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Comparison of Game Theory and Multiple Objective Dynamic

Prioritization Workload Scheduling Methods in a High Performance

Computing Environment

James McGalliard, FEDSIMCMG Southern RegionRaleigh - April 11, 2014

Richmond – April 17, 2014

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

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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

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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

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Some Terminology

Multiple Objective Dynamic Prioritization Game Theory Agent Strategy Nash Equilibrium Price of Anarchy

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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.

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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

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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

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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

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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

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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

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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

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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)

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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

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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

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

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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

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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”

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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)

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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

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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

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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

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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

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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

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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

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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

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New Simulation: Results Solve using both dynamic

prioritization and game theory methods and compare…

Results are pending

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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

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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