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Gimme More! !
Supporting User Growth in a!
Performant and Efficient Fashion
Arun Kejariwal, Winston Lee

(@arun_kejariwal)

(@winstl)

Capacity Engineering @ Twitter

November 2013


@Twitter 1
User Experience
•  Anytime, Anywhere, Any device
q  5.2 billion mobile users by 2017 [1]
q  More than 10 billion mobile devices/connections by 2017 [1]
q  Worldwide mobile data traffic will reach 11.2 exabytes/month by 2017 (13x increase) [1]

•  Real-time performance








[1] http://newsroom.cisco.com/release/1135354 (Feb. 5, 2013)

@Twitter 2
Capacity Planning: Why bother?
•  Organic growth
q  Over 230M monthly active users [1]

•  User engagement
•  Evolving product landscape
q  Cards, Photos, Vines
§  Mobile video will increase 16-fold between 2012 and 2017 [2]

•  Events planned or unplanned





[1] http://www.sec.gov/Archives/edgar/data/1418091/000119312513400028/d564001ds1a.htm
[2] http://www.cisco.com/en/US/solutions/collateral/ns341/ns525/ns537/ns705/ns827/white_paper_c11-520862.html

@Twitter 3
Approaches to Capacity Planning
•  Throw hardware at the problem
o  How much?
o  What kind? (Inventory management etc.)
o  Operationally inefficient!

•  Reactive approach


Bottomline

Poor UX



@Twitter 4
Systematic Capacity Planning
•  Objectives
q  Check under-allocation
§  Performance
§  Availability
o 

Adversely impact user experience 

q  Check over-allocation
§  Operational efficiency
o 

Adversely impacts bottomline

•  Determine capacity needed proactively via forecasting
q  Business metrics
q  System resource usage



@Twitter 5
Systematic Capacity Planning: Forecasting
•  Key questions
q  Which data?
§  Raw
§  Periodic Max
§  Moving average

q  Data granularity
§  Minutely
§  Daily
o 

Depends

q  Which model?
§  Linear
§  Spline
§  Holt-Winters

Non-Trivial!

§  ARIMA



@Twitter 6
Good old Linear Regression
Linear Regression based Forecast
Adjusted R-squared: 0.6062
Raw Data

Forecast

@Twitter 7
Linear Regression using periodic max
Linear Regression Using Maxes based Forecast
Adjusted R-squared: 0.5673
Standard Error

2.45x

Raw Data

Forecast

@Twitter 8
Splines
•  Smooth Spline
q λ: penalty for “wiggliness”
Spline based Fitting
Raw Data

Fitted

@Twitter 9
Splines
Spline based Forecast
Raw Data

Forecast

@Twitter 10
Splines
Boundary 2

Boundary 1

•  Sensitive to nature of time series at the boundary

@Twitter 11
Splines – Take 2
Spline based Forecast (Boundary 1)
Raw Data

Forecast

8.31x higher than end of time series

@Twitter 12
Splines – Take 3
Spline based Forecast (Boundary 2)
Raw Data

Forecast

3.77x higher than end of time series

@Twitter 13
Holt-Winters
•  Triple exponential smoothing
Estimate of linear trend
Seasonal correction factors
Holt-Winters based Fitting
Raw Data

Fitted

@Twitter 14
Holt-Winters
Holt-Winters based Forecast
Raw Data

Upper 95% CI

Forecast

@Twitter 15
ARIMA
•  Auto-Regressive Integrated Moving Average 
q  (p, d , q)
Moving Average order
Integrated order
Autoregressive order
Autoregressive component
Moving Average component

@Twitter 16
ARIMA
•  Fitting

Auto ARIMA based Fitting
Raw Data

Fitted

@Twitter 17
ARIMA – Take 1
ARIMA based Forecast

(p, d, q): (0,1,1)(0,1,1)[7] 

Raw Data

Upper 95% CI

Forecast

@Twitter 18
ARIMA – Take 2
Auto ARIMA based Forecast

(p, d, q): (1,1,1)(2,0,0)[7]

Raw Data

Upper 95% CI

Forecast

@Twitter 19
Impact of Outliers

@Twitter 20
Forecast without outlier

@Twitter 21
Good “enough”?

@Twitter 22
Impact of “Corrections”

@Twitter 23
Implications of data characteristics
ARIMA based forecast
Raw Data

Upper 95% CI

Forecast

@Twitter 24
Forecast without the boundary case
ARIMA based Forecast - 
Without initial spike
Raw Data

Upper 95% CI

Forecast

@Twitter 25
Forecast with truncation
ARIMA based Forecast - Truncated and Without initial spike

Raw Data

Upper 95% CI

Forecast

@Twitter 26
Lessons learned
•  Data fidelity
q  Anomalies
q  Absence of seasonality

•  Modeling
q  Never perfect
§  Assess forecasting error

q  Continuous refinement
§  Incoming data stream is dynamic
o 

Organic growth

o 

New products

o 

Behavioral aspect



@Twitter 27
Acknowledgements
•  Capacity Engineering Team
•  Management team

@Twitter 28
Join the Flock

Like problem solving? 

Like challenges? 

Be at cutting Edge 

Make an impact

•  We are hiring!!
q  https://twitter.com/JoinTheFlock
q  https://twitter.com/jobs
q  Contact us: @arun_kejariwal, @winstl

@Twitter 29

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Gimme More! Supporting User Growth in a Performant and Efficient Fashion

  • 1. Gimme More! ! Supporting User Growth in a! Performant and Efficient Fashion Arun Kejariwal, Winston Lee (@arun_kejariwal) (@winstl) Capacity Engineering @ Twitter November 2013 @Twitter 1
  • 2. User Experience •  Anytime, Anywhere, Any device q  5.2 billion mobile users by 2017 [1] q  More than 10 billion mobile devices/connections by 2017 [1] q  Worldwide mobile data traffic will reach 11.2 exabytes/month by 2017 (13x increase) [1] •  Real-time performance [1] http://newsroom.cisco.com/release/1135354 (Feb. 5, 2013) @Twitter 2
  • 3. Capacity Planning: Why bother? •  Organic growth q  Over 230M monthly active users [1] •  User engagement •  Evolving product landscape q  Cards, Photos, Vines §  Mobile video will increase 16-fold between 2012 and 2017 [2] •  Events planned or unplanned [1] http://www.sec.gov/Archives/edgar/data/1418091/000119312513400028/d564001ds1a.htm [2] http://www.cisco.com/en/US/solutions/collateral/ns341/ns525/ns537/ns705/ns827/white_paper_c11-520862.html @Twitter 3
  • 4. Approaches to Capacity Planning •  Throw hardware at the problem o  How much? o  What kind? (Inventory management etc.) o  Operationally inefficient! •  Reactive approach Bottomline Poor UX @Twitter 4
  • 5. Systematic Capacity Planning •  Objectives q  Check under-allocation §  Performance §  Availability o  Adversely impact user experience q  Check over-allocation §  Operational efficiency o  Adversely impacts bottomline •  Determine capacity needed proactively via forecasting q  Business metrics q  System resource usage @Twitter 5
  • 6. Systematic Capacity Planning: Forecasting •  Key questions q  Which data? §  Raw §  Periodic Max §  Moving average q  Data granularity §  Minutely §  Daily o  Depends q  Which model? §  Linear §  Spline §  Holt-Winters Non-Trivial! §  ARIMA @Twitter 6
  • 7. Good old Linear Regression Linear Regression based Forecast Adjusted R-squared: 0.6062 Raw Data Forecast @Twitter 7
  • 8. Linear Regression using periodic max Linear Regression Using Maxes based Forecast Adjusted R-squared: 0.5673 Standard Error 2.45x Raw Data Forecast @Twitter 8
  • 9. Splines •  Smooth Spline q λ: penalty for “wiggliness” Spline based Fitting Raw Data Fitted @Twitter 9
  • 10. Splines Spline based Forecast Raw Data Forecast @Twitter 10
  • 11. Splines Boundary 2 Boundary 1 •  Sensitive to nature of time series at the boundary @Twitter 11
  • 12. Splines – Take 2 Spline based Forecast (Boundary 1) Raw Data Forecast 8.31x higher than end of time series @Twitter 12
  • 13. Splines – Take 3 Spline based Forecast (Boundary 2) Raw Data Forecast 3.77x higher than end of time series @Twitter 13
  • 14. Holt-Winters •  Triple exponential smoothing Estimate of linear trend Seasonal correction factors Holt-Winters based Fitting Raw Data Fitted @Twitter 14
  • 15. Holt-Winters Holt-Winters based Forecast Raw Data Upper 95% CI Forecast @Twitter 15
  • 16. ARIMA •  Auto-Regressive Integrated Moving Average q  (p, d , q) Moving Average order Integrated order Autoregressive order Autoregressive component Moving Average component @Twitter 16
  • 17. ARIMA •  Fitting Auto ARIMA based Fitting Raw Data Fitted @Twitter 17
  • 18. ARIMA – Take 1 ARIMA based Forecast (p, d, q): (0,1,1)(0,1,1)[7] Raw Data Upper 95% CI Forecast @Twitter 18
  • 19. ARIMA – Take 2 Auto ARIMA based Forecast (p, d, q): (1,1,1)(2,0,0)[7] Raw Data Upper 95% CI Forecast @Twitter 19
  • 24. Implications of data characteristics ARIMA based forecast Raw Data Upper 95% CI Forecast @Twitter 24
  • 25. Forecast without the boundary case ARIMA based Forecast - Without initial spike Raw Data Upper 95% CI Forecast @Twitter 25
  • 26. Forecast with truncation ARIMA based Forecast - Truncated and Without initial spike Raw Data Upper 95% CI Forecast @Twitter 26
  • 27. Lessons learned •  Data fidelity q  Anomalies q  Absence of seasonality •  Modeling q  Never perfect §  Assess forecasting error q  Continuous refinement §  Incoming data stream is dynamic o  Organic growth o  New products o  Behavioral aspect @Twitter 27
  • 28. Acknowledgements •  Capacity Engineering Team •  Management team @Twitter 28
  • 29. Join the Flock Like problem solving? Like challenges? Be at cutting Edge Make an impact •  We are hiring!! q  https://twitter.com/JoinTheFlock q  https://twitter.com/jobs q  Contact us: @arun_kejariwal, @winstl @Twitter 29