From last lecture
• A preemptive method where the priority
of the process determines whether it
continues to run or it is disrupted
TDDC47: Concurrent and real-time
programming
Lecture 6: Scheduling II
Si i Nadjm-Tehrani
Simin
N dj
T h
i
”Most important process first!”
Real-time Systems Laboratory
Department of Computer and Information Science
Linköping University
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34 pages
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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
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process
P1, P2, P3
P1
P3
P1
P2
P1, P3
...
50
60
80
90
time
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Schedulability test
For this example
U = 10/20+10/50+5/30 = 0,87
Theorem:
(sufficient condition)
n=3
For n processes,
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)
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Schedulability is not guaranteed!
(but processes may still meet their
deadlines...)
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arrival time
0
20
30
40
50
60
• Try with 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
10
20
30
• P
Process sett schedulable
h d l bl if Ri ≤ Ti for
f all
ll
processes
40
...
50
60
90
time
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Response time analysis
• Response time: the time between the
release and the completion time
• 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?
win 1  Ci 
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Exact analysis
• Mathematical equations for computing
worst case response times Ri for each
process
process
P1, P2, P3
P1
P3
P1
P2
P1, P3
preemption
0
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For example 4 scenario:
When the test fails
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 G = 3(2 1/3 -1) = 0,78
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 win 
 Cj
jhp ( i )  T j 

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Not schedulabe task set
When response time analysis gives a
“no” answer:
• 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
• Change U by reducing Ci (code
optimisation, faster processor, ...)
or
• Increase Ti for some process (can one
do this?)
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Theorems
[Nice proofs in Buttazzo book – can lend
if interested]
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What does the test mean?
Utilisation based test:
G = n ( 2 1/n - 1)
Example (2)
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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Recall: Better methods for...
• Processes with long WCET
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Dynamic priorities
• Allow
– processes with long Ti and short
deadline
– Process dependencies: when
processes share resources and must
be synchronised
• Next scheduling algorithm: change
priorities dynamically
– RMS does not require splitting the code
• Sporadic events
– RMS only runs them when they arrive
• Processes with long period but short
deadline
– Can run a variant of RM when Di  Ti
Deadline monotonic
• Dealing with overruns
– RMS makes lower priority processes suffer
most
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Earliest deadline first (EDF)
Process sets
• Event that leads to release of process Pi
appears with minimum inter-arrival
interval Ti
• Pi has a max computation time Ci
• The p
process must be finished before its
deadline Di  Ti
• Processes are independent (do not share
resources)
• Online
• Preemptive
• Dynamic
D
i priorities
i iti
Policy: Always run the process that is
closest to its deadline
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• EDF: The process with nearest absolute
deadline (di) will run first
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Example (3)
Consider following processes:
P1
WCET (Ci)
5
Deadline (Di = Ti)
20
Arrival times (ri)
0, 20,...
0,
P2
10
12
12,...
Compare to RMS
For same task set:
WCET (Ci)
Deadline (Di = Ti)
Arrival times (ri)
P1
5
20
0 20,...
0,
20
P2
10
12
0 12,...
0,
12
...?
Preemption
0
10
15
20
time
25
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0
10
15
...?
20
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Theorem
A set of periodic tasks P1,...,Pn for
which Di = Ti is schedulable with EDF iff
U= C1/T1+...+Cn/Tn 
time
25
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Example (4)
Consider following task set:
WCET (Ci)
Deadline (Di = Ti)
P1
2
5
P2
4
7
Is it schedulable?
U = 2/5 + 4/7 = 0,97
For Example 3:
C1/T1 + C2/T2 = 5/20 + 10/12 = 1,08!
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Yes!
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EDF vs. RMS
Sharing resources
• EDF gives higher processor utilisation
(Example 4 not schedulable with RMS!)
• EDF has simpler exact analysis for the
mentioned type of task sets
• RMS can be implemented to run faster
at run-time (if we ignore the time for
context switching)
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• Assume that processes synchronise
using semaphores
• We schedule the processes with fixed
priorities but relax the independence
requirement
i
t
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Priority Inversion
How to avoid it?
• A low priority process (P1) locks the
resource
• A high priority process (P2) has to wait
on the semaphore (blocked state)
• A medium priority process (P3)
preempts P1 and runs to completion
before P2!
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• When P2 is blocked by P1 one raises the
priority of P1 to the same level as P2
temporarily
• Afterwards, when the semaphore is
released
l
db
by P1, it goes back
b k to
t its
it prior
i
priority level
• P3 can not interrupt P1 any more!
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Priority inheritance
• Guarantees upper bound for blocking
time, since high priority process P2 is
blocked only under the time that P1 uses
the resource
• Is
I transitive
t
iti
Example
Let P1 have lower priority than P2.
Preemption
S1
P1
S1?
Blocked
But ...
Does not avoid deadlock!
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Blocked
S2?
S2
P2
Inheritance
time
0
Here Si denotes the process locks semaphore Si.
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Ceiling Protocols
Terminology
e.g. Immediate priority Ceiling Protocol (ICP):
Note that:
• blocked – when waiting for a
resource (other than CPU)
• not dispatched or preempted when waiting for CPU
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• A process that obtains its first resource
inherits the resource’s ceiling priority - the
highest priority among all processes that can
possibly
p
y claim that resource
• Dynamic priority for a process is the max of
own (fixed) priority and the ceiling values of
all resources it has locked
• When a resource is released, the process
priority returns to the normal level (or to
another engaged resource’s ceiling)
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Properties
• A process is blocked max once by
another process with lower priority
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ICP & Deadlock
• The ICP prevents deadlocks (How?)
We will prove that!
• Moreover, it prevents starvation (How?)
• The blocking delay is a function of the
length of the critical section
• Do not even need to use semaphores!
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