1. Performance Analysis of Applications with Stochastic Task Execution Times Sorin Manolache, Petru Eles, Zebo Peng University of Linköping, Sweden {sorma, petel, zebpe}@ida.liu.se

2. 2 Overview Toolset consisting of three tools Computation model: set of annotated task graphs Main performance indicator: expected deadline miss ratio per task or task graph

3. 3 Computation Model B C D A E F P1P1 P2P2 Deadlines Late task policy Scheduling policy Period 2 46 12 9 3 Execution times execution time probab

4. 4 Internals  Concurrently constructs and analyses the GSMP underlying the system. Method of supplementary variables + tricks for memory reduction.  Constructs the GSMP. Approximates the GSMP with a much larger CTMC. Exploits the regular structure of the CTMC for on-the-fly generation of its infinitesimal generator.  Recursively computes the finishing time distribution, ignoring some dependencies among some of the random variables modelling the system.

5. 5 Limitations We assume non-preemptive execution in all three methods First method is efficient only in the case of monoprocessor applications Third method is limited to fixed-priority scheduling

6. 6 Scalability Third method is polynomial O(N  LCM/h  |ETPDF|/h) First two methods build the GSMP underlying the application  Analysis visits each state that described the behaviour of the system   Theoretically exponential, but practically…

7. 7 …Practically First method (for monoprocessors) 20 independent tasks 200 dependent tasks

8. 8 …Practically Second method (for multiprocessors) 60 dependent tasks on 2 processors 18 dependent tasks on 6 processors

9. 9 Accuracy First method gives exact results Second method relies on approximating generalised distributions with Coxian distributions  problems with non-smooth distributions Third method gives approximate results. Its accuracy is experimentally investigated

10. 10 Case Study AB CD E Tasks A and B have exponentially distributed execution times, average rate = 1/7 and 1/2 respectively Task C, D, and E execute for 4, 5, and 6 time units respectively Interprocessor communication takes 0.5 time units Tasks on the orange processor in descending order of priorities: E, C, D.

11. 11 Case Study (cont’d)

12. 12 Conclusions Three performance analysis approaches for applications with stochastic task execution times Multiproc.AccuracyExponential Design space exploration Exact approach NoExact Theoretically yes, practically not a problem No ETPDF approx. Yes Good for smooth distributions Yes, in the number of processors No Equation- based Yes Coarser than ETPDF approx. No. Linear in the number of tasks. Yes