The presentation walks through the high level methodology and details some of the statistical apprache

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A Systematic Approach to !
Capacity Planning in the Real World
Bryce Yan, Arun Kejariwal
(@bryce_yan, @arun_kejariwal)
Capacity Engineering @ Twitter
June 2013

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User Experience
• Anytime, Anywhere, Any device
• Real-time performance
• Additional challenges
[2] http://static.googleusercontent.com/external_content/untrusted_dlcp/research.google.com/en/us/people/jeff/Berkeley-Latency-Mar2012.pdf
[1] Xu et al. NSDI 2013 - https://www.usenix.org/system/files/conference/nsdi13/nsdi13-final77.pdf
Fault Tolerance
Variability [2]

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Approaches to Capacity Planning
• Throw hardware at the problem
• Reactive approach
o How much?
o What kind? (Inventory management etc.)
PoorUX
Bottomline

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Capacity Planning is Non-trivial
• Organic growth
 Over 200M monthly active users [1]
• Events planned or unplanned
 Events/incidents (e.g., Superbowl’13 blackout)
 Behavioral response
o Demographics, Cultural
o Retweets, Photos, Vines
 Tax different services/applications
o Different capacity requests
[2] http://arstechnica.com/information-technology/2012/10/hurricane-sandy-takes-data-centers-offline-with-flooding-power-outages/
[3] http://www.zdnet.com/amazons-compute-cloud-has-a-networking-hiccup-7000005776/
[2, 3]
[1] https://twitter.com/twitter/status/281051652235087872

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Capacity Planning is Non-trivial (cont’d)
• Evolving product development landscape
 New features
 New products
• New hardware platforms
 Purchase pipeline
 How much and when to buy – Cost performance trade-off
• Overall goal
User Experience
Operational footprint

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Capacity Modeling Overview

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Capacity Modeling
• Takes core drivers as inputs to generate usage demand
 Forecasts the amount of work based on core driver projections
• Relates the work metric to a primary resource to identify the capacity
threshold
 Primary resources
 Computing power (CPU, RAM)
 Storage (disk I/O, disk space)
 Network (network bandwidth)
• Generate hardware demand based on the limiting primary resource

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Core Drivers
• Underlying business metrics that drive demand for more capacity
 Active Users
 Tweets per second (TPS)
 Favorites per second (FPS)
 Requests per second (RPS)
• Normalized by Active Users to isolate user engagement
• Project user engagement and Active Users independently

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Active Users aka User Growth
Normalized Core Drivers for Engagement
Core Drivers (cont’d)
PerActiveUserValues
Time
Favorites
Retweets
Poly. (Favorites)
Linear (Retweets)
ActiveUserCount
Time
Active
Users
Linear (Active
Users)

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Core Drivers (cont’d)
Time
User Growth: Active Users
Active
Users
Linear (Active
Users)
Time
Engagement: Photos/Active User
Photos
Linear (Photos)
Time
Core Driver: Photos per Day
Photos
Photos
Forecast

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Capacity Threshold
• Primary resource scalability threshold
 Determined by load testing
 Synthetic load
 Replaying production traffic
 Real-time production traffic
 Test systems may be
 Isolated replicas of production
 Staging systems in production
 Production systems
ServiceResponseTime
CPU
Average Response Times vs CPU
X

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Hardware Demand
• Core driver  capacity threshold  scaling formula  server count
• Example
 Core driver: Requests per Second
 Per server request throughput determined by
capacity threshold
 Scaling formula for Sizing
 Number of Servers = (RPS) / Per Server Threshold
CoreDriver(RPS)/ServerCount
Time
RPS (Actuals)
RPS (Forecast)
# Servers (Actuals)
# Servers (Forecast)

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Statistical Approach to Capacity Modeling

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Capacity Planning Methodology
• Predict expected value based on historical and temporal statistical analysis
 Metrics
 Average, Standard deviation, 95th, 99th percentile
 Techniques
 Moving Average – EMA (exponential moving average)
 Correlation
 β analysis
 MACD
 Forecasting - ARIMA
• Limitations
 Changing usage patterns
 Organic growth, behavioral, cultural
 Event driven
 Super Bowl: How a game would turn out?

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Capacity Planning Methodology (contd.)
• Correlation Analysis
 Assess the relation between resource metric(s) and core driver
 Caution: Correlation does not imply causation
Core Driver
Network
CPU
Time

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1
0.95
0.99
0.98
0.97
0.94
0.81
1
0.89
0.95
0.87
0.98
0.86
1
0.97
0.99
0.88
0.75
1
0.94
0.95
0.8
1
0.85
0.71
1
0.79 1
CoreDriver1
CoreDriver2
CoreDriver3
CoreDriver4
CoreDriver5
CoreDriver6
CoreDriver7
Core Driver 1
Core Driver 2
Core Driver 3
Core Driver 4
Core Driver 5
Core Driver 6
Core Driver 7
Core Driver Correlations
Capacity Planning Methodology (contd.)
• Correlation matrix
 Capture interactions in a Service Oriented Architecture (SOA)
 Other Use: User engagement

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Rolling Correlation
Time
Capacity Planning Methodology (contd.)
• Correlation varies over time
 Growing user base
 New products, features
• Rolling correlation analysis – capture time varying nature
 Raw times series
 EMA
 Challenge: What should be the window width?

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Capacity Planning Methodology (contd.)
• Relative Growth
 How does INTC moves with respect to S&P 500?
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
12/13/08
12/20/08
12/27/08
1/3/09
1/10/09
1/17/09
1/24/09
1/31/09
2/7/09
2/14/09
2/21/09
2/28/09
3/7/09
3/14/09
3/21/09
3/28/09
4/4/09
4/11/09
4/18/09
4/25/09
5/2/09
5/9/09
DailyReturns
S&P 500
INTC
β: 1.35
: β Analysis

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Capacity Planning Methodology (contd.)
0
200
400
600
800
1000
1200
1400
1600
0
200
400
600
800
1000
1200
1400
1600
Resource
CoreDriver
Time
Core Driver
Resource
β: 1.08
• Relative Growth:β Analysis
 Relative growth of a core driver and a resource driver

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Capacity Planning Methodology (contd.)
• β varies over time
 New products, features
 New metric to log
Rolling Beta
Time

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Capacity Planning Methodology (contd.)
• Growth: Detecting breakout
 MACD: Moving Average Convergence Divergence
 Difference of n- and m-width, n>m, EMA
 Diverging EMAs
o Commonly used as a
buy/sell signal in
context of a stock
o Early detection of
potential capacity ask
"MACD"
MACD Signal
Time

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Acknowledgements
• Winston Lee, Capacity Engineer, Twitter
• Management team

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Join the Flock
• We are hiring!!
 https://twitter.com/JoinTheFlock
 https://twitter.com/jobs
 Contact us: @bryce_yan, @arun_kejariwal
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