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

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

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

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

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

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

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

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

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

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

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

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

Questions?