1. An On-line Approach to Reduce Delay Variations on Real-Time Operating Systems
Shengyan Hong

2. Delay Variation What is delay variation?
Difference between the max delay and the min delay of a real-time task
WCRTi (BCRTi): the worst (best) case response time of the task i

3. Delay Variation Why interested in reducing delay variation?
It degrades control system performance
Sources of delay variations
Task preemptions
Variations in task workload
Perturbations in physical environment
A 3DOF helicopter containing 4 periodic tasks
Position tasks: elevation, pitch and travel
Speed task

4. Task Model Original Task Model (Ci, Di, Pi) IMF Task Model
Ci: task execution time, Di: task deadline, Pi: task period
IMF Task Model
Initial, Mandatory and Final subtasks
ADVR Task Model
Assume Cif=Cii
Final subtask (Cif, Difnew, Pifnew=Pi/Mi)
Mandatory subtask (Cimnew, Dimnew, Pi)
Maximize Mi as much as possible
where Ci*, Di*, Oi* are the execution time, relative deadline and offset of the corresponding subtasks

5. Problem Formulation Minimize delay variations of final subtasks
Dif: the deadline of the final subtask of task i, Cif: the execution time of the final subtask of task i
(Dif-Cif): the upper bound of delay variation
N: task number of the task set
Wi: a weighting factor that reflects the criticality of task i
Such that
task set is schedulable under EDF, and
subtask execution dependencies are observed

6. ADVR Heuristic
Search an initial solution with optimal model transformation
Split original task period
Repeatedly search for a better solution based on the previous solution
Find smaller deadlines of final subtasks
Update the deadlines of mandatory subtasks
If ADVR has not converged, return to the previous step
Achieve fast convergence
Time complexity is pseudo polynomial

7. What is S.Ha.R.K.? S.Ha.R.K. is an Open Source Real-time Kernel
It Supports:
Provide primitives to create, activate and run real-time tasks using scheduling algorithms.
Share data among tasks using resource reservation algorithms
Device drivers for most common hardware
ADVR implemented in S.Ha.R.K.
Task model modification
Scheduler internal data structure and algorithm modification
Application modification

8. Solutions Found Experimental Evaluation:
Compare ADVR with TBB, DRB
Part 1: tested on 9000 randomly generated task sets
Part 2: a case study of adaptive delay variation reduction
9000 randomly generated task sets each consisting of 5 tasks
Utilization: fraction of time that the processor is working
ADVR performs best
ADVR founds the solutions of all the task sets

9. Total Average Delay Variation
ADVR performs best
Difference between ADVR and the other methods increases with the increasing of utilization levels

10. Average Execution Time
ADVR and DRB have comparable execution speed
DRV is a greedy algorithm, whose convergence is fast

11. Iteration Number of ADVR
Util.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Avg. 13 12 14 20 16 19 23 32
Max 41 29 25 70 87 94 80 83
121
ADVR is suitable for on-line use
ADVR finds an optimal solution for most of task sets within 50 iterations

12. Case Study: 3DOF Helicopter
Implemented in S.Ha.R.K.
Compare results by ADVR with original Delay Variations, and those by TBB and DRB
The smaller DV, the better the method is.
When workload changes, see which method can adapt to it.
Task Name
Decomp.
Exec. Time
Deadline
Period
Speed
Yes
5000
27000
Elevation
8000
30000
32000
Pitch No
10000
45000
50000
Travel
13000
60000
70000
Task Name
Decomp.
Exec. Time
Deadline
Period
Speed
Yes
5000
27000
Elevation
8000
30000
32000
Pitch No
10000
45000
500000
Travel
13000
60000
70000
Task Name
Delay Variations of Orig/DRB/TBB/ADVR
Speed
33.33/41.48/Fail/ 7.7
Elevation
28.13/31.25/Fail/ 0.87
Pitch
44.00/34.00/Fail/22.09
Travel
48.57/32.86/Fail/39.86
Task Name
Delay Variations of Orig/DRB/TBB/ADVR
Speed
33.33/41.48/Fail/ 2.96
Elevation
28.13/31.25/Fail/ 0.08
Pitch
4.40/ 3.40/Fail/06.28
Travel
48.57/32.86/Fail/15.57
Task Name
Delay Variations of Orig/DRB/TBB/ADVR
Speed
33.33/41.48/Fail/ 2.96
Elevation
28.13/31.25/Fail/ 0.08
Pitch
44.00/34.00/Fail/62.80
Travel
48.57/32.86/Fail/15.57

13. Questions?