The maths behind microscaling

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The fast instantiation speed of containers promises a sea change in the way you scale workloads within your infrastructure, through the concept of microscaling In this talk we'll briefly make sure everyone is up to speed on the idea of microscaling, and then you'll explore some of the maths behind it, and look at the limits for what’s possible, both theoretically and experimentally. Find out more on microscaling at http://microscaling.org.

Technology

The Maths behind
Microscaling
Liz Rice
@lizrice | @microscaling

What is Microscaling?
Assumptions
Some theory
Some experiments

container scaling
work
performance metrics

work
performance metrics
container scaling
VM autoscaling

Orchestration
Cattle not pets
Heterogenous services

True for regular
autoscaling too
VMs take much longer to scale

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
numberofcontainersn

x(t) is proportional to n(t)
nope!
error e
time t
numberofcontainersn
d(t) is proportional to e(t)
d

Woah, the future!
error e
time t
d(t) is proportional to e(t + T)
T
d

error e
time t
Proportional term
d(t) = Kp e(t)
The further we are from 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?

Container parameters
=
metadata
Talk to us about
advantages of
container labelling

github.com/microscaling
app.microscaling.com
Liz Rice
@lizrice | @microscaling

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