1. 1 Memory and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng Department of Computer and Information Science Linköpings universitet

2. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 2 Outline n Introduction n Task model and problem formulation n Analysis method n Experimental results n Conclusions and future work

3. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 3 Introduction PartitioningAllocationMappingScheduling Functionality as an annotated task graph Mapped and scheduled tasks on the allocated processors The schedulability analysis gives the design fitness estimate

4. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 4 Motivation n“Classical” schedulability analysis works on the WCET model nEstablished analysis methods

5. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 5 Applications nSoft real-time applications (missing a deadline is acceptable) nWCET becomes pessimistic nLeads to processor under-utilization nEarly design phases, early estimations for future design guidance nAlternative Models: nAverage nInterval nStochastic

6. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 6 nApplication characteristics (data dependent loops and branches) nArchitectural factors (pipeline hazards, cache misses) nExternal factors (network load) nInsufficient knowledge Sources of Variability

7. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 7 nL. Abeni and G. Butazzo, “Integrating Multimedia Applications in Hard Real-Time Systems”, 1998 nA. Atlas and A. Bestavros, “Stochastic Rate Monotonic Scheduling”, 1998 nA. Kalavade, P. Moghe, “A Tool for Performance Estimation for Networked Embedded Systems”, 1998 nJ. Lehoczky, “Real Time Queueing Systems”, 1996 nT. Tia et al., “Probabilistic Performance Guarantee for Real-Time Tasks with Varying Computation Times”, 1995 nT. Zhou et al., “A Probabilistic Performance Metric for Real-Time System Design”, 1999 Related Work

8. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 8 Outline n Introduction Ô Task model and problem formulation n Analysis method n Experimental results n Conclusions and future work

9. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 9 Problem Formulation nInput nSet of task graphs nSet of execution time probability distribution functions (continuous) nScheduling policy nOutput nRatio of missed deadlines per task or per task graph nLimitations nDiscarding, non-pre-emption

10. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 10 Task Model ACBDEFGHIJ 2 64 12 60 120 24 53 15 9 9 360

11. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 11 Outline n Introduction n Task model and problem formulation Ô Analysis method n Experimental results n Conclusions and future work

12. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 12 Analysis Method nRelies on the analysis of the underlying stochastic process nA state of the process should capture enough information to be able to generate the next states and to compute the corresponding transition probabilities

13. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 13 PMIs B, t k, {A}B, t k+1, {A} 053 B, t 0, {} B, t 1, {} A, 0, {B}

14. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 14 PMIs B, t k, {A}B, t k+1, {A}B, t 0, {}B, t 1, {} A, 0, {B} B, [0, 3), {}B, [3, 5), {A} 05369101215 nA PMI is delimited by the arrival times and deadlines nThe sorting of the tasks according to their priorities is unique inside of a PMI

15. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 15 Stochastic Process A, [0, 3), {B} B, [0, 3), {} -, [0, 3), {} B, [3, 5), {A} A, [3, 5), {} A, [5, 6), {B} 30 053 30300533058

16. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 16 Analysis [0, 3) [3, 5) [5, 6) [6, 9) [9, 10) [10, 12) [12, 15)

17. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 17 Outline n Introduction n Task model and problem formulation n Analysis method Ü Experimental results n Conclusions and future work

18. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 18 Experimental Results Influence of number of tasks on the process size Tasks 10111213141516171819 Number of process states 20000 155000 65000 110000

19. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 19 Experimental Results Influence of dependency degree on the process size Dependency degree 0123456789 Number of process states 1000 1000000 10000 100000

20. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 20 Experimental Results Influence of the period LCM on the process size Least common multiple 250040005500 Number of process states 0 1800000 600000 1200000 1000

21. Memory- and Time-Efficient Schedulability Analysis of Task Sets with Stochastic Execution Times Sorin Manolache, Petru Eles, Zebo Peng 21 Conclusions nSchedulability analysis of set of tasks with stochastic execution times nConstruction and analysis of the process at the same time  sliding window size between 16 to 172 times smaller than the total number of process states nFuture work: extension for multiprocessor case