09]

sort all tasks in decreasing order of utilization

3 4 2 5 1 6 8 7

highest utilization lowest utilization

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Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 3 4 2 5 1 6 8 7

highest utilization lowest utilization

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Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 3 4 2 5 1 6 7

highest utilization lowest utilization

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SLIDE 14

Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 3 4 2 5 1 6 7

highest utilization lowest utilization

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SLIDE 15

Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 3 4 2 5 1 6 2 7 6 1

highest utilization lowest utilization

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SLIDE 16

Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 3 4 2 5 1 6 2 7 6 1 P2

highest utilization lowest utilization

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SLIDE 17

Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 3 4 2 5 1 7 6 1 P2 6 2

highest utilization lowest utilization

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SLIDE 18

Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 3 4 2 1 7 6 1 P2 5 6 2

highest utilization lowest utilization

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Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 3 2 1 7 6 1 P2 5 6 2 4

highest utilization lowest utilization

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SLIDE 20

Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 2 1 7 6 1 P2 5 6 2 4 3

highest utilization lowest utilization

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SLIDE 21

Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 1 7 6 1 P2 5 6 2 4 3 2 1 2 2

highest utilization lowest utilization

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Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 7 6 1 P2 5 6 2 4 3 2 1 P3 2 2 1

highest utilization lowest utilization

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SLIDE 23

Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 7 6 1 P2 5 6 2 4 3 2 1 P3 1 2 2

highest utilization lowest utilization

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Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 7 6 1 P2 5 6 2 4 3 2 1 P3 1 2 2 key feature: depth-first partitioning with decreasing utilization order

highest utilization lowest utilization

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Lehoczky’s Algorithm [ ECRTS’09]

pick up one processor, and assign as many tasks as possible

P1 8 7 6 1 P2 5 6 2 4 3 2 1 P3 1 2 2 Utilization Bound: 6 5 %

highest utilization lowest utilization

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Our Algorithm

width-first partitioning with increasing priority order

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Our Algorithm

sort all tasks in increasing priority order

7 6 5 4 3 2 1 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

7 6 5 4 3 2 1 P1 P2 P3 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

6 5 4 3 2 1 P1 P2 P3 7 highest priority lowest priority

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SLIDE 30

Our Algorithm

select the processor on which the assigned utilization is the lowest

5 4 3 2 1 P1 P2 P3 7 6 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

4 3 2 1 P1 P2 P3 7 6 5 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

3 2 1 P1 P2 P3 7 6 5 4 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

2 1 P1 P2 P3 7 6 5 4 3 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

1 P1 P2 P3 7 6 5 4 3 2 1 2 2 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

1 P1 P2 P3 7 6 5 4 3 2 1 2 2 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

P1 P2 P3 7 6 5 4 3 2 1 1 2 1 1 2 2 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

P1 P2 P3 7 6 5 4 3 2 1 1 2 1 1 2 2 highest priority lowest priority

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Our Algorithm

select the processor on which the assigned utilization is the lowest

P1 P2 P3 7 6 5 4 3 2 1 1 2 1 1 2 2 highest priority lowest priority key feature: w idth-first partitioning w ith increasing prio order

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Comparison

maximal number of task splitting both are M-1

P1 8 7 6 1 P2 5 6 2 4 3 1 P3 1 2 3 2 P1 P2 3 P3 1 1 8 4 2 7 6 5 1 2

Ours: width-first Lehoczky’s: depth-first

(decreasing utilization order) (increasing priority order)

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Comparison

Ours: width-first Lehoczky’s: depth-first

why is our algorithm better?

P1 8 7 6 1 P2 5 6 2 4 3 1 P3 1 2 3 2 P1 P2 3 P3 1 1 8 4 2 7 6 5 1 2

(increasing priority order) (decreasing utilization order)

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Comparison

P1 8 7 6 1 P2 5 6 2 4 3 1 P3 1 2 3 2 P1 P2 3 P3 8 4 2 7 6 5 1 1 1 2 key point: by our algorithm , split tasks generally have high priorities on each processor

Ours: width-first Lehoczky’s: depth-first (increasing priority order)

(decreasing utilization order)

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Split Task

d

r d r P1 P2 P3 subtasks should be executed in the correct order

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Split Task

synthetic utilization:

  • riginal utilization:

split tasks cause “utilization increase”

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Our Algorithm

intuition

  • high priority tasks have better chance to meet

their deadlines P1 P2

… …

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Our Algorithm

intuition

  • an extreme scenario:

each subtask has the highest priority on each processor can meet their deadlines anyway no “utilization increase”

P1 P2

… …

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Theorem

for a task set in with each task satisfies

reasonable constraint in real-life systems

we have

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 8

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 8

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 8

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 8

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 1 8 5 2

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 1 8 5 2

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 1 8 5 2

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 1 8 5 2

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 1 8 5 2

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Our Algorithm

problem of heavy tasks

P1 P2 P3 highest priority lowest priority 4 3 2 1 7 6 5 1 8 5 2

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The idea w orks for all tasks!

To get rid of the constraint

  • pre-assign tasks with high utilization
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The idea w orks for all tasks!

5 4 3 2 1 P1 P2 P3 highest priority lowest priority

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The idea w orks for all tasks!

P1 P2 P3 highest priority lowest priority 4 pre-assign the heavy task 5 3 2 1

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The idea w orks for all tasks!

P1 P2 P3 highest priority lowest priority 3 2 5 1 1 1 2 4

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Theorem

By introducing the pre-assignment to the algorithm, we have

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Conclusion

Proposed multiprocessor scheduling algorithms with Liu and Layland’s utilization bound

works on “light” task sets with a simple width-first algorithm works on any task set with a hybrid algorithm

pre-assigning

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Conclusion

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THANKS! THANKS!

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Multiprogramming in a Hard-Real-Time Environment

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partitioned and Pfair Static-Priority Scheduling on multiprocessors are 50% . ECRTS 2003: 33-40

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Multiprocessor Scheduling with Utilization Bound 38% . OPODIS 2008: 73-88

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Scheduling with Few preemption. RTCSA 2006: 322-334

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Lehoczky Partitioned Fixed-Priority Preemptive Scheduling for Multi-core

  • Processors. ECRTS 20006
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EDF Scheduling on Real-Time Multiprocessor Systems”, RTSS 2004.

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