1. Tai, Yu-Chang 4/29/2013 Future Generation Computer Systems(FGCS.J) journal homepage: www.elsevier.com/locate/fgcs Saeid Abrishami a, ∗, Mahmoud Naghibzadeha, Dick H.J. Epemab

2. * Introduction * Scheduling system model * IaaS cloud partial critical paths algorithms * An illustrative example * Time complexity * Performance evaluation * Conclusions

3. * Clouds are different from utility Grids - on-demand resource provisioning - homogeneous networks - the pay-as-you-go pricing model * consider the benefits of using Cloud computing for executing scientific workflows -there exist several commercial Clouds, such as Amazon

4. Infrastructure as a Service (IaaS) Clouds, has some potential benefits for executing scientific workflows 1. users can dynamically obtain and release resources on demand, and charged on a pay-as-you-go basis 2.resource provisioning 3. illusion of unlimited resources important parameter : economic cost -faster resources are more expensive than slower ones -time-cost tradeoff in selecting appropriate services -belongs to the multi-criteria optimization problems minimize the execution cost of the workflow, while completing the workflow before the user specified deadline IaaS Cloud Partial Critical Paths (IC-PCP) IaaS Cloud Partial Critical Paths with Deadline Distribution (IC-PCPD2)

5. * An application is modeled by a directed acyclic graph G(T, E) * T is a set of n tasks {t 1, t 2,..., t n } * E is a set of dependencies e i,j =(t i,t j ) * two dummy tasks t entry and t exit to the beginning and the end of the workflow (zero execution time and they are connected with zero-weight dependencies to the actual entry and exit tasks)

6. * services S = {s 1,s 2,…,s m } with different QoS parameters such as CPU type and memory size, and different prices * The pricing model is based on a pay-as-you-go basis similar to the current commercial Clouds, i.e., the users are charged based on the number of time intervals that they have used the resource, even if they have not completely used the last time interval c1=5 c2=2 c3=1

7. * ET(t i, s j ) : execution time of task t i on computation service s j * average bandwidth between the computation services is roughly equal * TT(e i,j ) : data transfer time of a dependency e i,j * MET(t i ) : Minimum Execution Time of a task t i -execution time of task t i on a service s j ∈ S which has the minimum ET(t i, s j ) between all available services titi p p titi c c

8. * SS (t i ) = s j,k : Selected Service for each scheduled task ti * s j,k : kth instance of service sj. * AST (t i ) : Actual Start Time of ti * assigned node :has already been assigned to (scheduled on) a service * Critical Parent : of a node ti is the unassigned parent of t i that has the latest data arrival time at ti, that is, it is the parent tp of ti for which EFT(t p ) + TT(e p,i ), is maximal * PCP: The Partial Critical Path of a node t i is: - empty if t i does not have any unassigned parents -consists of the Critical Parent tp of t i and the Partial Critical Path of t p if has any unassigned parents

9. IC-PCP

10. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~3__16 0~5__16 0~2__193~7__24 7~10__23 7~11__22 8~13__30 14~17__30 D=30 14~19__30 1 3 2 0 10 20 30

11. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~3__16 0~5__16 0~2__193~7__24 7~10__23 7~11__22 8~13__30 14~17__30 D=30 Path{t2,t6,t9} 14~19__30 1 S 2,1 28 3 2 2 14~17__2321~24__23 12~20__2320~28__300~3__12 0~12__14 0 10 20 30

12. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~3__12 0~12__14 0~2__193~7__24 14~17__23 12~20__22 8~13__30 21~24__30 D=30 Path{t3} 20~28__30 1 S 2,1 28 3 2 2 0~9__12 S 3,1 91 0 10 20 30

13. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~9__12 0~12__14 0~2__193~7__24 14~17__23 12~20__22 8~13__30 21~24__30 D=30 Path{t5,t8} 20~28__30 1 S 2,1 28 3 2 2 S 3,1 91 14~22__2422~28__30 3~7__23 0~2__18 S 2,2 14 6 0 10 20 30

14. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~9__12 0~12__14 0~2__18 3~7__23 14~22__24 12~20__22 8~13__30 22~28__30 D=30 Path{t1,t4} 20~28__30 1 S 2,1 28 3 2 2 S 3,1 91 8~18__23 0~8__13 S 2,2 6 19~24__30 S 3,2 18 2 0 10 20 30 14

15. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~9__12 0~12__14 0~8__13 14~22__24 12~20__22 22~28__30 D=30 Path{t7} 20~28__30 1 S 2,1 28 3 2 2 S 3,1 91 8~18__23 S 2,2 6 19~24__30 S 3,2 18 2 18~29__30 S 3,3 11 1 COST=2*5+1*4=14 0 10 20 30 14 5 2 1

16. * Applicable * applicable instance for a path if it satisfies two conditions: - The path can be scheduled on the instance such that each task of the path is finished before its latest finish time - The new schedule uses (a part of) the extra time of the instance,which is the remaining time of the last time interval of thatinstance. P C P Cost=zero C

17. IC-PCPD2 Call PLANNING(G(T,E)) Assign subdeadline on PCP node (assigned node)

18. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~3__16 0~5__7 0~2__63~7__24 7~10__13 7~11__17 8~13__30 14~17__30 D=30 14~19__30 sb=0 t entety t4t4 0~5__6 S 1,1 S 2,1 S 3,1 t2t2 t3t3 t1t1 6~10__2411~16__30 t1t1 0 10 2030

19. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~3__16 0~5__7 0~5__66~10__24 7~10__13 7~11__17 11~16__30 14~17__30 D=30 14~19__30 sb=0 t entety t4t4 t5t5 S 1,1 S 2,1 S 3,1 t2t2 t3t3 t1t1 t1t1 t2t2 0 10 2030

20. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~3__16 0~5__7 0~5__66~10__24 7~10__13 7~11__17 11~16__30 14~17__30 D=30 14~19__30 sb=0 t entety t4t4 0~9__16 t5t5 t6t6 S 1,1 S 2,1 S 3,1 t2t2 t3t3 t1t1 11~15__1718~23__30 t1t1 t2t2 t3t3 0 10 2030

21. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~9__16 0~5__7 0~5__66~10__24 7~10__13 11~15__17 11~16__30 14~17__30 D=30sb=0 t entety t4t4 t5t5 t6t6 t7t7 S 1,1 S 2,1 S 3,1 t2t2 t3t3 t1t1 18~23__30 t1t1 t2t2 t3t3 6~16__2417~22__30 17~20__30 t4t4 S 3,2 0 10 2030

22. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~5__7 0~5__6 7~10__13 D=30sb=0 t entety t4t4 0~9__16 t5t5 t6t6 t7t7 t8t8 S 1,1 S 2,1 S 3,1 t2t2 t3t3 t1t1 11~15__17 18~23__30 t1t1 t2t2 t5t5 t3t3 6~16__24 17~22__30 17~20__30 t4t4 S 3,2 0 10 2030

23. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~5__7 0~5__6 7~10__13 D=30sb=0 t entety t4t4 0~9__16 t5t5 t9t9 t6t6 t7t7 t8t8 S 1,1 S 2,1 S 3,1 t2t2 t3t3 t1t1 11~15__17 18~23__30 t1t1 t2t2 t5t5 t3t3 6~16__24 17~22__30 17~20__30 t4t4 S 3,2 S 1,2 t6t6 0 10 20 30

24. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~5__7 0~5__6 7~10__13 D=30sb=0 t entety t4t4 0~9__16 t5t5 t9t9 t6t6 t7t7 t8t8 S 1,1 S 2,1 S 3,1 t2t2 t3t3 t1t1 11~15__17 18~23__30 t1t1 t2t2 t5t5 t3t3 6~16__24 17~22__30 17~20__30 t4t4 S 3,2 S 1,2 t6t6 17~29__30 t7t7 16~28__30 0 10 2030

25. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~5__7 0~5__6 7~10__13 D=30sb=0 t entety t4t4 0~9__16 t5t5 t9t9 t6t6 t7t7 t8t8 S 1,1 S 2,1 S 3,1 t2t2 t3t3 t1t1 11~15__17 18~23__30 t1t1 t2t2 t5t5 t3t3 6~16__24 16~28__30 17~20__30 t4t4 S 3,2 S 1,2 t6t6 t7t7 17~25__30 t8t8 S 3,3 0 10 2030

26. 258258 4 6 10 4 8 11 5 8 11 5 12 16 3 8 11 368368 359359 5 8 14 0~5__7 0~5__6 7~10__13 D=30sb=0 t entety t4t4 0~9__16 t5t5 t9t9 t6t6 t7t7 t8t8 S 1,1 S 2,1 S 3,1 t2t2 t3t3 t1t1 11~15__17 18~23__30 t1t1 t2t2 t5t5 t3t3 6~16__24 16~28__30 17~25__30 t4t4 S 3,2 S 1,2 t6t6 t7t7 18~26__30 t8t8 S 3,3 t9t9 S 2,2 COST=5*2+2*2+1*4=18 0 10 2030 5 2 1

27. O(n+e)~O(n^2) O(n-1) O(m*n)=O(n^2) IC-PCP=O(n^2) O(n) O(n^2)

28. IC-PCPD2=O(n^2) Call PLANNING(G(T,E)) Assign subdeadline on PCP node O(n+e)~O(n^2) O(n) O(n^2)

29. Algo1 IC-PCP Algo2 IC-PCPD2 Algo3 IC-LOSS normalize the total cost of each workflow execution Cheapest schedule : scheduling all workflow tasks on a single instance of the cheapest computation service Fastest schedule : scheduling each workflow task on a distinct instance of the fastest computation service, while all data transmission times are considered to be zero MF = makespan of the Fastest schedule deadline factor α set the deadline = α ・ MF -Since the problem has no solution for α = 1, we let α ranges from 1.5 to 5 in our experiments, with a step length equal to 0.5

30. Algo1 IC-PCP Algo2 IC-PCPD2 Algo3 IC-LOSS 1>2>31>2>3 1>2>31>2>3 1>2>31>2>31≈2>31≈2>31>2>31>2>32>1>32>1>3 1>2>31>2>31≈2>31≈2>31>2>31>2>32>1>32>1>3

31. * The new algorithms consider the main features of the current commercial Clouds such as on-demand resource provisioning, homogeneous networks, and the pay-as-you-go pricing model * The time complexity of both algorithms is O(n2), The polynomial time complexity makes them suitable options for the large workflows * IC-PCP outperforms both, IC-PCPD2 and IC-Loss in most cases * experiments show that the computation times of the algorithms are very low, less than 500 ms for the large workflows * intend to improve our algorithms for the real Cloud environments