[ucarion]

This sounds a lot like the control-theory problem of balancing the proportional, integral, and derivative coefficients of a PID controller [1]?

I'm curious how you reached this condition as a requirement:

> The moral of the story here is make sure you pick a metric that reacts to the change in request rate as quickly as your request rate changes!

It makes sense intuitively, but I'm having trouble proving to myself that this is necessary+sufficient.

[1]: https://en.wikipedia.org/wiki/PID_controller

[jedberg]

So I studied control theory after I left Reddit and you’re indeed right, it’s a PID issue.

Picking a metric that reacts to changes quickly is neither necessary nor sufficient, but it certainly helps reduce the error on your calculation. You need to know how far off your set point you are and so you need as accurate a measurement as possible.

Imagine a cruise control for a car where the speedometer had a five second delay. You’d still stay at your desired speed on average but it would vary a lot more and require more work to get back to the desired speed. It would have to accelerate harder and brake harder.

[ucarion]

Oh I see! I was misunderstanding what you meant by "quickly"; it seems you're referring to the sensor delay / how tight the feedback loop is.

Thanks for explaining!

[brandmeyer]

See also Bode stability analysis.

Delay in the feedback path counts against phase margin, requiring you to reduce the loop bandwidth to maintain stability.