James McGalliard, FEDSIM
CMG Southern Region
Raleigh - April 11, 2014
Richmond – April 17, 2014
1
Agenda





Background
Why We Model
Multiple Objective Dynamic Prioritization
Game Theory
Comparison of Dynamic Prioritization and
Game Theory Methods
 Conclusions
2
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
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
Some Terminology







Multiple Objective
Dynamic Prioritization
Game Theory
Agent
Strategy
Nash Equilibrium
Price of Anarchy
5
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
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
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
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
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
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
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
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
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
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
Game Theory, cont’d.
 For example, the prisoner’s dilemma…
16
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
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
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
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
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
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
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
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
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
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
New Simulation: Results
 Solve using both dynamic prioritization and
game theory methods and compare…
 Results are pending
27
Conclusions
 As a practical matter, independent users/agents
will in fact tend to behave in their own selfinterests
 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
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
29