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The Maths behind
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
Orchestration
Cattle not pets
Heterogenous services
True for regular
autoscaling too
VMs take much longer to scale
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
numberofcontainersn
x(t) is proportional to n(t)
nope!
error e
time t
numberofcontainersn
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
Control theory!
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?
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/microscaling
app.microscaling.com
Liz Rice
@lizrice | @microscaling
The maths behind microscaling
The maths behind microscaling
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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.

Published in: Technology
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The maths behind microscaling

  1. 1. The Maths behind Microscaling Liz Rice @lizrice | @microscaling
  2. 2. What is Microscaling? Assumptions Some theory Some experiments
  3. 3. What is Microscaling?
  4. 4. Traffic spike
  5. 5. Too much work Spare capacity
  6. 6. container scaling work performance metrics
  7. 7. work performance metrics container scaling VM autoscaling
  8. 8. Orchestration Cattle not pets Heterogenous services
  9. 9. True for regular autoscaling too VMs take much longer to scale
  10. 10. Performance targets
  11. 11. How many containers? Request processing time Rate of requests known? predictable?
  12. 12. performance target actual performance error time t
  13. 13. performance target p time t actual performance x e(t) = x(t) - p(t) e(t) → 0 error e
  14. 14. x(t) is proportional to n(t) n(t) = k x(t) error e time t numberofcontainersn
  15. 15. x(t) is proportional to n(t) nope! error e time t numberofcontainersn d(t) is proportional to e(t) d
  16. 16. Time delays It’s a dynamical system
  17. 17. Woah, the future! error e time t d(t) is proportional to e(t + T) T d
  18. 18. Control theory!
  19. 19. error e time t Proportional term d(t) = Kp e(t) The further we are from target the more containers we need
  20. 20. error e time t Derivative term The faster we approach target the fewer containers we need d(t) = Kp e(t) + Kd ė(t)
  21. 21. error e time t Integral term d(t) = Kp e(t) + Kd ė(t) + Ki e(t) Offset errors accumulated over time ∫
  22. 22. Which values for K? Discrete containers?
  23. 23. Simulator
  24. 24. It works! But it’s non-trivial to tune
  25. 25. Known behaviours Machine learning
  26. 26. Container parameters = metadata Talk to us about advantages of container labelling
  27. 27. github.com/microscaling app.microscaling.com Liz Rice @lizrice | @microscaling

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