1. On Schedulability and Time Composability of Data 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 2 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks7/11/2012 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

3. Related Work 3 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks7/11/2012 CWS [Li et al.] 2008 [Xue et al.] Constructing the complete schedule 1993 [Kao et al.] Per-stage deadlines 1997 Holistic Analysis [Pellizzoni et al.] 2005 Real-time Calculus [Thiele et al.] 2000 Delay Composition Algebra [Jayachndran et al.] 2009 [Fohler et al.] Constructing the complete schedule 1997 [Zhang et al.] Per-stage deadlines 2005 Holistic Analysis [Tindell et al.] 1994 Real-time Calculus [Jonsson et al.] 2008 [Koubaa et al.] Comparing Real-time Calculus & Holistic 2004

4. Aggregation Model 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. 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 4 Off i : the (maximum) offset from time zero at which a job J i of workflow F i arrives C i,j : worst-case processing time of J i on resource j D i : end-to-end deadline of J i

5. Intuition 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 5 Workflow graph and execution trace for seemingly candidate aggregation composition approach J l : job under consideration J h : higher priority job J l1, J l2, J l3, J l4 : lower priority jobs Non-preemptive scheduling

6. End-to-End Delay ( l ) = 88 - ɛ Delay Bound ( l ) = ? Using Delay Composition Theorem for Pipelines 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 6 E2E Delay ( l ) = 88 - ɛ > Delay Bound ( l ) = 80 + 3ɛ !?

7. Revisit Event Due to reversal in the arrival order, it is possible for to again delay ′ at a downstream stage 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 7 J i’ : job under consideration J i : higher priority job J l1, J l2, J l3 : lower priority jobs Non-preemptive scheduling Along the other branch, delays job ′ and arrives ahead of it to the merge- stage Along one branch, ′ completes execution and arrives ahead of to the merge-stage

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 in an aggregation tree is bounded as, where Off i is the offset of job J i from time zero. 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 8

9. Delay Bound Proof Sketch By induction on the number of revisit events 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 9

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 in an aggregation tree is bounded as, where Off i is the offset of job J i from time zero. 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 10

11. Schedulability Analysis The schedulability of a job of an aggregation workflow can be determined by analyzing the schedulability of an equivalent hypothetical uniprocessor constructed by reduction rules obtained based on the composition theorem. 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 11 The reduction process on an aggregation tree

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 load parameters The number of stages The number of tasks Job resolution Deadline ratio Offset resolution 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 12

13. End-to-End Delay Bound Accuracy w.r.t. the Number of Stages 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 13 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 Less Pessimistic More Pessimistic

14. 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 14 End-to-End Delay Bound Accuracy w.r.t. the Number of Tasks Under both non-preemptive and preemptive scheduling, more than 20% improvement when the number of jobs over 80 Less Pessimistic More Pessimistic

15. Resource Utilization w.r.t. Job Resolution 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 15 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) Many small jobsA few big jobs

16. 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 16 Resource Utilization w.r.t. Deadline Ratio 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) Homogenous deadlinesWide range of deadlines

17. 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 17 Resource Utilization w.r.t. Offset Resolution Improvement when offset resolution below 100 times of the minimum job deadline Logarithmic Scale Small offsetsWide range of offsets

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. 7/11/2012F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks 18

19. Thank you. Questions … ? 19 F. Saremi et al., On Schedulability and Time Composability of Data Aggregation Networks7/11/2012