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Roman Trüb, rtrueb@ethz.ch

Computer Engineering Group, ETH Zurich

1

Embedded Systems – Exercise 4:

Scheduling Periodic and Mixed Task Sets

11./13.11.2020Roman Trüb

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Exercise Structure

Goal of today’s exercise:

▪ Learn and apply scheduling schemes for periodic and mixed task sets.

Agenda:

▪ Wednesday 16:15 – 17:00 Clicker quiz (recorded)

Lecture summary (recorded)

Solving a sample task (recorded)

Tasks of exercise 4 (recorded)

Q & A

▪ Friday 16:15 – 17:00 Solution discussion (recorded)

Q & A

Available Assistants:

▪ Roman Trüb - TA

▪ Joël Küchler - SA

Roman Trüb

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Clicker Quiz

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Clicker Quiz – Question 1

Schedulable with EDF

Test failed

Task set is not schedulable with EDF

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Clicker Quiz – Question 2

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Schedulable with RM

With this test result, no statement can be made since

schdulablility test condition is not necessary.

Task set could still be schedulable with RM.

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Clicker Quiz – Question 3

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Clicker Quiz – Question 4

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Lecture Summary

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Scheduling Algorithms

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Periodic with

D = T

Periodic with

D < TMixed Tasks

Static

PriorityRM DM Polling Server

Dynamic

PriorityEDF EDF

Total

Bandwidth

Server

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Scheduling Periodic Task Sets [6-33f]

Roman Trüb

Periodic with

D = T

Periodic with

D < TMixed Tasks

Static

PriorityRM DM Polling Server

Dynamic

PriorityEDF EDF

Total

Bandwidth

Server

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Rate Monotonic (RM)

Roman Trüb

Static priority assignment:

Tasks with shorter period get higher priority

t

tT1

tT3

tT2

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Rate Monotonic (RM)

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Static priority assignment:

Tasks with shorter period get higher priority

t

tT1

tT3

High

Low

tT2

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Rate Monotonic (RM)

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Static priority assignment:

Tasks with shorter period get higher priority

t

tT1

tT3

High

Low

tT2

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Rate Monotonic (RM)

Roman Trüb

Static priority assignment:

Tasks with shorter period get higher priority

t

tT1

tT3

High

Low

tT2

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Rate Monotonic (RM)

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Static priority assignment:

Tasks with shorter period get higher priority

t

tT1

tT3

High

Low

tT2

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Rate Monotonic (RM)

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Static priority assignment:

Tasks with shorter period get higher priority

t

tT1

tT3

High

Low

tT2

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RM – Schedulability Test

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Sufficient

(but not necessary)

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Scheduling Periodic Task Sets [6-33f]

Roman Trüb

Periodic with

D = T

Periodic with

D < TMixed Tasks

Static

PriorityRM DM Polling Server

Dynamic

PriorityEDF EDF

Total

Bandwidth

Server

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Deadline Monotonic (DM)

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Static priority assignment:

Tasks with smaller relative deadline get higher priority

tT3

t

tT1

tT2

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Deadline Monotonic (DM)

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Static priority assignment:

Tasks with smaller relative deadline get higher priority

t

tT1

tT2

High

Low

tT3

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Deadline Monotonic (DM)

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Static priority assignment:

Tasks with smaller relative deadline get higher priority

t

tT1

tT2

High

Low

tT3

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Deadline Monotonic (DM)

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Static priority assignment:

Tasks with smaller relative deadline get higher priority

t

tT1

tT2

High

Low

tT3

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Deadline Monotonic (DM)

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Static priority assignment:

Tasks with smaller relative deadline get higher priority

t

tT1

tT2

High

Low

tT3

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Deadline Monotonic (DM)

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Static priority assignment:

Tasks with smaller relative deadline get higher priority

t

tT1

tT2

High

Low

tT3

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DM – Schedulability Test

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Sufficient

(but not necessary)

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RM & DM – Schedulability Test

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Necessary &

Sufficient

Ri Ri+Ci

Worst-case

Interference:

Longest Response Time Ri(computed iteratively)

Assumption: Tasks are

ordered according to their

priorities:

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Scheduling Periodic Task Sets [6-33f]

Roman Trüb

Periodic with

D = T

Periodic with

D < TMixed Tasks

Static

PriorityRM DM Polling Server

Dynamic

PriorityEDF EDF

Total

Bandwidth

Server

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Earliest Deadline First (EDF)

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Dynamic Priority Assignment:

Always execute the task with the currently closest deadline

t

tT1

tT3

tT2

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Earliest Deadline First (EDF)

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Dynamic Priority Assignment:

Always execute the task with the currently closest deadline

t

tT1

tT3

tT2

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Earliest Deadline First (EDF)

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Dynamic Priority Assignment:

Always execute the task with the currently closest deadline

t

tT1

tT3

tT2

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Earliest Deadline First (EDF)

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Dynamic Priority Assignment:

Always execute the task with the currently closest deadline

t

tT1

tT3

tT2

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EDF – Schedulability Tests

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Di= Ti Di< Ti

Sufficient

(but not necessary)

Necessary &

Sufficient

Utilization:

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Mixed Task Scheduling

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• Mixed (or hybrid) task set contains both periodic and

aperiodic tasks

• Basic idea for scheduling:

• Schedule the periodic tasks as usual

• Serve the aperiodic tasks via a "server" that behaves

like a periodic task but serves the aperiodic tasks

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Scheduling Mixed Task Sets [6-64f]

Roman Trüb

Periodic with

D = T

Periodic with

D < TMixed Tasks

Static

PriorityRM DM Polling Server

Dynamic

PriorityEDF EDF

Total

Bandwidth

Server

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Polling Server (RM)

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Idea: Introduce an artificial periodic task (Cs, Ts) which serves the aperiodic

requests

Schedulability test for mixed task set:Sufficient

(but not necessary)

Sufficient

(but not necessary)

Aperiodic guarantee (schedulability test for aperodic requests):

Assumption: aperiodic task finishes

before new aperiodic request arrives

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Scheduling Mixed Task Sets [6-64f]

Roman Trüb

Periodic with

D = T

Periodic with

D < TMixed Tasks

Static

PriorityRM DM Polling Server

Dynamic

PriorityEDF EDF

Total

Bandwidth

Server

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Total Bandwidth Server (EDF)

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Idea: For every aperiodic request a deadline which is based on the server’s

parameters (Cs, Ts) is assigned. The aperiodic requests are then scheduled with

EDF as any other periodic instance.

Assignment of the deadlines to the aperiodic requests:

NOTE: recursive

computation!

Aperiodic requests

are assumed to be

ordered by increasing

release time ri

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Total Bandwidth Server (EDF)

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Schedulability test for mixed task set: Necessary & Sufficient

Set of periodic tasks with

utilization Up and a Total

Bandwidth Server with utilization

Us is schedulable with EDF

Utilization of Total Bandwidth Server:

Utilization of the periodic tasks:

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Sample Task

(Task 4a)

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First Try Sufficient (But Not Necessary) Scheduling Test.

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Test failed. No statement can be made (since test is sufficient but not necessary).

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RM & DM – Schedulability Test

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Necessary &

Sufficient

Ri Ri+Ci

Worst-case

Interference:

Longest Response Time Ri(computed iteratively)

Assumption: Tasks are

ordered according to their

priorities:

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Apply Sufficient and Necessary Scheduling Test [6-54]

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1. Order tasks according to their priorities (relative deadlines for DM):

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Apply Sufficient and Necessary Scheduling Test [6-54]

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1. Order tasks according to their priorities (relative deadlines for DM):

2. Apply iterative algorithm to find longest response time for each task, starting

with last task

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Apply Sufficient and Necessary Scheduling Test [6-54]

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1. Order tasks according to their priorities (relative deadlines for DM):

2. Apply iterative algorithm to find longest response time for each task, starting

with last task

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Apply Sufficient and Necessary Scheduling Test [6-54]

Roman Trüb

1. Order tasks according to their priorities (relative deadlines for DM):

2. Apply iterative algorithm to find longest response time for each task, starting

with last task

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Apply Sufficient and Necessary Scheduling Test [6-54]

Roman Trüb

1. Order tasks according to their priorities (relative deadlines for DM):

2. Apply iterative algorithm to find longest response time for each task, starting

with last task

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Apply Sufficient and Necessary Scheduling Test [6-54]

Roman Trüb

1. Order tasks according to their priorities (relative deadlines for DM):

2. Apply iterative algorithm to find longest response time for each task, starting

with last task

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Apply Sufficient and Necessary Scheduling Test [6-54]

Roman Trüb

1. Order tasks according to their priorities (relative deadlines for DM):

2. Apply iterative algorithm to find longest response time for each task, starting

with last task

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Apply Sufficient and Necessary Scheduling Test [6-54]

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Test failed.

Task set is not schedulable using the Deadline Monotonic scheduling scheme.

1. Order tasks according to their priorities (relative deadlines for DM):

2. Apply iterative algorithm to find longest response time for each task, starting

with last task

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Exercise 4

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Exercise 4 - Solution

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Task 1 – Solution

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a) Maximum utilization of the server:

b) Order tasks by increasing release time: J4, J6, J5

Then, calculate new deadlines recursively:

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Task 1 – Solution

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b) EDF schedule with aperiodic tasks:

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Task 2 – Solution

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a) Sufficient test:

Test failed! Since it is not necessary, we still don’t know if the task set is

schedulable with RM or not.

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Task 2 – Solution

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b) Necessary test: Iterative algorithm

1) Order tasks by their priority (already ok in this case)

2) Start with task which has lowest priority:

Necessary test succeeds task set is schedulable with RM

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Task 2 – Solution

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c) RM schedule

(there are no deadline misses)

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Task 3 – Solution

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a) Aperiodic guarantee:

b) Sufficient schedulability test for RM Polling Server:

Test succeeded!

Substituting values & considering minimum

Task set is schedulable with RM

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Exercise Session is Over

▪ The assistants are now available until roughly 17:00 to answer questions.

▪ Zoom: Ask in this Zoom channel

▪ Matrix-Chatroom: Ask a question in the chatroom so other students can also profit from the

response (or respond even quicker!)

▪ Email: For individual questions, you can also reach me under rtrueb@ethz.ch .

Roman Trüb