On Schedulability and Time Composability of Data Aggregation Networks

1. On Schedulability andTime Composability ofData Aggregation Networks Fatemeh Saremi*, Praveen Jayachandran†, Forrest Iandola*, Md Yusuf Sarwar Uddin*, Tarek Abdelzaher*, and Aylin Yener‡ * Department of Computer Science, University of Illinois, Urbana, IL † IBM Research, India ‡ Department of Electrical Engineering, Pennsylvania State University, University Park, PA Email: saremi1@illinois.edu, prjayach@in.ibm.com, {iandola1, mduddin2, zaher}@illinois.edu, yener@ee.psu.edu

2. Motivation Aircraft radar detects presence of the submarine Ship receives observation data and fuses it with a reference database to identify submarine Coordination of input from multiple sonars is used to track the submarine F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

3. Related Work Real-time Calculus [Thiele et al.] 2000 Real-time Calculus [Jonsson et al.] 2008 Holistic Analysis [Tindell et al.] 1994 [Kao et al.] Per-stage deadlines 1997 [Zhang et al.] Per-stage deadlines 2005 Delay Composition Algebra [Jayachndran et al.] 2009 [Xue et al.] Constructing the complete schedule 1993 [Fohler et al.] Constructing the complete schedule 1997 Holistic Analysis [Pellizzoni et al.] 2005 [Koubaa et al.] Comparing Real-time Calculus & Holistic 2004 CWS [Li et al.] 2008 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

4. Aggregation Model • Offi: the (maximum) offset from time zero at which a job Jiof workflow Fiarrives • Ci,j: worst-case processing time of Ji on resource j • Di: end-to-end deadline of Ji • Each job of every workflow is assigned a priority • "i<=k" means Priority(i)<=Priority(k) • Low number == high priority • The relative priority of each job remains the same across all the stages on which it executes • MERGE Semantics: A job does not become eligible to execute on the merge-stage until all pipelines have finished processing it. F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

5. Jl: job under consideration Jh: higher priority job Jl1, Jl2, Jl3, Jl4: lower priority jobs Non-preemptive scheduling Intuition Workflow graph and execution trace for seemingly candidate aggregation composition approach F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

6. End-to-End Delay (𝐽l) = 88 - ɛDelay Bound (𝐽l) = ? • Using Delay Composition Theorem for Pipelines E2E Delay (𝐽l) = 88 - ɛ > Delay Bound (𝐽l) = 80 + 3ɛ !? F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

7. Ji’: job under consideration Ji : higher priority job Jl1, Jl2, Jl3: lower priority jobs Non-preemptive scheduling Revisit Event Along one branch, 𝐽𝑖′ completes execution and arrives ahead of 𝐽𝑖 to the merge-stage Along the other branch, 𝐽𝑖 delays job 𝐽𝑖′ and arrives ahead of it to the merge-stage • Due to reversal in the arrival order, it is possible for 𝐽𝑖 to again delay 𝐽𝑖′ at a downstream stage F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

8. Non-preemptive Delay Composition Theorem for Aggregation Workflows Under a non-preemptive scheduling policy that assigns the same priority across all stages for each job, the worst-case end-to-end delay of a job of work flow 𝐹𝑘 in an aggregation tree is bounded as, where Offi is the offset of job Ji from time zero. F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

9. Delay Bound Proof Sketch • By induction on the number of revisit events F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

10. Preemptive Delay Composition Theorem for Aggregation Workflows Assuming a preemptive scheduling policy that assigns the same priority across all stages for each job, the worst-case end-to-end delay of a job of workflow 𝐹𝑘 in an aggregation tree is bounded as, where Offi is the offset of job Ji from time zero. F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

11. Schedulability Analysis • The schedulability of a job 𝐽𝑘of an aggregation workflow can be determined by analyzing the schedulability of an equivalenthypothetical uniprocessor constructed by reduction rules obtained based on the composition theorem. The reduction process on an aggregation tree F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

12. Evaluation • How different parameters can affect the performance of the Aggregation Delay Composition framework? • How accurately are the worst-case e2e delays estimated? • How efficiently are system resources utilized? • With respect to the following system and loadparameters • The number of stages • The number of tasks • Job resolution • Deadline ratio • Offset resolution F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

13. End-to-End Delay Bound Accuracyw.r.t. the Number of Stages Less Pessimistic More Pessimistic Under preemptive scheduling, 6% and 24% improvement respectively at 7 and 63 stages Under non-preemptive scheduling, 14% and 34% improvement respectively at 7 and 63 stages F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

14. End-to-End Delay Bound Accuracyw.r.t. the Number of Tasks Less Pessimistic More Pessimistic Under both non-preemptive and preemptive scheduling, more than 20% improvement when the number of jobs over 80 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

15. Resource Utilizationw.r.t. Job Resolution Many small jobs A few big jobs Consistent improvement under both non-preemptive and preemptive scheduling (The drop in DCA under non-preemptive is due to the blocking delay component becoming significantly large as job sizes increase) F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

16. Resource Utilizationw.r.t. Deadline Ratio Homogenous deadlines Wide range of deadlines Consistent improvement under both non-preemptive and preemptive scheduling (The drop in both DCA and Holistic under non-preemptive scheduling is due to larger blocking delays being imposed on higher priority jobs as the variability in deadlines increases) F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

17. Resource Utilizationw.r.t. Offset Resolution Logarithmic Scale Small offsets Wide range of offsets Improvement when offset resolution below 100 times of the minimum job deadline F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

18. Conclusions • Investigated timing properties and delay composability of multi-criticality distributed workload in multisensor data aggregation systems • Elaborated on why it is challenging to analyze such systems • Proposed a theoretical framework to analyze schedulability of multisensor data aggregation systems characterized by the “MERGE” primitive under non-preemptive as well as preemptive scheduling • Confirmed by extensive simulation results that our theoretical framework is significantly more accurate than traditional analysis techniques and effectively utilizes distributed resources, and that it is especially beneficial for large systems. F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks

19. Thank you. Questions … ? F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks