1. Risat Pathan Chalmers University of Technology, Sweden
Improving the Schedulability and Quality of Service for Federated Scheduling of Parallel Mixed-Criticality Tasks on Multiprocessors
Risat Pathan
Chalmers University of Technology, Sweden

2. Outline Background State-of-the-art and its limitations
Improving Schedulability
Improving QoS
Results and Conclusion
J. Li, D. Ferry, S. Ahuja, K. Agrawal, C. Gill, and C. Lu. Mixed-criticality federated scheduling for parallel real-time tasks. In Proc. of RTAS, April 2016.
J. Li, J. J. Chen, K. Agrawal, C. Lu, C. Gill, and A. Saifullah. Mixed-criticality federated scheduling for parallel real-time tasks. Real-Time Systems, Sep 2017.

3. Background: Parallel non-MC Tasks (DAG)
𝐶 𝐴 =3
𝐶 𝐵 =4
𝐶 𝐷 =3
𝐶 𝑐 =2
𝐶=10
A sequential task with
WCET C = 10
Period T = 20
A parallel task with
Total work C=12
Length of longest path L=10
Period T=20

4. Background: Federated Scheduling of non-MC parallel tasks
Phase 1: Assigning processors to the tasks Phase 2: Scheduling Algorithm
Each task is either a heavy task or a light task
Each heavy task is assigned a number of dedicated processors
Nodes of each heavy task are scheduled using some greedy scheduler only on its dedicated processors
All the light tasks are assigned to the remaining (shared) processors
Light tasks are executed sequentially
Partitioned scheduling of sequential tasks
A heavy task
Total work C=24
Period T=20
Utilization U=1.2
𝐶 𝐴 =3
𝐶 𝐵 =8
𝐶 𝐷 =3
𝐶 𝑐 =10
𝐶 𝐵 =4
𝐶 𝑐 =2
A light task
Total work C=12
Utilization U=0.6

5. Example: Federated Scheduling of non-MC parallel tasks5 10 20 30 5 10 3 14 1 7 3 2 1
C=25 T =100 U=0.25
C=50 T =40 U=1.25
Light Task
Heavy Task
C=8 T=16 U=0.5
C=60 T =30 U=2.0
Light Task
Heavy Task
M1 = 3
Analysis
M2 = 4
Analysis
M3 = 1
Analysis
Sched Test: If M1+M2+M3 <=P, then all deadlines are met.
where P=# of processors

6. Parallel Mixed-Critical (MC) Tasks
Dual-Criticality System
Each task is either a high (HI) or a low (LO) critical task
𝐶 𝐴 =3
𝐶 𝐵 =4
𝐶 𝐷 =3
𝐶 𝑐 =2
𝐶𝑂 𝐵 =8
𝐶𝑂 𝑐 =6
A parallel MC task with
Total work CN=12
Length (longest path) LN=10
Period T=15
𝐶 𝑁 =10 , 𝐶 𝑂 =12
CO=20
LO=14
A sequential MC task with
WCET CN = CO=12
Period T = 20
Nominal WCET
Overloaded WCET
Overloaded Work
and critical path length
Nominal work and
critical path length

7. MC Parallel Task Model
We consider n implicit-deadline parallel MC sporadic tasks
Task i  (Zi, Ti, Ci, Li) where Zi  {LO, HI} and Ti= period (also deadline)
If Zi =HI, then Ci = <CN , CO> where CN ≤ CO
Li = <LN , LO> where LN ≤ LO
If Zi =LO, then Ci = CN and Li=LN
Each task is also assigned a virtual deadline Vi

8. Federated Scheduling of MC tasks
Phase 1: Assigning processors to MC tasks
Phase 2: Runtime MC scheduling

9. States/Criticality Behaviors
Typical State
Critical State
Both LO and HI-crit tasks execute
No task overrun its virtual deadline
Only HI-crit tasks execute
Task do not overrun LiHI and CiHI
starts at time t
t+s
Some task does not signal completion by its virtual deadline
STATE SWITCHES AT (t+s)
LO-crit tasks are dropped at time (t+s) to provide more processors to high critical tasks

10. Example: Processors Assignment to Tasks
(Federated Scheduling of MC tasks) 5 10 20 3 14 1 7 30 5 10 3 2 1
UN=0.25
Light, Low Crit
UN= UO=0.5
UN=1.25
Light, High Crit
Heavy, Low Crit
UN= UO=2.0
Heavy, High Crit
MN =2
MO =0
Analysis
MN =3
MO =8
Analysis
MN =1
MO =1
Analysis
Each task i is also assigned its virtual deadline Vi

11. Federated MC Scheduling (Runtime)
The system starts in typical state
All the light MC tasks execute on Mlight processors
Partitioned MC scheduling of sequential tasks
Each heavy task i executes on MiN dedicated processors based on greedy scheduling
If some task does not complete by its virtual deadline, then state switches to critical state
The heavy task i now executes on MiO dedicated processors
The additional (MiO-MiN) processors are taken by dropping some LO-criticality tasks

12. Schedulability Test Consider P=8 Processors
State-of-the-art Test: Federated Scheduling of MC tasks
Consider P=8 Processors
Σ MN=2+3+1=6 (Success in Typical State)
Σ MO=0+8+1=9 (Failure in Critical State) 5 10 20 3 14 1 7 30 5 10 3 2 1
Light Low Crit
Light High Crit
Heavy Low Crit
Heavy High Crit
MN =2
MO =0
Analysis
MN =3
MO =8
Analysis
MN =1
MO =1
Analysis
Schedulability Test
If Σ MN <= P, then all the deadlines are met in typical state
If Σ MO <= P, then all the deadlines are met in critical state

13. State-of-the-art Test: Federated Scheduling of MC tasks
Consider P=8 processors
Σ MN=2+3+1=6 (Success in Typical State)
Σ MO=0+8+1=9 (Failure in Critical State) 5 10 20 3 14 1 7 30 5 10 3 2 1
Light Low Crit
Light High Crit
Heavy Low Crit
Heavy High Crit
MN =2
MO =0
Analysis
MN =3
MO =8
Analysis
MN =1
MO =1
Analysis
Do we have some other assignment of processors such that the task set is schedulable?
Schedulability Test
If Σ MN <= P, then all the deadlines are met in typical state
If Σ MO <= P, then all the deadlines are met in critical state

14. Improving the Schedulability and Quality of Service for Federated Scheduling of Parallel Mixed-Criticality Tasks on Multiprocessors

15. The main contribution
A new schedulability test for each heavy MC task i is proposed
TEST(MN, MO, i) = True and False
For MN=1 to P
For MO=1 to P
if TEST(MN, MO, i)==TRUE
“Valid alternative (MN, MO) for i”
We select one (MN, MO) form all the alternatives such that the overall task set is schedulable

16. Schedulability Test Consider P=8 processors Σ MN=2+4+1=7 (Success)
Improving Schedulability: Federated Scheduling of MC tasks
Consider P=8 processors
Σ MN=2+4+1=7 (Success)
Σ MO=0+6+1=7 (Success)
Consider P=8 processors
Σ MN=2+3+1=6 (Success)
Σ MO=0+8+1=9 (Failure)
Consider P=8 processors
Σ MN=2+3+1=6 (Success)
Σ MO=0+8+1=9 (Failure) 5 10 20 3 14 1 7 30 5 10 3 2 1
Light Low Crit
Light High Crit
Heavy Low Crit
Heavy High Crit
MN =2
MO =0
Analysis
MN =3
MO =8
Analysis
MN =1
MO =1
Analysis
MN =4
MO =6
Schedulability Test
If Σ MN <= P, then typical ok
If Σ MO <= P, then critical ok

17. Schedulability Test Consider P=8 processors Consider P=8 processors
Improving QoS: Federated Scheduling of MC tasks
Although schedulable, the low-crit heavy task is dropped.
Do we have some other assignment of processors to the heavy tasks such that the LO-crit task is not dropped?
Consider P=8 processors
Σ MN=2+4+1=7 (Success)
Σ MO=0+6+1=7 (Success)
Consider P=8 processors
Σ MN=2+5+1=8 (Success)
Σ MO=2+5+1=8 (Success) 5 10 20 3 14 1 7 30 5 10 3 2 1
Light Low Crit
Light High Crit
Heavy Low Crit
Heavy High Crit
LO Critical (Heavy) High Critical (Heavy) LO and HI critical (Light)
MN =2
MO =0
Analysis
MN =3
MO =8
Analysis
MN =1
MO =1
Analysis
MN =4
MO =6
Schedulability Test
If Σ MN <= P, then typical ok
If Σ MO <= P, then critical ok
MN =2
MO =2
MN =5
MO =5

18. Other Contributions
Each task may have O(P) possible ways of assigning processors (MN, MO)
N tasks may have O(PN) possible ways of selecting the alternative
A dynamic programming algorithm is proposed to find the allocation of the processors to the tasks in polynomial time
There may be multiple valid ways to allocate the processors to the tasks
By selecting the allocation that requires the minimum number of processors during the critical state, we see that some LO crit tasks are not dropped.
An ILP is formulated to maximize the number of LO-crit taskshat are never dropped
Simulation shows better QoS w.r.t. the state of the art

19. Simulation Randomly generated task sets are evaluated
Our-MCF test are compared with MCFS-Improve [RTAS16, RTJ17] test

20. Acceptance Ratio, M=16

21. Acceptance Ratio, M=16, 32, 64, 128

22. QoS metric: Average fraction of LO-crit tasks that are never dropped
For each schedulable task set,
The fraction of LO-crit tasks that are never dropped is computed
For example, if 2 out of 10 LO-crit tasks are never dropped, then this fraction is 20%
Metric: Average fraction of LO-crit tasks that are never dropped

23. QoS

24. Conclusion
A new way to assign the processors to MC parallel tasks for federated scheduling
Improves the schedulability and the QoS of the system
Future work: Greedy vs. other scheduler

25. Thank You risat@chalmers.se

26. Weighted Schedulability