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

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. Computation Model Period 2 4 6 12 9 3 Execution times execution time
probab E
Deadlines B C
Late task policy F
Scheduling policy D P1 P2

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

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

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. Case Study
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. A B E C D

11. Case Study (cont’d)

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