using Shapers Yue Tang 1 , Yuming Jiang 2 , Xu Jiang 1 , Nan Guan 1 1 - - PowerPoint PPT Presentation

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Improving Multiprocessor Real-Time Systems with Bursty Inputs under Global EDF using Shapers

Yue Tang1, Yuming Jiang2, Xu Jiang1, Nan Guan1

1 The Hong Kong Polytechnic University 2Norwegian University of Science and Technology

SLIDE 2

Outline

• Motivation

2019/5/16 2

• Framework
• Analysis Details
• Evaluation

SLIDE 3

Outline

• Motivation

2019/5/16 3

• Framework
• Analysis Details
• Evaluation

SLIDE 4

Motivation

2019/5/16 4

• Bounded delay is essential for real-time systems
• Global EDF is a widely used scheduling strategy

SLIDE 5

Motivation

2019/5/16 5

• Bounded delay is essential for real-time systems
• Global EDF is a widely used scheduling strategy
• How to calculate delay bound for GEDF?

SLIDE 6

Motivation

2019/5/16 6

• Bounded delay is essential for real-time systems
• Global EDF is a widely used scheduling strategy
• How to calculate delay bound for GEDF?
• Most work considers periodic tasks

SLIDE 7

Motivation

2019/5/16 7

• Bounded delay is essential for real-time systems
• Global EDF is a widely used scheduling strategy

However

• How to calculate delay bound for GEDF?
• Most work considers periodic tasks
• Bursty tasks are more general

SLIDE 8

Motivation

2019/5/16 8

• Bursty tasks are more general in real applications

I/O FPGA DSP I/O ECU I/O input stream input stream

• utput stream
• utput stream

SLIDE 9

Motivation

2019/5/16 9

• Bounded delay is essential for real-time systems
• Global EDF is a widely used scheduling strategy

However

• How to calculate delay bound for GEDF?
• Most work considers periodic tasks
• Bursty tasks are more general
• Model bursty tasks as periodic tasks

Possible solution?

SLIDE 10

Motivation

2019/5/16 10

• Does modeling bursty tasks as periodic tasks work for calculating delay bound?

Choose the period of periodic tasks 5 10 15 20 25 30 35 t T = 1 ? 9 11 Overestimate workload → too pessimistic T = 5 ? Underestimate workload → wrong results (Assume D = 5, one task on uniprocessor) In the extreme case, more than one job arrives simultaneously (e.g., 3 events at time 10) 5 10 15 20 25 30 35 t Can not set the period !

No !

SLIDE 11

Motivation

2019/5/16 11

• Bounded delay is essential for real-time systems
• Global EDF is a widely used scheduling strategy

However

• How to calculate delay bound for GEDF?
• Most work considers periodic tasks
• Bursty tasks are more general
• Model bursty tasks as periodic tasks

Possible solution? Our contribution !

• Change bursty tasks to periodic tasks using shapers

SLIDE 12

Our Contribution

2019/5/16 12

• Use shapers to calculate delay bound for multiprocessors under global EDF
• Design a heuristic algorithm to adjust the parameters of shapers for higher acceptance ratio

SLIDE 13

Outline

• Motivation

2019/5/16 13

• Framework
• Analysis Details
• Evaluation

SLIDE 14

Framework

2019/5/16 14

bursty periodic system shapers

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scheduler

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Why our approach is correct?

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SLIDE 15

Correctness

2019/5/16 15

• ur calculated delay bound

(changing bursty tasks as periodic)

bursty periodic system shapers

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scheduler

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SLIDE 16

Correctness

2019/5/16 16

• ur calculated delay bound

(changing bursty tasks as periodic)

bursty periodic system shapers

…

1

S

2

S

1



2



m



m

 

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scheduler

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1

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2

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n

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calculated delay bound (modeling bursty tasks as periodic)

m

S

SLIDE 17

Correctness

2019/5/16 17

• ur calculated delay bound

(changing bursty tasks as periodic)

bursty periodic system shapers

…

1

S

2

S

1



2



m



m

 

1

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2

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scheduler

…

1

P

2

P

n

P

calculated delay bound (modeling bursty tasks as periodic) 5 10 15 20 25 30 35 t 5 10 15 20 25 30 35 t Assume D = 5, one task on uniprocessor If consider the delay bound at the scheduler → schedulable If consider the overall delay → unschedulable

m

S

SLIDE 18

Outline

• Motivation

2019/5/16 18

• Framework
• Analysis Details
• Evaluation

SLIDE 19

System Model

2019/5/16 19

• Task Model

For each task, it has

• Scheduling strategy

A more general global EDF scheduling Worst case execution time C Relative deadline D Priority indicator λ Arrival curve α: maximum number of arrived events in any length of time interval Relative deadline only decides a task’s finish time The priority of a task is decided by priority indicator

SLIDE 20

Shaper

2019/5/16 20

• Behavior

Process job sequences and force its output job sequences to confirm to some time constraints

• Shaper Component

Arrival curve α Shaping function σ shaper shaper Output arrival curve α’ = α σ

• When generating periodic outputs, the shaper/shaping function is uniquely decided by period T.

SLIDE 21

Shaper

2019/5/16 21

• Behavior

Process job sequences and force its output job sequences to confirm to some time constraints

• Larger number of simultaneously arrived jobs → larger delay bound at the shaper

shaper

• Smaller period of shaper → smaller delay bound at the shaper

SLIDE 22

Global EDF Component

2019/5/16 22

• Model the global EDF (GEDF) scheduler as a GEDF component

Delay = Caldelay (input tasks, analysis techniques) Global EDF component

1 2

' ( ' , ' ,..., ' )

m

    =

1 2

( , ,..., )

m

    =  (Decided by Caldelay function)

bursty periodic system shapers

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2

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scheduler

…

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SLIDE 23

Model the System with Shapers

2019/5/16 23

• A system with shapers is modeled as a sequence of abstract components

bursty periodic system shapers

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system

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GEDF component

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SLIDE 24

How to Analyze (for given shapers)

2019/5/16 24

• Theorem

For each task, the overall delay bound is equal to the sum of that at the shaper and that of the scheduler Di

Di = Di

1 + Di 2 system

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GEDF component

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Di

1

Di

2



SLIDE 25

How to Choose Shapers

2019/5/16 25

• For periodic outputs, the behavior is decided by the period of shapers
• Why difficult to decide the period T

① Increase T → larger Di

1 , smaller Di 2

Di = Di

1 + Di 2

Decrease T → smaller Di

1 , larger Di 2

② The calculation Di

2 depends on other tasks

③ Enumerating all possible values is low-efficient

• We propose a heuristic algorithm for higher acceptance ratio

Di

system

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GEDF component

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Di

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SLIDE 26

Outline

• Motivation

2019/5/16 26

• Framework
• Analysis Details
• Evaluation

SLIDE 27

Evaluation (acceptance ratio)

2019/5/16 27

The only one existing work for bursty inputs under global EDF Proposed approach, setting the period of the shaper based on the input task

With simultaneously arrived jobs Without simultaneously arrived jobs

Proposed approach, setting the period of the shaper based on the heuristic Proposed approach, setting the period of the shaper arbitrarily

SLIDE 28

Evaluation (normalized delay bound)

2019/5/16 28

The only one existing work for bursty inputs under global EDF

With simultaneously arrived jobs Without simultaneously arrived jobs

Proposed approach, setting the period of the shaper based on the heuristic Proposed approach, setting the period of the shaper arbitrarily The normalized delay bound is calculated based on that when setting the period based on the input

SLIDE 29

Thanks for attention !