1. A stochastic scheduling algorithm for precedence constrained tasks on Grid Future Generation Computer Systems (2011) Xiaoyong Tang, Kenli Li, Guiping Liao, Kui Fang, Fan Wu 2016/3/51 Shang-Chi Wu

2. Outline Introduction Stochastic scheduling SHEFT Algorithm Performance evaluation Conclusions and future work 2016/3/52

3. Introduction How to efficiently arrange the users’ application tasks into machines on Grid computing system is a scheduling problem List scheduling is a very popular method for precedence constrained task scheduling based on the DAG model 2016/3/53 DAG v entry v exit 15 55 3 13 11 1716 21 15

4. List scheduling Assign priorities to the tasks of the DAG and place the tasks in a list A task with a higher priority is scheduled before a task with lower priority 2016/3/54

5. Introduction Most of the researches assume that parameters such as task processing time and communication time between precedence constrained tasks are fixed and deterministic which are known advance 2016/3/55 v entry v exit 15 55 3 13 11 1716 21 15

6. stochastic scheduling The crucial assumption is that the task processing time w(v i ) and communication time w(e i, j ) are not known in advance The task processing time and communication time are random variables from which we are just given their distribution function 2016/3/56 exponentially distribution normal distribution

7. Scheduling models in stochastic scheduling 2016/3/57

8. Scheduling models in stochastic scheduling Example Q | vi ∼ stoch, prec | E[C max ] 2016/3/58 Stochastic scheduling problem to minimize the makespan of precedence constrained tasks on Grid heterogeneous parallel machines

9. Stochastic Scheduling Take the variance of random variable and the expected value into account Approximate weight of random variable Aw(X) is defined as 2016/3/59

10. Stochastic Scheduling The processing time of tasks and communication time of edges in stochastic DAG are assumed to follow exponentially distributions 2016/3/510

11. The SHEFT algorithm 2016/3/511

12. Stochastic task priorities phase 2016/3/512

13. Machine selection phase 2016/3/513

14. Algorithm complexity analysis 2016/3/514 O(V|V|m)

15. Performance evaluation Compare the performance of the SHEFT algorithm with two scheduling algorithms in Grid systems –HEFT –DCP Give the expected value as the weight of task for HEFT and DCP algorithms 2016/3/515

16. heterogeneous earliest-finish-time (HEFT) 2016/3/516

17. dynamic critical path(DCP) 2016/3/517

18. Performance evaluation 16 heterogeneous machines that computation capacities varies from Pentium II to Pentium IV The communication capacity of links are assumed to be uniformly distributed between 10 and 100 Mbits/s 2016/3/518

19. Performance evaluation Three fundamental characteristics of DAG are considered –DAG size, v (50~300) –Height of the DAG ( h ) –The maximum and minimum λ value ( λ max, λ min ) of task processing time and communication time between tasks with exponentially distribution 2016/3/519

20. Performance impact of 100 tasks 2016/3/520

21. Performance impact of 200 tasks 2016/3/521

22. Performance impact of 300 tasks 2016/3/522

23. Performance impact of 10 machines 2016/3/523

24.  As the DAG size increases, the improvement becomes more significant Performance impact of 16 machines 2016/3/524

25. Performance evaluation The above simulation results also show a fact that the deterministic scheduling algorithm (such as HEFT and DCP) is not suitable for stochastic scheduling problem 2016/3/525

26. Conclusions SHEFT algorithm –a modified version of the deterministic scheduling algorithm –corporate the stochastic attribute of task processing time and edge communication time into scheduling 2016/3/526

27. Conclusions SHEFT outperforms the existing well- known scheduling algorithms –minimize the makespan –minimize makespan standard deviation –improve the speedup 2016/3/527

28. Future work Extend algorithm to consider more other constraints, such as deadline, release time etc. Study the problem context under large- scale heterogeneous distributed computing systems with security and reliability requirements How the average execution time and standard deviation of tasks are obtained 2016/3/528

29. Thank you for your listening 2016/3/529