modeling and analysis of data flow graphs using the ... · modeling and analysis of data flow...

Modeling and Analysis of Data Flow Graphsusing the Digraph Real-Time Task Model

Morteza Mohaqeqi, Jakaria Abdullah, and Wang Yi

Uppsala University

Ada-Europe 2016

Overview

Introduction

Data Flow Graphs:Signal processingStream processingData dependency

a b

[1, 3] [2]

[1, 1, 4][2]

Design ObjectivesThroughput maximization

Design Constraints

Buffer overflow/underflow avoidanceSchedulability

Mohaqeqi et al. (Uppsala University) Analysis of Data Flow Graphs 1 / 19

Overview

An Overview

A Set of DataFlow Graphs

Processor

Schedule


Transform

Real-Time Tasks

Processor

Schedule


The Problem: Our Approach:

Overview

An Overview


Processor

Schedule


Transform

Real-Time TasksPeriodic

Processor

Schedule



Overview

An Overview


Processor

Schedule


Transform

Real-Time TasksDigraph RT

Processor

Schedule



Overview

Previous Work

a b

periodictask

periodictask

DRTperiodicperiodic

Our work

Strictly period schedule[Bouakaz 2014]

Digraph Real-Time (DRT)task model [Stigge et al 2011]

Our work

Strictly Period Schedule[Bouakaz 2014]

Digraph Real-Time (DRT)task model [Stigge et al 2013]


Outline

1 Introduction

2 Method

3 Evaluation

4 Conclusion


Introduction

(Static) Data Flow Graphs

SynchronousData Flow

a b[2] [1]

Fixed token production(consumption) rateFixed execution time

Cyclo-StaticData Flow

a b

[1, 3] [2]

[1, 1, 4][2]

Variable token production(consumption) rateVariable execution time


Introduction

Semantics

Empty buffer

’a’ can be fired

a b[2] [1]

size = 2


Introduction

Semantics

Empty buffer’a’ can be fired

a b[2] [1]

size = 2a


Introduction

Semantics

Full buffer

’a’ cannot be fired’b’ can be fired

a b[2] [1]

size = 2


Introduction

Semantics

Full buffer’a’ cannot be fired’b’ can be fired

a b[2] [1]

size = 2b


Introduction

Semantics

’a’ cannot be fired’b’ can be fired

a b[2] [1]

size = 2b


Introduction

Semantics

Empty buffer’a’ can be fired

a b[2] [1]

size = 2a


Introduction

Constraints

Design Constraints

Underflow/overflow avoidanceSchedulability


Introduction

Underflow and Overflow

Underflow avoidance

a b[2] [1]

tTa

t0 5 10Tb

Cannot be fired

offset

t0 5 10

tokens buffer size=5

no overflow


Introduction


Produce token as soon as possibleConsume token as late as possible

a b[2] [1]

tTa

t0 5 10Tb

Cannot be fired

offset

t0 5 10

tokens

buffer size=5

no overflow


Introduction


Produce token as soon as possibleConsume token as late as possible

a b[2] [1]

tTa

t0 5 10Tb

Cannot be fired

offset

t0 5 10

tokens buffer size=5

no overflow


Introduction

Constraints

Design Constraints

Underflow/overflow avoidance

Schedulability

a b[2] [1]

tTa

t0 5 10Tb

offset

Ca = 2

Cb = 2

Unschedulable!Larger Periods Lower Throughput


Introduction

Constraints

Design Constraints


a b[2] [1]

tTa

t0 5 10Tb

offset

Ca = 2

Cb = 2

Unschedulable!Larger Periods Lower Throughput


Introduction

Constraints

Design Constraints


a b[2] [1]

tTa

t0 5 10Tb

offset

Ca = 2

Cb = 2

Unschedulable!

Larger Periods Lower Throughput


Introduction

The Problem

Design Parameters

PeriodsOffsets

Constraints

No underflowNo overflowSchedulability

Objective

Throughput maximization


Introduction

Cyclo-Static Data Flow Graphs

Repeating pattern

a b[10, 10, 0, 0] [5, 5, 5, 5]

tTa

t0 5 10 15Tb

5 5 5 5 5 5 5 5

10 10 0 0 10 10 0 0 10 10


Introduction


Repeating pattern

a b[10, 10, 0, 0] [5, 5, 5, 5]

tTa

t0 5 10 15Tb

5 5 5 5 5 5 5 5

10 10 0 0 10 10 0 0 10 10

size=25

t0 5 10 15

tokens

510152025


Introduction


Repeating pattern

a b[10, 10, 0, 0] [5, 5, 5, 5]

tTa

t0 5 10 15Tb

5 5 5 5 5 5 5 5

10 10 0 0 10 10 0 0 10deadline


Introduction


Repeating pattern

a b[10, 10, 0, 0] [5, 5, 5, 5]

tTa

t0 5 10 15Tb

5 5 5 5 5 5 5 5

10 10 0 0 10 10 0 0 10deadline

t0 5 10 15

tokens

510152025

size=20


Introduction

We need a non-periodic task model


Introduction

Scheduling Data Flow Graphs

Synchronous Data FlowFixed behaviorPeriodically repeating

a b[2] [1]

t0 4 8 12

t0 4 8 12

Ta

Tb

offset

Cyclo-Static Data FlowChanging behaviorRepeating pattern

a b

[1, 3] [2]

[1, 1, 4][2]

The Digraph Real-Time task model.


Introduction

The Digraph Real-Time (DRT) Task Model

A graph-based representationDifferent job types

v1 v2

v3

〈2, 5〉〈1, 3〉

〈1, 6〉

8

10

5

10

8

t0 5 10 15 20

v1 v2 v3 v1

v1 v2 v3 v1


Method

Example

MP3 playback application

MP3 SRC APP DAC[0 0 576 0 576] [480] [441] [1] [1] [1]

CMP3 = [670, 2700, 720, 2700, 720] CSRC = 2500 CSRC = 22 CSRC = 22

DRT task for the actor MP3

v0 v1 v2

v3

v4

v5

〈0, 0〉〈670, d1〉

〈2700, d2〉

〈720, d3〉

〈2700, d4〉

〈720, d5〉

0 p1

p2

p3p4

p5


Method

Example

MP3 playback application

MP3 SRC APP DAC[0 0 576 0 576] [480] [441] [1] [1] [1]

CMP3 = [670, 2700, 720, 2700, 720] CSRC = 2500 CSRC = 22 CSRC = 22

DRT task for the actor SRC

v6 v7

〈0, 0〉〈2500, d〉

p1p2


Evaluation

Obtained DRT tasks

v0 v1 v2

v3

v4

v5

〈0, 0〉〈670, 5366〉

〈2700, 21624〉

〈720, 5766〉

〈2700, 21624〉

〈720, 5766〉

0 5366

21624

576621624

5766

Table: Task set parameters for the DRT tasks (µs)

Period Offset

SRC 25061.809 60649.578

APP 56.829 110801.612

DAC 56.829 110943.686


Evaluation

Evaluation Results

Table: Total buffer requirement and throughput for each method

Buffer Requirement Throughput (s−1)

Periodic Task Set 2273 16013

DRT Task Set 2155 17596

Improvement 5% 9.8%


Conclusion

Conclusion

Using a more general task modelMore flexibilityLarger state-space

DRTperiodic

Schedulable Data Flows

Linear approximation


Modeling and Analysis of Data Flow Graphsusing the Digraph Real-Time Task Model

Morteza Mohaqeqi, Jakaria Abdullah, and Wang Yi

Uppsala University

Ada-Europe 2016

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