1. 1 A Cooperative Game Framework for QoS Guided Job Allocation Schemes in Grids Riky Subrata, Member, IEEE, Albert Y. Zomaya, Fellow, IEEE, and Bjorn Landfeldt, Senior Member, IEEE IEEETRANSACTIONS ON COMPUTERS, VOL. 57, NO. 10, OCTOBER 2008 Present by Ting-Wei, Chen

2. 2 Index  Introduction  Cooperative Game Framework  Pareto Optimal and Fair Job Allocation Algorithm  Experiments  Conclusion

3. 3 Introduction  Game theoretic solution to the QoS sensitive grid job allocation problem  Model the QoS-based grid job allocation problem as a cooperative game  Present the structure of the Nash Bargaining Solution

4. 4 Cooperative Game Framework (cont.)  Send jobs to more than one broker  The broker decides which provider will process the job  Sends the job to that provider  First-come-first-serve

5. 5 Cooperative Game Framework (cont.)  Broker → Provider Constraint  Signal

6. 6 Cooperative Game Framework (cont.)  Nash Bargaining Game –Two players –If the two proposals sum to no more than the total good –Then both players get their demand –Otherwise, get nothing

7. 7 Cooperative Game Framework (cont.)  Model the grid load-balancing problem –The m players are the service provider –Each player has a performance function –Each player has a minimum initial performance – –Solve the optimization problem –Equivalent optimization problem

8. 8 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  The average processing time of a job –Waiting time at the queue at a provider –The expected transfer time of a job from any player to provider

9. 9 Pareto Optimal and Fair Job Allocation Algorithm (cont.) –The average completion time of jobs for provider

10. 10 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  Maximum expected service time  Maximum rate of jobs a provider  Note:

11. 11 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  Nash bargaining solution is determined by solving the following optimization problem

12. 12 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  in terms of …(17)  Concave function

13. 13 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  First, maximize the objective function (17)  Lagrangian is a function that summarizes the dynamic of the system

14. 14 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  A necessary condition …(19)  Solving (19), get …(20)

15. 15 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  Solve for …(22)  Using (22) and constraint →

16. 16 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  Setting into (20)

17. 17 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  Cooperative Job Allocation –According to the time equation –Calculate two variables α and d α’s equation

18. 18 Pareto Optimal and Fair Job Allocation Algorithm (cont.) is the maximum positive integer  Finally

19. 19 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  Simultaneously maximize the QoS level of all the providers  User’s fairness criterion –Concerned in the users and brokers –The average job completion time for brokers are the same

20. 20 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  Fairness index  Provides a fair allocation for each brokers  Amount of jobs to be sent from broker to provider

21. 21 Pareto Optimal and Fair Job Allocation Algorithm (cont.)  Periodically calculates an optimum job allocation strategy  Remain in equilibrium until the system’s states change

22. 22 Experiments (cont.)  QoS goals on the average job completion time –CG generally gives better performance than NG and PS CG (Cooperative Game Algorithm) PS (Proportional-Scheme Algorithm) NG (Noncooperative Game Algorithm)

23. 23 Experiments (cont.)  Proportional-scheme –Allocates jobs to providers in proportion to its computing power –The faster providers are sent more jobs by the brokers –Can’t take into account the communication delays incurred in transferring job

24. 24 Experiments (cont.)  Noncooperative game algorithm –Players are brokers –Minimize their own average job completion time

25. 25 Experiments (cont.)  Concerned about the aggregate number of jobs arriving at each broker  Not the individual jobs from each user  The actual arrival rate of each broker

26. 26 Experiments (cont.)  Response Times Average job completion time for each broker.

27. 27 Experiments (cont.)  Effect of System Loads Average job’s completion time versus system load

28. 28 Experiments (cont.)  Effect of Service Time –The Bounded Pareto distribution

29. 29 Experiments (cont.)  The mean (first moment) of the distribution  The second moment

30. 30 Conclusion  Fair to all users  Represents a Pareto optimal solution to the QoS objective

31. 31 Thank you for your attention