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The Maths behind Microscaling
Liz Rice@lizrice | @microscaling
What is Microscaling?AssumptionsSome 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
OrchestrationCattle not pets
Heterogenous services
True for regular autoscaling tooVMs take much longer to scale
Performance targets
How many containers?
Request processing time
Rate of requestsknown?
predictable?
performance target
actual performance
error
time t
performance target ptime 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
num
ber o
f con
tain
ers
n
x(t) is proportional to n(t)
nope!
error e
time t
num
ber o
f con
tain
ers
n
d(t) is proportional to e(t)
d
Time delaysIt’s a dynamical system
Woah, the future!
error e
time t
d(t) is proportional to e(t + T)
T
d
Control theory!
error e
time t
Proportional term
d(t) = Kp e(t)
The further we are from targetthe more containers we need
error e
time t
Derivative term
The faster we approach targetthe 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
It works!But it’s non-trivial to tune
Known behaviours
Machine learning
Container parameters =
metadata
Talk to us about advantages of container labelling
github.com/microscalingapp.microscaling.com
Liz Rice@lizrice | @microscaling
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