Simulation of Auction Mechanism Model for Energy-Efficient High Performance Computing

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Simulation of Auction Mechanism Model for

Energy-Efficient High Performance Computing

Kishwar Ahmed, Samia Tasnim*, and Kazutomo Yoshii**

University of South Carolina Beaufort *Florida A&M University

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Outline

• Background

• Energy-efficient auction mechanism model

• Mechanism model simulation

• Conclusions

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HPC Cloud

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HPC is Power-Hungry

Frontera 23PFlops 6MW Tianhe-2A 61PFlops 19MW Sunway Taihulight 93PFlops 16MW Sierra 94PFlops 8MW Summit 148PFlops 11MW To p su pe rc om pu te rs (N ov em be r 2 01 9) Exascale tire

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HPC is Energy-Costly

6 Other 8% Mainteinance 14% Hardware 36% Staff 14% Energy 28% HPC cost distribution

Lifelong energy cost ≈ investment cost

Source: “Total Cost of Ownership in High Performance Computing. HPC data center cost considerations: investment, operation and maintenance.” in SoSE 2014

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How to reduce

energy cost

of HPC systems, while

rewarding

HPC users for their participation?

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Our Solution

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• Energy reduction based on DVFS

• Auction mechanism to reward HPC users

Energy-efficient auction mechanism model

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• Based on parallel discrete-event simulation

Mechanism model simulation

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Outline

• Background

• Energy-efficient auction mechanism model

• Mechanism model simulation

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Energy-Efficient Auction Mechanism Model

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• Resource allocation model

• Exploiting dynamic voltage frequency scaling (DVFS)

• _{Auction mechanism model}

• Bid determination

• Winning bidder determination

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Resource Allocation Model

!_" = $_" ⋅ &((_)*+) ⋅ -_. !_"′ = $_" ⋅ &((_"′) ⋅ -_.

Δ!_" = !_" − !_"’

Δ-_" = 100 ⋅ [-((_)*+) − -((_"’)] / [-((_)*+)

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Enable Users’ Participation

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HPC users rewarded based on a

VCG-based auction mechanism model

• How to ensure their participation?

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VCG-Based Auction Model

• _{Vickery-Clarke-Groove (VCG) mechanism}

• A sealed-bid auction mechanism

• Truth-telling is a dominant strategy

• Participants are rewarded for truthful participation

• Two stages

• _{HPC users submit their energy reduction bid}

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An Example Scenario

14 (Δ"₁ , b₁₎ (Δ"₂_{, b}₂₎ (Δ"3, b 3) (Δ"1, p1) (Δ"2, p2) User#2 User#3 User#1 User#1 User#2 HPC operator (Δ"1, b1) (Δ"2, b2) (Δ"3, b3)

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Determining Bids

• Inconvenience cost

• ! converts time change to monetary value

• _{E.g., 0.0044$/hour at Rice University HPC cluster}

• Bid determined by user i

• "_# is a truthfulness parameter

• By default value is 1 (i.e., no cheating) c_# = ! ⋅ Δ(₎

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Determining Winning Bidders

Operator solves the following optimization to determine the winning bidders Minimize: subject to: 16 ! "#$ % &_" ! "#$ % Δ(_" ≥ (_*+

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Determining Price

• Payment of bidder i (p_i) is obtained as

• Optimal welfare (for the other users) if user i was not participating

• _minus _{welfare of the}_{other players} _{from the chosen outcome}

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Outline

• Background

• Energy-efficient auction mechanism model

• Mechanism model simulation

• Conclusions

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Scheduling Simulator

Job

Dispatcher ExecutionerJob

Scheduling Policies

Waiting Jobs Running Jobs

Job Arrival

Job Departure

Application

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Simulus: Parallel Discrete Event Simulator

• Discrete-event simulator in Python

• Open-source: https://simulus.readthedocs.io/en/latest/index.html

• Supports parallel and distributed simulation

• Several advanced features to ease modeling and simulation

• Includes documentation and many examples

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Model Simulation

50 100 150 200 250 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Average Power (Watt)

Quantum ESPRESSO Gadget Seissol WaLBerla PMATMUL STREAM 0 20 40 60 80 100 120 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Execution Time (Min)

Quantum ESPRESSO Gadget Seissol WaLBerla PMATMUL STREAM

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Energy Reduction and Inconvenience Cost

5 10 15 20 25 30 35 40 45 50

User#1 User#2 User#3 User#4 User#5 User#6

Energy Reduction (KJ) Users 22 10 12 14 16 18 20 22

User#1 User#2 User#3 User#4 User#5 User#6

Time Increase (%)

Users

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User Reward and Utility

0 2 4 6 8 10

User#1 User#2 User#3 User#4

Reward (Cents) 0 0.005 0.01 0.015 0.02 0.025 0.03

User#1 User#2 User#3 User#4

Utility

Truthful Untruthful

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Impact of Energy Reduction Target

24 0 20 40 60 80 100 120 140 50 75 100 125 Energy Reduction (KJ)

Energy Reduction Target (KJ)

0 1 2 3 4 5 6 7 50 75 100 125 Reward (Cents)

Energy Reduction Target (KJ)

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Conclusions

• HPC systems are power-hungry and energy-costly

• We proposed

• VCG-based auction mechanism model • _{Truthful participation from HPC users}

• We developed

• A job scheduling simulator

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Thank You!

Questions?

Acknowledgements: