James McGalliard , FEDSIM CMG Southern Region Raleigh - April 11, 2014

1. Comparison of Game Theory and Multiple Objective Dynamic Prioritization Workload Scheduling Methods in a High Performance Computing Environment James McGalliard, FEDSIM CMG Southern Region Raleigh - April 11, 2014 Richmond – April 17, 2014

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

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 CMGpresentation & paper focused on the MapReduce framework

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

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

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.

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

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

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

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

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

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

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)

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

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

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

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

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”

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)

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

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

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

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

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

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

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

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

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

29. Conclusions • 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