1. Scheduling and Resource Access Protocols: Basic Aspects
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2. A Classic Policy Rate Monotonic Scheduling. Task set : {J1, J2, …, Jn}
Each task is periodic. T1, T2,.., Tn
i = 0 for each i.
Di = Ti for each i.
Pre-emption allowed.
Only one processor
No precedence constraints
No shared resources.
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3. RMS
The RMS algorithm:
Assign a static priority to the tasks according to their periods.
Priority of a task does not change during execution.
Tasks with shorter periods have higher priorities.
Preemption policy:
If Ti is executing and Tj arrives which has higher priority (shorter period), then preempt Ti and start executing Tj.
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4. RMS Example
(3, 2)
(5, 1)
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5. RMS Example
(3, 1)
(5, 2)
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6. RMS Results RMS is optimal.
If a set of of periodic tasks (satisfying the assumptions set out previously) is not schedulable under RMS then no static priority algorithm can schedule this set of tasks.
RMS requires very little run time processing.
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7. Process Utilization Factor
Task set = {T1, T2, …, Tn}
Process Utilization Factor
 Ci / Ti
C1 / T1 + C2 / T2 + … Cn / Tn
If this factor is GREATER than 1 then the task set can not be scheduled.
Why?
If UF ≤ 1 it may be RMS-schedulable.
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8. RMS Schedulability Task set = {T1, T2, …, Tn}
If UF  Ulub then it is guaranteed to be schedulable.
Ulub - The least upper bound of processor
utility.
For RMS, Ulub = n( 21/n – 1)
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9. Process Utilization Factor
Task set = {T1, T2, …, Tn}
If UF  Ulub then it is guaranteed to be schedulable.
But if UF is greater than Ulub and not greater than 1, we must check explicitly whether the task set is RMS-schedulable.
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10. RMS Schedulability n Ulub   0.690 1 1.000 2 0.828 3 0.780 4 0.757 5
0.743 6
0.735 7
0.729  
This is only a sufficient criterion!
This criterion may fail and yet an RMS may exist.

11. RMS Example UF = 0.66 + 0.20 = 0.86 (3, 2) Ulub = 0. 828 (5, 1)
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12. RMS Example UF = 0.33 + 0.40 = 0.73 (3, 1) Ulub = 0. 828 (5, 2)
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13. EDF Earliest Deadline First.
Tasks with earlier deadlines will have higher priorities.
Applies to both periodic and aperiodic tasks.
EDF is optimal for dynamic priority algorithms.
A set of periodic tasks is schedulable with EDF iff the utilization factor is not greater
than 1.
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14. An Example {T1, T2} T1 = ( 5, 2) T2 = (7, 4) UF = 0.4 + 0.57 = 0.97
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15. An RMS Schedule?
Time-Overflow
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16. The Example
UF = = 0.97
Guaranteed to be schedulable under EDF!
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17. An EDF Schedule
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18. Shared Resources Inter-process communication Material taken from:
Shared resources, critical sections, priority inversion, access protocols.
Material taken from:
Buttazzo’s Book: parts of chapter 7.
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19. The Host Computer
DSP
Processor
Timer
ASIC
Memory
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20. Tasks
TASK1
TASK2
TASK3
TASK4
DATA SETS
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21. Resource Constraints resource: Shared resource: Exclusive resource:
software structure used by a task during its execution.
A data structure, variables, an area of main memory, a file, a piece of code, a set of registers of a peripheral device.
Shared resource:
Used by more than one task.
Exclusive resource:
No simultaneous access.
Require mutual exclusion.
Operating must provide a synchronization mechanism to ensure sequential access..
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22. Critical Section Critical section:
A piece of code belonging to task executed under mutual exclusion constraints.
Mutual exclusion enforced by semaphores.
wait(s)
Blocked if s = 0.
signal(s)
s is set to 1 when signal(s) executes.
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23. Structure of Critical Sections.
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24. Wait State
A task waiting for an exclusive resource is blocked on that resource.
Tasks blocked on the same resource are kept in a wait queue associated with the semaphore protecting the resource.
A task in the running state executing wait(s) on a locked semaphore (s = 0) enters the waiting state.
When a task currently using the resource executes signal(s), the semaphore is released.
When a task leaves its waiting state (because the semaphore has been released) it goes into the ready state:
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25. Waiting State
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26. Blocking via Exclusive Resource
J1 has higher priority than J2.
Preemption is in play.
Only one processor available.

27. Resource Access Protocols
Multiple tasks.
Uniprocessor
Shared resources.
Need proper protocols for accessing shared resources.
Resource access protocols.
Avoid priority inversion!
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28. Priority Inversion. J1 J2 J3 0 1 2 3 4 5 6 7 J1 > J2 > J3
J1 > J2 > J3
[3, 6] priority inversion period. J1 waits for the execution of J2 and the critical section of J3
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29. Priority Inversion
The Mars pathfinder Mission in 1997 ran into serious problem.
The spacecraft began experiencing total system resets with loss of data each time.
It turned out to be due to priority inversion.
See the web page and the links there in the IVLE area!
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30. Avoiding Priority inversion
Disallow preemption during the execution of a critical section.
Works only if critical sections are short.
Might unneccesarily block higher priority processes that do not even use any shared resources!
Resource access protocols:
Priority inheritance protocol.
Priority ceiling protocol.
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31. Priority Inheritance Protocol
Tasks have nominal and active priorities.
Nominal priority:
assigned by the scheduling algorithm (RMS, EDF,..)
Active priority
assigned by the protocol –dynamically- to avoid priority inversion.
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32. Priority Inheritance Protocol
Basic idea :
When Ji blocks higher-priority tasks, then its active priority is set to the highest of the priorities of the tasks it blocks.
Ji inherits -temporarily – the highest priority of the blocked tasks.
This prevents medium priority tasks from preempting Ji and prolonging the blocking duration of the higher priority tasks.
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33. Priority Inheritance Protocol
The Protocol:
Jobs are scheduled based on their active priorities.
If Ji tries to enter a critical section and the corresponding resource is being held by Jj then Ji is blocked; it is said to be blocked by Jj.
When a job is blocked on a semaphore, it transmits its active priority to the job that holds the semaphore; in general, a task inherits the highest priority of the jobs blocked by it.
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34. Priority Inheritance Protocol
The Protocol:
When Jk exits a critical section, it unlocks the semaphore; the job with the highest priority that is blocked on the semaphore, if any, is awakened. The priority of Jk is set to the highest priority of the job it is currently blocking. If none, its priority is set to its nominal one.
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35. Example
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36. Nested Critical Sections
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37. Priority Inheritance Protocol
Good news:
If there are m distinct semaphores that can block a job J then J can be blocked for at most the duration of at most one critical section, one for each of the semaphores.
It can never be as long as the WCET of a lower priority task.
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38. Priority Inheritance Protocol
Bad news:
Chained Blocking:
J can get blocked on n critical sections held by n distinct lower priority jobs.
Deadlocks.
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39. Chained Blocking
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40. Deadlock
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41. Priority Ceiling Protocol
Extension of the Priority Inheritance Protocol.
Avoids chained blocking and deadlocks.
Basic Idea:
A task is not allowed to enter a critical section if there are already locked semaphores which could block it eventually (due to a sub-critical section nested within the entering critical section).
Hence, once a task enters a critical section, it can not be blocked by lower priority tasks till its completion.
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42. Priority Ceiling Protocol
The Protocol:
Each semaphore S is assigned a priority ceiling C(S). It is the priority of the highest priority task that can lock S. This is a static value.
Suppose J is currently running and it wants to lock the semaphore S. J is allowed to lock S only if the priority of J is strictly higher than the priority ceiling C(S’) of the semaphore S’ where:
S’ is the semaphore with the highest priority ceiling among all the semaphores which are currently locked by jobs other than J.
In this case, J is said to blocked by the semaphore S’ (and the job currently holding S’).
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43. Priority Ceiling Protocol
The Protocol:
When J gets blocked by S’ then the priority of J is transmitted to the job that currently holds S’.
When J’ leaves a critical section guarded by S’ then it unlocks S’ and the highest priority job, if any, which is blocked by S’ is awakened.
The priority of J’ is set to the highest priority of the job that is blocked by some semaphore that J’ is still holding. If none, the priority of J’ is set to be its nominal one.
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44. Example
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45. C (S0) = ? C(S1) = ? C(S2) = ?
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46. C (S0) = P0 C(S1) = P0 C(S2) = P1
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47. t2 : J1 can not lock S2. Currently J2 is holding S2 and C(S2) = P1 and the current priority of J1 is also P1.
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48. t5 : J0 can not lock S0. Currently J2 is holding S2 and S1 and C(S1) = P0 and the current priority of J0 is also P0. The (inherited) priority of J2 is now P0.
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49. t6 : J2 unlocks S1. It awakens J0
t6 : J2 unlocks S1. It awakens J0. But J2’s (inherited) priority is now only P1 while P0 > C(S2) = P1. So J0 preempts J2 and runs to completion.
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50. t7 : J2 resumes execution with priority P1.
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51. t8 : J2 unlocks S2 and goes back to its nominal priority P2
t8 : J2 unlocks S2 and goes back to its nominal priority P2. So J1 preempts J0 and runs to completion.
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52. Two Key Properties
Under priority ceiling protocol, a job can be blocked for at most the duration of one critical section.
The priority ceiling protocol prevents deadlocks.
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53. Blocking Times Bi ----- The maximum blocking time of Ji.
Dj,k ---- The duration the critical section in Jj whose access is regulated by the semaphore Sk.
If Dj,k is 0 this means Jj does not use Sk.
Then:
Bi = max{ Dj,k | Pj < Pi, C(Sk)  Pi }
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