a comparison of game theory and multiple objective dynamic prioritization 2014.04.11
TRANSCRIPT
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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