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The Maths of Microscaling
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Liz Rice
November 08, 2016
Technology
2
220
The Maths of Microscaling
Using control theory to scale containers in real time, in response to demand
Liz Rice
November 08, 2016
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Transcript
The Maths of Microscaling Liz Rice @lizrice | @microscaling
What is Microscaling? Assumptions Some theory Some experiments
What is Microscaling?
Traffic spike
Too much work Spare capacity
container scaling work performance metrics
work performance metrics container scaling VM autoscaling
True for regular autoscaling too VMs take much longer to
scale
Orchestration Heterogenous services Cattle not pets
Performance targets
How many containers? Request processing time Rate of requests known?
predictable?
performance target actual performance error time t
performance target p time t actual performance x e(t) =
x(t) - p(t) e(t) → 0 error e
x(t) is proportional to n(t) n(t) = k x(t) error
e time t number of containers n
x(t) is proportional to n(t) nope! error e time t
number of containers n d(t) is proportional to e(t) d
Time delays It’s a dynamical system
Woah, the future! error e time t d(t) is proportional
to e(t + T) T d
None
Control theory!
PID controller
error e time t Proportional term d(t) = Kp e(t)
The further we are below target the more containers we need
error e time t Derivative term The faster we approach
target the fewer containers we need d(t) = Kp e(t) + Kd ė(t)
error e time t Integral term d(t) = Kp e(t)
+ Kd ė(t) + Ki e(t) Offset errors accumulated over time ∫
Which values for K? Discrete containers?
Simulator goo.gl/KAqT5y
It works! But it’s non-trivial to tune
Known behaviours Machine learning
Container parameters = metadata microbadger.com
github.com/microscaling @lizrice | @microscaling app.microscaling.com microbadger.com