1. EEE 6494 Embedded Systems Design
Real-Time Scheduling
Algorithms
서강대학교 전자공학과

2. Agenda Real-Time System Classifications of Scheduling Assumption
RM (Rate Monotonic)
EDF (Earliest Deadline First)
LLF (Least Laxity First)
Shared Resources
Conclusion

3. Real-Time System What is a real-time system?
Correctness of system operation depends on temporal characteristics as well as logical/functional characteristics
Characteristics definition of each task for analyzing a real-time system
Core execution time (or computation time)
Activation time (or release time)
Deadline
A point in time by which the task must complete
Hard real-time system vs. Soft real-time system
Relative deadline vs. Absolute deadline

4. Response Time = TimeActuation – TimeSensed (from Release to Response)
A Service Release and Response
WCET (Ci)
Input/Output Latency
Interference Time
Interrupt
Dispatch
Preemption
Interference
Completion
(IO Queued)
Actuation
(IO Completion)
Input-
Latency
Dispatch-
Execution
Output-
Response Time = TimeActuation – TimeSensed
(from Release to Response)
Event
Sensed
Time

5. Real-time Scheduling Algorithms
Static/dynamic priority preemptive scheduling
Static schedulability analysis : Results used at run-time
- Good for periodic tasks but inflexible
Dynamic :
No explicit schedule, at run-time execute highest priority task first
Period driven - Rate monotonic (RM), Deadline Monotonic
Deadline driven - Earliest deadline first (EDF),
Slack driven - Least slack (LLF)
Flexible, but potentially dangerous
I Priority inversion
Shared resources – Deadlock possibility
Event-driven non-preemptive
Tasks represented by functions (event handlers)
Safe, but limited

6. Assumptions Liu and Layland assumed (in RM and EDF)
All tasks are periodic
Tasks are ready to run at their release time
Tasks are independent
: No shared resources, no synchronization
No overhead costs for preemption, scheduling or interrupt handling
Processing is fully preemptable

7. Rate Monotonic Scheduling Algorithm
Idea of RM algorithm
A lower-priority task is executing and a higher-priority task becomes available to execute, it will preempt the lower-priority task
Static scheduling
Shorter period tasks get higher priority

8. Priority : S1 > S2 > S3
Example of RM Scheduling
Tasks
Deadline (ms)
Computation Time (ms) S1
D1 = 30
C1 = 10 S2
D2 = 55
C2 = 10 S3
D3 = 60
C3 = 5
10/30+10/55+5/60 S1
time 5 15 25 35 45 55 65 75
activation S2 S3 85
Priority : S1 > S2 > S3
deadline
Preemption
S2 S1

9. Rate Monotonic Scheduling Algorithm
Schedulability Analysis( )
A set of n periodic tasks is schedulable by the RM algorithm if , where and
meaning that any task set can be scheduled by RM if , but not all task sets can be scheduled if
Ex) 10/30+10/55+5/60 p p

10. EDF Scheduling Algorithm
Idea of EDF algorithm
The scheduler reevaluates the deadlines of all tasks any time an interrupt occurs (a new task is activated or a task is finished), and allocates the resource to
the task having the earliest deadline
Dynamic scheduling
Deadline-based preemption

11. Example of EDF Scheduling
Task
Period
Relative Deadline
Computation Time S1
T1 = 30
D1 = 30
C1 = 10 S2
T2 = 40
D2 = 40
C2 = 15 S3
T3 = 50
D3 = 50
C3 = 10
10/30+15/40+10/50
activation
time 5 15 25 35 45 55 65 75
T1=30 S1 85 S2 S3
T2=40
T3=50
윤디자인연구소

12. EDF Scheduling Algorithm
Schedulability Analysis( )
A set of n periodic tasks is schedulable by the EDF algorithm if
(computation time Ci , period Ti )
meaning that any task set can be scheduled by EDF if
Ex) 10/30+15/40+10/50

13. Shared Resources Critical section Priority inversion
Program section where a shared resource is accessed
No other task can access this resource : Mutual exclusion
Priority inversion
A situation in which a higher priority job is blocked by lower priority jobs for an indefinite period of time

14. Priority : S1 > S2 > S3
Priority Inversion Protocol
priority inversion
Priority : S1 > S2 > S3
Can’t meet the deadline !!
activation S1
time 5 15 25 35 45 55 65 75 85
activation S2
time 5 15 25 35 45 55 65 75 85
activation S3
time 5 15 25 35 45 55 65 75 85
Critical section

15. Two solutions of priority inversion problem
PIP (Priority Inheritance Protocol)
PCP (Priority Ceiling Protocol)

16. PIP (Priority Inheritance Protocol)
If a task execution in a critical section blocks one or more higher priority tasks, then it temporarily inherits the highest priority of the blocked tasks
When a task exits the critical section, it resumes the original priority it had when it entered that critical section

17. Priority : S1 > S2 > S3
Example of PIP
Priority : S1 > S2 > S3
activation
priority inheritance
P(S1) P(S3) S1
time 5 15 25 35 45 55 65 75 85
activation S2
time 5 15 25 35 45 55 65 75 85
activation S3
time 5 15 25 35 45 55 65 75 85
Critical section

18. The PIP may also cause problems when more than one shared resource is used, by producing a chained blocking
Chained blocking
Execution: Task 4-> task 3 -> Task 2 -> Task1
Lowest-priority tasks execute first: may miss deadline

19. PCP (Priority Ceiling Protocol)
Solution for chained blocking
If a task execution in a critical section blocks, then it temporarily inherits the priority ceiling
The priority ceiling is equal to the highest priority of the tasks that concurrently hold or will hold that resource (Lookahead)
‘Ceiling’ may be misleading

20. Priority : S1 > S2 > S3 > S4
Another Example (PIP applied)
activation
priority inheritance
P(S2) P(S4)
priority inheritance
P(S1) P(S4) S1
time 5 15 25 35 45 55 65 75 85 95
activation S2
time 5 15 25 35 45 55 65 75 85 95
activation S3
time 5 15 25 35 45 55 65 75 85 95
activation S4
time 5 15 25 35 45 55 65 75 85 95
Critical section
Priority : S1 > S2 > S3 > S4

21. When PCP is applied Critical section activation S1 time activation S25 15 25 35 45 55 65 75 85 95
activation S2
time 5 15 25 35 45 55 65 75 85 95
activation S3
time 5 15 25 35 45 55 65 75 85 95
the highest priority(S1) is inherited S4
time 5 15 25 35 45 55 65 75 85 95
Critical section
Priority : S1 > S2 > S3 > S4

22. Schedulability Analysis( )
A set of n periodic tasks is schedulable by the EDF algorithm if (computation time Ci , period Ti ) And schedulable by the EDF based PCP algorithm if
We denote this worst case blocking time of a job in task ti by Bi
Ex) 10/60+10/75+5/75+25/95+25/75

23. Conclusion
The scheduling of jobs with hard deadlines is an important area in real-time systems
The choice of scheduling algorithm is very important in real-time systems