1. James McGalliard, FEDSIM CMG Southern Region Raleigh - April 11, 2014 Richmond – April 17, 2014 1

2. Agenda  Background  Why We Model  Multiple Objective Dynamic Prioritization  Game Theory  Comparison of Dynamic Prioritization and Game Theory Methods  Conclusions 2

3. Background  Current generation High Performance Computers are typically clusters of commodity microprocessors that can execute multiple jobs of assorted sizes (number of processors, run time) simultaneously  There are many workload scheduling alternatives  2013 Dynamic Prioritization CMG presentation & paper focused on the MapReduce framework 3

4. Background, cont’d.  My coauthor has proposed an extension of the 2013 results using game theory  Game theory-based workload scheduling has been studied extensively 4

5. Some Terminology  Multiple Objective  Dynamic Prioritization  Game Theory  Agent  Strategy  Nash Equilibrium  Price of Anarchy 5

6. Why We Model  Represent a subset of the attributes of some phenomenon of interest…  Using a set of symbols that convey meaning, such as significant elements of a system’s structure and dynamics  To gain insight by focusing on that subset  To test a hypothesis  To validate experience, live test results, etc. 6

7. Why We Model, cont’d.  Choice of attributes & symbols impacts what is seen  Analytical modeling using queueing theory has historically dominated computer performance evaluation modeling at CMG  Queuing models are computationally easy but forces assumptions that may not be realistic 7

8. Why We Model, cont’d.  FEDSIM historically favored simulation over analytical modeling  Simulation is more computationally demanding but needs fewer constraining assumptions  Is a more general purpose tool  Can have its own issues, such as spin up  Computation is cheaper than it used to be 8

9. Why We Model, cont’d.  Game theory and multiple objective dynamic optimization can both be studied using simulation, but with different attributes, symbols, and assumptions, e.g., single agent vs. multiple agents 9

10. Multiple Objective Dynamic Prioritization  Presented in 2013 at Raleigh and Richmond and at the annual national conference in La Jolla  Simulation of scheduling alternatives with a defined objective function across the known workload  Improved performance compared to the default FCFS workload scheduler  Multiple objectives evaluated from the perspective of the central scheduler/system administrator 10

11. Multiple Objective Dynamic Prioritization, cont’d.  These objectives could include sys admin’s – e.g., maximize hardware utilization…  Or users’ – e.g., minimize turnaround time; expansion factor…  Or any objective that can be calculated  A single agent - the central scheduler - but multiple perspectives 11

12. Multiple Objective Dynamic Prioritization, cont’d.  Assumed fractional knapsack allocation  Workload scheduling considerations included:  Wait Time  Run Time  Number of CPUs  Queue  Composite priorities  Dynamic priorities 12

13. Multiple Objective Dynamic Prioritization, cont’d.  Workload scheduling considerations included:  Resource awareness  Phase Based  Delay Timing  Pre-emption & Interruption  Social Scheduling  Variable Budget Scheduling  Complex workload structures (e.g., copy/compute) 13

14. Multiple Objective Dynamic Prioritization, cont’d.  Some new considerations:  Power consumption – based on number of cores, CPU time  Power consumption can also reflect resource awareness – locality  Reliability – modeled as a random process, included in the simulation 14

15. Game Theory  Many applications in applied mathematics  Assumes multiple agents as opposed to a single agent  Agents can act independently and are assumed to act in their own best interest 15

16. Game Theory, cont’d.  For example, the prisoner’s dilemma… 16

17. Game Theory, cont’d.  Active area of research, including study of machine scheduling  E.g., grid computing, with multiple independent local schedulers that cooperate in some way to distribute the workload  Or in systems with multiple users or users vs. the system admin  The latter is proposed by my coauthor 17

18. Game Theory, cont’d.  Some considerations in Game Theory studies of workload scheduling:  Distributed Scheduling  Hierarchical Scheduling  Cooperative vs. Non-cooperative  Complete vs. Incomplete Information  “Truth Telling” 18

19. Game Theory, cont’d.  More considerations in Game Theory studies of workload scheduling:  Bidding, Auctioning, Pricing, Bartering, Commodity Market  “Friendship”  Complex workload structures (e.g., phased & distributed) 19

20. Nash Equilibrium  Object of inquiry is often the distinction between the globally optimal solution and solutions where each independent agent strives for its own optimum  When no agent changes their strategy from one iteration to the next, the system is in equilbrium  When there exists a set of locally optimal solutions, such that no individual agent can improve their own objective by changing their strategy, this is called a Nash Equilibrium 20

21. Nash Equilibrium, cont’d.  Difference between global and local optima is called the “Price of Anarchy,” how much less optimal solution is with competing independent agents vs. global optimum  Global optimum is often too complex to calculate (“NP-complete”)  It has been shown that a Nash Equilbrium exists, provided that agents can use mixed strategies, where each agent selects from several choices based on a probability distribution 21

22. Dynamic Prioritization Vs. Game Theory Methods  In dynamic prioritization, strategy changes over time based on analysis of the workload using simulation  In game theory, strategies change over time based on a probability distribution  Results of each alternative are solved using simulation  The simulation uses a known historical or synthetic workload 22

23. Dynamic Prioritization Vs. Game Theory Methods, cont’d.  The Nash Equilibrium is rarely optimum  Dynamic prioritization can find the optimum solution (subject to parameter constraints) using brute force and should beat Nash  Nash generally entails probabilistic mixed strategies 23

24. Dynamic Prioritization Vs. Game Theory Methods, cont’d.  Dynamic prioritization is deterministic over its parameter constraints  Dynamic prioritization can simulate multiple agents’ priorities and in that sense have a game theoretic perspective  Dynamic prioritization will incorporate agents’ actions in the simulation once each job has been submitted to the queue – probability has become reality 24

25. Dynamic Prioritization Vs. Game Theory Methods, cont’d.  Dynamic prioritization is deterministic based on the currently submitted workload – does not forecast the future  This is feasible because repeated simulation has become computationally cheap  Game theory deals with future probabilities 25

26. New Simulation: Set Up  All users are considered collectively as one agent, all using the same strategy  The two agents are the User group and the System administrator  Users are unaware of the Sys admin’s strategy  User objectives: minimize run time & minimize expansion factor  Sys admin objectives: minimize power use; maximize system utilization; maximize reliability & maximize throughput 26

27. New Simulation: Results  Solve using both dynamic prioritization and game theory methods and compare…  Results are pending 27

28. Conclusions  As a practical matter, independent users/agents will in fact tend to behave in their own self- interests  Users are clever and their specific behavior is hard to predict  Often this will lead to mixed strategy behavior  Generally, there will be a Nash Equilibrium among the agents, with agents using mixed strategies and less than globally optimal performance 28

29. Conclusions 29  System Administrators have reason to consider the expected selfish behavior of users  Because of brute-force effectiveness, simulation should find optimal workload schedules in the presence of active, selfish user/agents  Studies using game theory provide new insights, test new hypotheses, and can help validate experience and live test results