Improving Multiprocessor Real-Time Systems with Bursty Inputs under Global EDF … · 2019. 5. 22. · Improving Multiprocessor Real-Time Systems with Bursty Inputs under Global EDF

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

Outline

• Motivation

2019/5/16 2

• Framework

• Analysis Details

• Evaluation

Outline

• Motivation

2019/5/16 3

• Framework


• Evaluation

Motivation

2019/5/16 4

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

Motivation

2019/5/16 5


• How to calculate delay bound for GEDF?

Motivation

2019/5/16 6



• Most work considers periodic tasks

Motivation

2019/5/16 7


However



• Bursty tasks are more general

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

output stream

output stream

Motivation

2019/5/16 9


However




• Model bursty tasks as periodic tasks

Possible solution?

Motivation

2019/5/16 10

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

Choose the period of periodic tasks

0 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)

0 5 10 15 20 25 30 35 t

Can not set the period !

No !

Motivation

2019/5/16 11


However




• Model bursty tasks as periodic tasks

Possible solution?

Our contribution !

• Change bursty tasks to periodic tasks using shapers

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

Outline

• Motivation

2019/5/16 13

• Framework


• Evaluation

Framework

2019/5/16 14

bursty periodic

system

shapers

…

1S

2S

1

2

m m

1

2

scheduler

…

1P

2P

nP

Why our approach is correct?

mS

Correctness

2019/5/16 15

our calculated delay bound

(changing bursty tasks as periodic)

bursty periodic

system

shapers

…

1S

2S

1

2

m m

1

2

scheduler

…

1P

2P

nPmS

Correctness

2019/5/16 16



bursty periodic

system

shapers

…

1S

2S

1

2

m m

1

2

scheduler

…

1P

2P

nP

calculated delay bound

(modeling bursty tasks as periodic)

mS

Correctness

2019/5/16 17



bursty periodic

system

shapers

…

1S

2S

1

2

m m

1

2

scheduler

…

1P

2P

nP

calculated delay bound

(modeling bursty tasks as periodic)

0 5 10 15 20 25 30 35 t

0 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

mS

Outline

• Motivation

2019/5/16 18

• Framework


• Evaluation

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

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.

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

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

…

1S

2S

1

2

m m

1

2

scheduler

…

1P

2P

nPmS

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

…

1S

2S

1

2

m m

1

2

scheduler

…

1P

2P

nP

system

…

1S

2SGEDF

component

1

2

m

1'

2'

'm

1

2

m

mS

mS

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 = Di1 + Di2

system

…

1S

2SGEDF

component

1

2

m

1'

2'

'm

1

2

m

mS

Di1 Di2

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 Di1 , smaller Di2

Di = Di1 + Di2

Decrease T → smaller Di1 , larger Di2

② The calculation Di2 depends on other tasks

③ Enumerating all possible values is low-efficient

• We propose a heuristic algorithm for higher acceptance ratio

Di

system

…

1S

2SGEDF

component

1

2

m

1'

2'

'm

1

2

m

mS

Di1 Di2

Outline

• Motivation

2019/5/16 26

• Framework


• Evaluation

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



based on the heuristic



arbitrarily

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



based on the heuristic



arbitrarily

The normalized delay bound

is calculated based on that

when setting the period

based on the input

Thanks for attention !

Documents

Improving Multiprocessor Real-Time Systems with Bursty Inputs under Global EDF … · 2019. 5. 22. · Improving Multiprocessor Real-Time Systems with Bursty Inputs under Global EDF