Optimization of Real-Time Systems with Deadline Miss Ratio Constraints

1. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints Sorin Manolache, Petru Eles, Zebo Peng {sorma, petel, zebpe}@ida.liu.se Linköping University, Sweden

2. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Introduction • Task execution times are not fixed stochastic task execution times • Probabilistic behaviour and implicitly probabilistic guarantees • Ratio of missed deadlines is an important indicator of system performance, obviously of stochastic nature soft real-time systems • Optimizing this indicator by means of mapping of tasks to processors and assignment of priorities to tasks multiprocessor applications 2

3. driven by • Performance analysis algorithm that obtains the deadline miss ratio per task for a given task mapping alternative  • The analysis algorithm is fast and sufficiently accurate Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Contribution • Task mapping and priority assignment heuristic for deadline miss ratio minimization • The heuristic is iterative and transformational 3

4. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Outline • Stochastic task execution times • Problem formulation • Mapping heuristic • Deadline miss ratio analysis • Experimental results • Conclusions 4

5. Affordable hardware <5% missed deadlines Probability Task execution time Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Stochastic execution times Expensive hardware 0% missed deadlines Probability Task execution time 5

6. 2s • Task graphs • Task periods • Task execution time probability density functions 2s 4s 6s • Task and task graph deadlines miss 4% 10s • Processors, buses, interconnection • Deadline miss ratio thresholds 10s Probability miss 2% miss 10% critical Task execution time Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Problem formulation, input • Message transmission time probability density functions 6

7. 1 1 • Task mapping 1 • Task priority assignment 2 2 1 such that devi is minimized, where 2 3 3 4 1 1 mi is the deadline miss ratio of task ti and Ti is its deadline miss ratio threshold 3 2 3 2 2 4 Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Problem formulation, output 7

8. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Mapping heuristic • Based on Tabu search [Glover, 1989] • At each iteration, an improvement of the cost function is sought by modifying the problem parameters (task mapping and/or task priority)—a move • The reversed modification is kept tabu for a small number of iterations • Thus, the heuristic is forced to exit local minima Cost function Problem parameters 8

9. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Mapping heuristic Initial solution Determine candidate moves No Yes Satisfied? Final solution Candidate moves Current solution Evaluate candidate move No All candidates evaluated? Yes Select best 9

10. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Moves • One move is performed every iteration • A move changes the mapping and/or the priority of exactly one task • The “best” move is selected and leads to the next temporary solution • At each step, there are N(N+P-2) move outcomes to evaluate (Exhaustive Neighbourhood search, ENS) • N—number of tasks • P—number of processors 10

11. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng RNS • By intelligently selecting a subset of promising candidate moves, the search could be significantly sped up • Restricted Neighbourhood Search (RNS) • Tasks are ranked and only the moves operating on the top [N/2] tasks are considered • For each selected task, the candidate processors are ranked and only the top 2 processors are considered • RNS reduces the set of candidate moves at each iteration P times compared to ENS 11

12. A A A A B E A B B B C C C C F … B D D … E E E F F F Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Task ranking D 12

13.  • Analysis complexity is reduced by two means: • Task start and finish times are approximated with discrete values • Two types of dependencies between some random variables are neglected Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Deadline miss ratio analysis • Exact DMR analysis for monoprocessor systems [ECRTS 2001] • Theoretically applicable to multiprocessor systems, however it becomes prohibitively expensive • Faster and approximate analysis for multiprocessor systems [ICCAD 2002] • However it is still too slow to be plugged into an optimization loop 13

14. A Z Z Y Y X X Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Deadline miss ratio analysis Z Y X P(X>max(Y, Z)) = P(X>Y)  P(X>Z) 14

15. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Deadline miss ratio analysis A C B A C B Time P(LC(t)) = P(LC(t)|AC<t) 15

16. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Deadline miss ratio analysis 16

17. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Experimental setup • 396 randomly generated benchmarks • # of tasks ranging from 20 to 40 • # of processors ranging from 3 to 8 • Mapping and priority assignment with • Exhaustive neighborhood search (ENS) • Restricted neighborhood search (RNS) • Comparison of cost function values and run times 17

18. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Experimental results 18

19. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Experimental results 19

20. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng LO-AET Laxity optimization based on average execution times of tasks • Why not • Use average task execution times instead of task execution time probability density functions • Optimize a performance indicator based on average task execution times, e.g. average laxity • And hope that it will lead also to an optimal deadline miss ratio 20

21. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Experimental results 21

22. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Experimental results 22

23. Optimization of Real-Time Systems with Deadline Miss Ratio Constraints--Sorin Manolache, Petru Eles, Zebo Peng Conclusions • Task mapping and priority assignment heuristic for soft real-time applications with stochastic task execution times • Fast analysis for approximation of task and task graph deadline miss ratios • Average execution time based heuristics fall short of providing quality results 23