This document summarizes a seminar presentation on scheduling fixed-priority tasks with preemption thresholds. The presentation covered scheduling basics, real-time scheduling goals, classification of scheduling algorithms, motivation for using fixed-priority scheduling with preemption thresholds (FPTS), preemptive vs. non-preemptive scheduling, the concept of limited preemptive scheduling with preemption thresholds, an example to motivate FPTS, schedulability analysis including worst-case response time calculation, critical instant, level-1 active period, algorithms to find optimal preemption thresholds and optimal priorities/thresholds.

1. Seminar System Architecture and Networking
(2IN95)
Scheduling Fixed-Priority
Tasks with Preemption
Threshold
Yun Wang Manas Saksena
Department of CSC Concordia University
Presented by
Deepak Vedha Raj Sudhakar (0925172)
01/12/2014

2. Agenda
➢ Scheduling Basics
➢ Goal of Real time Scheduling
➢ Classification of Scheduling algorithms
➢ Motivation for FPTS
➢ Preemptive Vs Non Preemptive Scheduling
➢ Limited Preemptive Scheduling with Preemption Thresholds(FPTS)
➢ Motivating example
➢ Schedulability Analysis
➢ Worst Case Response time
➢ Critical Instant
➢ Level - I active period
➢ Algorithms to find optimal thresholds
➢ Algorithm to find optimal priorities and thresholds
➢ Conclusion
2

3. Scheduling Basics
System Resources
➢ CPU time
➢ Memory
➢ I/O (access to devices)
➢ Network resources
➢ Energy
S
C
H
E
D
U
L
E
R
USER 1
USER 2
USER 3
USER N
.
.
3

4. Goal of Real time Scheduling
➢ Deadlines must be met
➢ Tasks are of different importance ⇒ No fairness
➢ Short response times are not sufficient, guaranteed response
times are needed.
➢ Parameters (Period , Deadline)
4

5. Classification of Real time Scheduling
5
FPPS FPNS FPDS , FPTS

6. Agenda
➢ Scheduling Basics
➢ Goal of Real time Scheduling
➢ Classification of Scheduling algorithms
➢ Motivation for FPTS
➢ Preemptive Vs Non Preemptive Scheduling
➢ Limited Preemptive Scheduling with Preemption Thresholds(FPTS)
➢ Motivating example
➢ Schedulability Analysis
➢ Worst Case Response time
➢ Critical Instant
➢ Level - I active period
➢ Algorithms to find optimal thresholds
➢ Algorithm to find optimal priorities and thresholds
➢ Conclusion
6

7. Priority-based Real-time Scheduling Assumptions
➢ All tasks are periodic (periodic task model)
➢ Tasks are preemptive at any time
➢ Preemption costs nothing
➢ Context switch costs nothing
➢ Scheduling decision costs nothing
➢ Tasks are independent
➢ Resources (except CPU) are sufficient
Costly Assumptions
7

8. Hidden Costs
➢ Scheduling costs
➢ Pipeline costs
➢ Cache-related costs
➢ Bus related costs
WCET( i
)∝ Total number of preemptions
WCET( i
)∝ Point of preemption
8

9. Preemptive Vs Non Preemptive
9
Preemptive Non preemptive
Better Schedulability ratio
(Least Upper bound = 69%)
Simpler WCET analysis
No Mutual exclusion problem
Stack Sharing possible
Minimize I/O delay and jitter

10. Requirements for resource constrained systems
➢ Better Schedulability ( FPPS)
➢ Reduced Stack requirements (FPNS)
➢ Reduced arbitrary preemptions (FPNS)
Solution : Limited preemptive Fixed Priority Scheduling
10

11. FPTS
11
θi
>= πi
θi
= πi
-> FPPS
θi
= πi
(max) -> FPNS

12. FPPS - Not Schedulable
12
Task Ci Ti Di Pi WCRT
T1 20 70 50 3 20
T2 20 80 80 2 40
T3 35 200 100 1 115

13. FPNS - Not Schedulable
13
Task Ci Ti Di Pi WCRT
T1 20 70 50 3 55
T2 20 80 80 2 75
T3 35 200 100 1 75

14. FPTS - Schedulable
14
Task Ci Ti Di Pi θi
WCRT
T1 20 70 50 3 3 40
T2 20 80 80 2 3 75
T3 35 200 100 1 2 95

15. Agenda
➢ Scheduling Basics
➢ Goal of Real time Scheduling
➢ Classification of Scheduling algorithms
➢ Motivation for FPTS
➢ Preemptive Vs Non Preemptive Scheduling
➢ Limited Preemptive Scheduling with Preemption Thresholds(FPTS)
➢ Motivating example
➢ Schedulability Analysis
➢ Worst Case Response time
➢ Critical Instant
➢ Level - I active period
➢ Algorithms to find optimal thresholds
➢ Algorithm to find optimal priorities and thresholds
➢ Conclusion
15

16. Schedulability Test
Task set is Schedulable if all tasks meet their deadlines
Condition : WCRT(Ti)<= D(i)
Question: How to determine WCRT(Ti)?
16

17. Response Time
Question: How to determine WCRT(Ti)?
Solution: Identify Critical Instant of task(Ti)
17[1] “Fig 8.7:Hard Real-Time Computing Systems by Giorgio C. Buttazzo”
Response time = ←------------Blocking time--------------------->+<------------------ Interference Time ------------->
Ph
= Priority
θi
= Threshold

18. Task Ci Ti Di Pi θi
T1 20 70 50 3 3
T2 20 80 80 2 3
T3 35 200 100 1 2
Critical Instant
Critical Instant results in
Maximum block time + Maximum interference time
18
Critical instant(T3) = Time when task T3 arrives at the same time as task T1 and task T2
Critical instant(T2) = Time when task T2 arrives at the same time as task T1 and task T3 just
started executing prior to arrival of task T2.
Critical instant(T1) = Time when task T3 just started executing prior to arrival of task T1

19. Critical Instant of Task 3
19
Question:
Does the first task instance
after critical instant
correspond to the worst case
response time of the task?
Answer : Not always

20. Self Pushing Mechanism
20
WCRT(T3) does not occur at first instance.
[1] “Fig 8.7:Hard Real-Time Computing Systems by Giorgio C. Buttazzo”

21. Level-I Active period
Question: How many task instances should I consider after
critical instant?
Answer: All instances in the Level-I Active period should be
considered
21

22. Level-I Active period
Level-I active period : Interval [a,b) for which level -I pending
workload (>=Pi) is positive. Null at a and b.
22
Level-I active
period
At t= 0-Δ , W1
p
(0-Δ) = 0
At t= 0 , W1
p
(0) > 0
At t= 10 , W1
p
(0) > 0
At t= 20 , W1
p
(0) > 0
At t= 40 , W1
p
(0) = 0

23. Schedulability test (Recap)
For all tasks (i=1 to n) do
Step 1 : Identify critical instant of task(i)
Step 2: Find Level-I active period of task(i)
Step 3: Determine WCRT(i)
Step 4: Check WCRT(i)<= D(i)
23

24. WCRT(T1)
Level-I active period
24
L1
(0) = C1
+ B1
= 20 + 20 = 40
L1
(1) = B1
+∑h:Ph>=1
⌈L1
(0)/Th
⌉ *Ch
= 20 + ⌈ 40/70⌉ * 20
= 40
L1
(0) = L1
(1) - Stop
WCRT(T1) = (finish time) F1
- Arrival time
= 40 - 0 = 40
Level-I
active
period

25. WCRT(T2)
25
Level-I active period
L2
(0) = C2
+ B2
= 20+ 35 = 55
L2
(1) = B2
+∑h:Ph>=2
⌈L2
(0)/Th
⌉ *Ch
= 35 + ⌈ 55/70⌉ * 20 + ⌈ 55/80⌉ * 20
= 75
L2
(2) = B2
+∑h:Ph>=2
⌈L2
(1)/Th
⌉ *Ch
= 35 + ⌈ 75/70⌉ * 20 + ⌈ 75/80⌉ * 20
= 95
L2
(3) = B2
+∑h:Ph>=2
⌈L2
(2)/Th
⌉ *Ch
= 35 + ⌈ 95/70⌉ * 20 + ⌈ 95/80⌉ * 20
= 115
L2
(4) = B2
+∑h:Ph>=2
⌈L2
(3)/Th
⌉ *Ch
= 35 + ⌈ 115/70⌉ * 20 + ⌈ 115/80⌉ * 20
= 115
L2
(3) = L2
(4) - Stop
WCRT(T2) = max{ RT(instance1) ,RT(instance2) }
= max { 75 , 35} = 75

26. WCRT(T3)
26
Level-I active period
Level-I active period
interval = [0 , 115)
WCRT(T3) = 95

27. Formula : Worst case response time
Computing Start time
Computing Finish time
Computing Worst case Response time
27

28. Agenda
➢ Scheduling Basics
➢ Goal of Real time Scheduling
➢ Classification of Scheduling algorithms
➢ Motivation for FPTS
➢ Preemptive Vs Non Preemptive Scheduling
➢ Limited Preemptive Scheduling with Preemption Thresholds(FPTS)
➢ Motivating example
➢ Schedulability Analysis
➢ Worst Case Response time
➢ Critical Instant
➢ Level - I active period
➢ Algorithm to find optimal thresholds
➢ Algorithm to find optimal priorities and thresholds
➢ Conclusion
28

29. Algorithm : Optimal Minimum Threshold assignment
Goal : Find minimum threshold assignment for a task set if one
exists
29
Algorithm
Taskset T = { Ci Ti Di Pi),
∀ i
∊ T
Task set Feasible or
not?
Threshold θi
∀ i
∊ T

30. Algorithm : Flowchart
30
Complexity : O
(n2
)

31. Algorithm : Example
Start from lowest priority task - T3
31
Task Ci Ti Di Pi θi
WCRT
T1 20 70 50 3 3 20
T2 20 80 80 2 2 40
T3 35 200 100 1 1 115

32. Algorithm : Example
Increase threshold of task T3 from 1 to 2.
Meets deadline , assign threshold θ3
= 2
32
Task Ci Ti Di Pi θi
WCRT
T1 20 70 50 3 3 20
T2 20 80 80 2 2 95
T3 35 200 100 1 2 95

33. Algorithm : Example
Increase threshold of task T2 from 2 to 3.
Meets deadline , assign threshold θ2
= 3
33
Task Ci Ti Di Pi θi
WCRT
T1 20 70 50 3 3 40
T2 20 80 80 2 3 75
T3 35 200 100 1 2 95

34. Algorithm : Example
Meets deadline , assign threshold θ1
= 3
34
Task Ci Ti Di Pi θi
WCRT
T1 20 70 50 3 3 40
T2 20 80 80 2 3 75
T3 35 200 100 1 2 95

35. Agenda
➢ Scheduling Basics
➢ Goal of Real time Scheduling
➢ Classification of Scheduling algorithms
➢ Motivation for FPTS
➢ Preemptive Vs Non Preemptive Scheduling
➢ Limited Preemptive Scheduling with Preemption Thresholds(FPTS)
➢ Motivating example
➢ Schedulability Analysis
➢ Worst Case Response time
➢ Critical Instant
➢ Level - I active period
➢ Algorithm to find optimal thresholds
➢ Algorithm to find optimal priorities and thresholds
➢ Conclusion
35

36. Algorithm : Optimal Priority and Threshold
assignment
Goal : Find optimal priority and minimum threshold assignment
for a task set if one exists.
36
Algorithm
Taskset T = { Ci Ti Di),
∀ i
∊ T
Task set Feasible or
not?
Priority Pi
∀ i
∊ T
Threshold θi
∀ i
∊ T

37. Algorithm : Optimal Priority and Threshold
assignment
37

38. Algorithm : Optimal Priority and Threshold
assignment
38

39. Algorithm : Example
TaskSet T = {T 1 , T2 , T3} Priority Ordered TaskSet = {}
Priority P = { 1, 2 , 3 }
39
Task Ci Ti Di Pi θi
WCRT
T1 20 70 50
T2 20 80 80
T3 35 200 100

40. Algorithm : Example
TaskSet T = {T 1 , T2 , T3} Priority Ordered TaskSet = {}
Priority P = { 1, 2 , 3 }
40
Task Ci Ti Di Pi θi
WCRT Lateness
WCRT (i)- Di
T1 20 70 50 1 55 5
T2 20 80 80
T3 35 200 100

41. Algorithm : Example
TaskSet T = {T 1 , T2 , T3} Priority Ordered TaskSet = {}
Priority P = { 1, 2 , 3 }
41
Task Ci Ti Di Pi θi
WCRT Lateness
WCRT (i)- Di
T1 20 70 50
T2 20 80 80 1 95 15
T3 35 200 100

42. Algorithm : Example
TaskSet T = {T 1 , T2 , T3} Priority Ordered TaskSet = {}
Priority P = { 1, 2 , 3 }
Sorted List = {T 1 , T2 , T3} (Ascending Lateness - { 5, 15 , 15} )
Refine (Sorted List) = {T2,T3}
// prune infeasible path ( T1 -> P1
= 1 , θ1
= 3)
42
Task Ci Ti Di Pi θi
WCRT Lateness
WCRT (i)- Di
T1 20 70 50
T2 20 80 80
T3 35 200 100 1 115 15

43. Algorithm : Example
TaskSet T = {T 1 , T3} Priority Ordered TaskSet = { T2(1)}
Priority P = { 2 , 3 }
43
Task Ci Ti Di Pi θi
WCRT Lateness
WCRT (i)- Di
T1 20 70 50 2 55 5
T3 35 200 100

44. Algorithm : Example
TaskSet T = {T 1 , T3} Priority Ordered TaskSet = { T2(1)}
Priority P = { 2 , 3 }
44
Task Ci Ti Di Pi θi
WCRT Lateness
WCRT (i)- Di
T1 20 70 50
T3 35 200 100 2 55 -45

45. Algorithm : Example
TaskSet T = {T1} Priority Ordered TaskSet = { T3(2),T2(1)}
Priority P = { 3 }
45
Task Ci Ti Di Pi θi
WCRT Lateness
WCRT (i)- Di
T3 35 200 100

46. Algorithm : Example
TaskSet T = {T1} Priority Ordered TaskSet = { T1(2),T2(1)}
Priority P = { 3 }
46
Task Ci Ti Di Pi θi
WCRT Lateness
WCRT (i)- Di
T1 20 70 50 3 20 30

47. Algorithm : Optimal Priority ordering
TaskSet T = {} Priority Ordered TaskSet = { T1(3),T3(2),T2(1) }
Priority P = {}
47
Task Ci Ti Di Pi θi
WCRT
T1 20 70 50 3
T2 20 80 80 1
T3 35 200 100 2

48. Algorithm : Optimal Priority and Threshold
assignment
48
1 {T1(3), T3(2), T2(1)}
2 {T1(1), T3(2), T2(3)}
3 {T1(1), T2(2) , T3(3)}
4 {T1(3), T2(2), T3(1)}
5 {T1(2), T2(3), T3(1)}
6 {T1(2), T2(1), T3(3)}

49. Missing Information
➢ Next Priority ordering selection information missing.
➢ Algorithmic Complexity not mentioned. Exponential
➢ Task ordering when heuristics value matches?
➢ Experimental Results showing advantages of FPTS missing
➢ Minimal threshold assignment algorithm does not limit the
preemptions
49

50. Agenda
➢ Scheduling Basics
➢ Goal of Real time Scheduling
➢ Classification of Scheduling algorithms
➢ Motivation for FPTS
➢ Preemptive Vs Non Preemptive Scheduling
➢ Limited Preemptive Scheduling with Preemption Thresholds(FPTS)
➢ Motivating example
➢ Schedulability Analysis
➢ Worst Case Response time
➢ Critical Instant
➢ Level - I active period
➢ Algorithm to find optimal thresholds
➢ Algorithm to find optimal priorities and thresholds
➢ Conclusion
50

51. Conclusion
➢ Limitation of Preemptions
➢ Why Limited Fixed priority scheduling techniques?
➢ How to perform Schedulability test by determining WCRT?
➢ Find minimum thresholds given priorities of the task set
➢ Find optimal priorities and feasible threshold assignment for
task set
51

52. References
1. Hard Real-Time Computing Systems by Giorgio C. Buttazzo
2. Y. Wang and M. Saksena. “Scheduling fixed-priority tasks with preemption threshold”. In Proc. 6th IEEE
Real-Time Computing Systems and Applications (RTCSA), pages 328–335, Dec. 1999.
3. Reinder J. Bril and Johan J. Lukkien Wim F.J. Verhaegh “Worst-case response time analysis of real-time
tasks under fixed-priority scheduling with deferred preemption revisited “ , TU/e, CS-Report 06-34,
December 2006
4. K. W. Tindell , A. Burns , A. J. Wellings, An extendible approach for analyzing fixed priority hard real-time
tasks, Real-Time Systems, v.6 n.2, p.133-151, March 1994
5. Buttazzo, G.C. ; Scuola Superiore Sant'anna, Pisa, Italy ; Bertogna, M. ; Gang Yao , Limited Preemptive
Scheduling for Real-Time Systems. A Survey . In Industrial Informatics, I,05 March 2012
6. N. Audsley. Optimal priority assignment and feasibility of static priority tasks with arbitrary start times.
Technical Report YCS 164, Department of Computer Science, University of York, England, Dec. 1999
52

53. Thank You for your Attention
Any Questions ?
53

54. Questions
1. Why is the worst case response time calculated as the maximum response time of the jobs in the Level-i active period?
2. How do you determine / measure the least upper bound utilisation schedulability criteria for FPTS?
3. What is the additional costs incurred by optimal priority and preemption threshold assignment algorithm? How does it
compare to the preemption costs incurred by FPPS?
4. Is the optimal priority and preemption threshold assignment done in static or dynamic manner?
5. How efficient it is for resource constrained set up ?
6. What is the difference between level-i active and level-i busy period?
7. FPTS increases schedulability of task set by combining FPPS & FPNS, but the worst case response time of some of
the tasks are increased (compared to FPDS) although they meet the deadlines.Does it have any impact on the
system?
8. What is the run-time complexity of the proposed algorithms based on task set (n)?
54

55. What to follow ?
Scalable real time system design using Preemption Thresholds
by Shashidhar B.L
55