Disadvantages of cyclic
TDDB47 Real Time Systems
• “Manual” scheduler construction
Lecture 2: RM & EDF
• Cannot deal with any runtime changes
– What happens if we add a task to the set?
• Denies the advantages of concurrent
programming
Mikael Asplund
Real-Time Systems Laboratory
Department of Computer and Information Science
Linköping University, Sweden
– Which?
The lecture notes are partly based on lecture notes by Calin Curescu, Simin NadjmTehrani, Jörgen Hansson, Anders Törne. They also loosely follow Burns’ and Welling
book “Real-Time Systems and Programming Languages”. These lecture notes should
only be used for internal teaching purposes at Linköping University.
Lecture 2: RM & EDF
Mikael Asplund
29 pages
Lecture 2: RM & EDF
Mikael Asplund
States of a process
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Priority-based scheduling
• Every task has an associated priority
• Run task with the highest priority
– At every scheduling decision moment
• Examples
– Rate Monotonic (RM)
• Static priority assignment
– Earliest Deadline First (EDF)
• Dynamic priority assignment
– And many others …
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Schedulability Test
• Test to determine whether a feasible schedule exists
• Sufficient
+ if test is passed, then tasks are definitely schedulable
- if test is not passed, we don’t know
• Necessary
+ if test is passed, we don’t know
- if test is not passed, tasks are definitely not schedulable
• Exact
• sufficient & necessary at the same time
Lecture 2: RM & EDF
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Rate Monotonic (RM)
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Assumption
Rate Monotonic
• Each process is assigned a (unique) priority based
on its period; the shorter the period, the higher the
priority
• All tasks have their initial release at time 0
• Assumes the “Simple task model”
• Fixed priority scheduling
• Preemptive
– Unless stated otherwise
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Lecture 2: RM & EDF
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Example 1
• Assume we have the following task set
• OBS: not scheduled yet …
Lecture 2: RM & EDF
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Example 1 (cont’d)
• Scheduled with RM
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Schedulability test for RM
• Sufficient, but not necessary:
N
∑
i= 1

Ci
Ti
Example 2
• Taskset
• Period (Ti)
• WCET (Ci)
≤N  21 / N −1 
P1
20
7
P2
50
10
P3
30
5
• Necessary, but not sufficient:
N
∑
i= 1
Lecture 2: RM & EDF
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
Ci
Ti
≤1
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Harmonic periods
Example 3
• Taskset:
• Exact schedulability test for RM if periods are harmonic:
N
∑
i= 1

C
≤1
T
• Gantt chart:
i
i
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Exact schedulability test
The first time is the hardest
• The scedulability of a given taskset for RM can be
decided by:
• Theorem
– If all tasks meet their first deadline, then they will meet
all future ones.
– Drawing a schedule
– Proof: paper by Liu and Layland, 1973
– Doing a response time analysis
• Why?
• Complexity: Pseudo-polynomial time
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Response time analysis
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Optimality of scheduling algorithms
• Tasks suffer interference from higher priority tasks
• “A scheduler is optimal if it always finds a schedule when a
schedulability test indicates there is one.”
• Response time: the time that passes since the task is
released and until it finishes
R i =C i +I i
R i =Ci 
∑
j∈hp i 
 
Ri
Tj
– Burns, 1991
• “An optimal scheduling algorithm is one that may fail to
meet a deadline if no other scheduling algorithm can meet
it.”
Cj
– Stankovic et al., 1995
• “An optimal scheduling algorithm is guaranteed to always
find a feasible schedule, given that a feasible schedule does
exist.”
• Iterative formula for calculating response time
1
w n+
=Ci 
i
Lecture 2: RM & EDF
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∑
j∈hp i 
 
w ni
Tj
– Hansson, 1998
Cj
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Optimality of RM
What to do if not schedulable
• Change the task set utilitsation
– by reducing Ci
• Rate Monotonic is optimal among fixed priority schedulers
• code optimisation
• faster processor
– If we assume the “Simple Process Model” for the tasks
• Increase Ti for some process
– If your program and environment allows it
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Lecture 2: RM & EDF
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RM characteristics
• Easy to implement.
• Drawback:
– May not give a feasible schedule even if processor is
idle at some points.
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Earliest Deadline
First (EDF)
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Earliest Deadline First (EDF)
• Always runs the process that is closest to its deadline.
• Dynamic priority scheduling
– Evaluated at run-time
– What are the events that should trigger a priority reevaluation?
Schedulability test for EDF
• Utilitsation test
– Necessary and sufficient
• Or “exact” test
N
∑
• Assumes the “Simple task model”
– Actually more relaxed: Di < Ti
i= 1

Ci
Ti
≤1
• Preemptive
– Unless stated otherwise
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Optimality of EDF
Example 4
• Consider following task set:
• WCET (Ci)
• EDF is optimal among dynamic priority schedulers
P1 P2
2 4
• Deadline (Di = Ti)
– If we assume the “Simple Process Model” for the tasks
• Or a more relaxed one where Di < Ti
5 7
• Is it schedulable with EDF?
• Is it schedulable with RM?
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Domino Effect
EDF vs. RM
• EDF can handle tasksets with higher processor utilisation.
– Example 4 not schedulable with RMS!
• EDF has simpler exact analysis
• RMS can be implemented to run faster at run-time
– Depends on the OS
– But they usually like fixed priorities more
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Lecture 2: RM & EDF
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Reading material
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Dynamic Scheduling
• Chapter 13 in Burns & Wellings
• Chapter 4 in Butazzo
– for the proofs of sufficient condition and optimality
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