Recap from last lecture
TDDD07 Real-time Systems
Lecture 2: Scheduling II
Simin Nadjm-Tehrani
Real-time Systems Laboratory
Department of Computer and Information Science
Linköping University
Undergraduate course on Real-time Systems
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• Real-time systems have well-defined
timing requirements
• Many systems have a soft real-time
character
• But first we look at the extreme case
• Computational processes that need to
meet every deadline for each instance of
each process
• Most commonly used: Cyclic scheduling
with Major/Minor cycle
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When is the schedule correct?
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Harmonic processes
• All processes should be run at least as
often as every (original) Ti
Easy to find minor/major cycle
Recall example 2:
• All processes fit in the minor cycles they
are placed in
process
period
A
20
B
40
C
60
• We started with harmonic processes …
If sum of WCETs fits in...
...
0
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20
120
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Next try...
• In either case we need to
What if periods are not harmonic?
Or the WCET sum does not fit?
– change the task set parameters
– recall that all processes should be run at
least as often as every (original) Ti
• Place the processes in new minor cycle
and major cycle until repetition appears
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Example (3.1)
process
period
A
75
Jitter control
B
100
• Many applications need to minimise
jitter in reading data from sensors or
producing output to actuators
Alternative 1:
Choose minor cycle as greatest
common divisor, and move processes
backwards in time when they clash.
Drawbacks?
...
0
25
100
time
150
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Example (3.2)
process
period
A
75
B
100
0
Drawbacks?
...
75
time
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process
period
A
75
B
100
Alternative 3:
A mix of the last two
Alternative 2:
Run process B more often than necessary,
e.g. once every 75 time units.
minor cycle
Example (3.3)
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Drawbacks?
minor cycle
0
50
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If they don’t fit?
...
time
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Note: No preemption!
• Break some process that does not fit
into two or more processes and run the
different parts in different minor cycles
Creates new
processes out of the
old one!
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Drawbacks?
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Now let’s check!
You should be able to answer how the
typical scheduling questions are
answered in a cyclic schedule context …
During run-time:
• What is the de facto “deadline” for each
process?
• How does one know that processes
meet their deadlines?
• What happens if they don’t?
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What if dependent?
• So far we assumed all processes are
independent
• Dependence can be due to sharing resources
or computation precedence requirements
– Computation precedence automatically taken care of
as each instance of a process reads the inputs at the
beginning of a minor cycle (produced by another
process at the end of some prior minor cycle)
– Mutual access to resources does not take place as
each process is running alone with no interruptions
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Summary
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But...
• Simple at run-time
• No overheads for context switching
• Processes can exchange data without
the need for explicit (dynamic)
synchronisation
• Cycles can be hard to determine and
can become looong ...
• Long WCET can create problems
• Sporadic processes are run periodically
– Can lead to high processor utilisation
• Very inflexible!
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Better methods needed
For:
• Processes with long WCET
• Sporadic events
• Processes with long period but short
deadline
• Run-time process dependence
– specially in terms of overruns
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Priority-based scheduling
• A preemptive method where the priority
of the process determines whether it
continues to run or it is disrupted
”Most important process first!”
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RMS
Priorities
• Each process has a period Ti that is the
shortest interval between its release
times
Rate Monotonic Scheduling:
• On-line
• Preemptive
• Priority-based with fixed (static)
priorities
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• Processes are assigned priorities
dependent on length of Ti
– The shorter Ti the higher the priority
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Consider following scenario:
Example (4)
Period (Ti)
WCET (Ci)
Priority
P1
P2
20
10
high
50
30
10
5
low medium
arrival time
0
20
30
40
50
60
P3
preemption
0
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10
20
30
40
process
P1, P2, P3
P1
P3
P1
P2
P1, P3
...
50
60
80
90
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Schedulability Tests
time
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RMS Schedulability
• Sufficient
– if test is passed, then tasks are definitely
schedulable
– if test is not passed, we don’t know
Theorem:
• Necessary
– if test is not passed, tasks are definitely not
schedulable
– if test is passed, we don’t know
• Exact test:
(sufficient condition)
For n processes, RMS will guarantee their
schedulability if the total utilisation
U = C1/T1 + ... + Cn/Tn
does not exceed the guarantee level
G = n (2 1/n -1)
– sufficient & necessary at the same time
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For this example
When the test fails
U = 10/20+10/50+5/30 = 0,87
n=3

G = 3(2
1/3
• Try testing the critical instant: Assume that
all processes are released simultaneously
at time 0, and then arrive according to
their periods
• Check whether each process meets its
deadline for all releases before the first
deadline for the process with lowest
priority
-1) = 0,78
Schedulability is not guaranteed!
(but processes may still meet their
deadlines...)
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For example 4 scenario:
Example (4)
Period (Ti)
WCET (Ci)
Priority
P1
P2
20
10
high
50
30
10
5
low medium
arrival time
0
20
30
40
50
60
P3
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10
20
30
40
...
50
60
time
Response time analysis
• Tasks suffer interference from higher
priority tasks
Ri  Ci  I i
Ri  Ci 

jhp ( i )
 Ri 
 Cj
Tj 
• Iterative formula for calculating response
time
• Assumptions?
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90
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win 1  Ci 
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Exact schedulability test
• Mathematical equations for computing
worst case response times Ri for each
process
• Response time: the time between the
release and the completion time
• Process set schedulable if Ri ≤ Ti for all
processes
process
P1, P2, P3
P1
P3
P1
P2
P1, P3
preemption
0
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
jhp ( i )
 win 
 Cj
 Tj 
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Not schedulabe task set
When response time analysis gives a
“no” answer:
• Change U by reducing Ci (code
optimisation, faster processor, ...)
or
• Increase Ti for some process (can one
do this?)
Theorems
• Optimality: RMS is optimal among
methods with fixed priority
(in what sense?)
• Lowest upper bound: For arbitrarily
large n, it suffices that processor
utilisation is < 0.69
[Nice proofs in Buttazzo book]
$B
2 Bonus points!
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What does the test mean?
Utilisation based test:
G = n ( 2 1/n - 1)
Example (5)
Period (Ti)
WCET (Ci)
For a given n, the highest ceiling under
which we only find schedulable task sets
P1
P2
P3
20
7
50
10
30
5
U = 7/20 + 10/50 + 5/30 = 0,72
>0,69 but...
< G = 0,78
(irrespective of release times, with all
possible Ci, Ti)
The schedulability of this task set
is guaranteed!
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Better methods needed
For:
• Processes with long WCET
• Sporadic events
• Processes with long period but short
deadline
• Run-time process dependence
– specially in terms of overruns
Did we fix these?
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Summarising RMS
• Processes with long WCET
– RMS does not require splitting the code
• Sporadic events
– RMS only runs them when they arrive
• Processes with long period but short deadline
– Can allocate fixed priorities based on
deadlines for the cases Di  Ti - Deadline
monotonic scheduling
• Run-time process dependence
– Overruns: highest priority task not affected!
How about mutual access?
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Dynamic priorities
Earliest deadline first (EDF)
• Online decision
• Preemptive
• Dynamic priorities
• Next: We look at regimes that change
priorities dynamically
Policy: Always run the process that is
closest to its deadline
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