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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