To bring queuing down to an acceptable level (<10ms), you’d need to crank your app to 4,000 dynos, or fifty times your allotment in the intelligent case.

from James Somers (Ft. Andrew Warner, ATodd, Chrissy & LEMON) – Heroku's Ugly Secret on Rap Genius

Meaning

And of course the naive router scales much worse too. Here are the results from re-running the same simulation with 18,000 requests per minute instead of 9,000 requests per minute:

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