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I saw this statement awhile ago, and I'm bit confused about how it works.

Suppose you have an email server that can only receive 3 emails every minute, and additional emails are filtered out. (Aside: It's not clear to me if every minute is disjoint if it this is a rolling 1 minute window, but I think it's the former.) The emails received by this email server are sent to a single person. Now it is stated that this condition guarantees that the person won't receive more than 5 messages every 10 seconds, though I don't see how this is possible if my aside is correct?

Here's an example that seems to contradict the premise. Suppose in the first minute you have emails that come in at the $58, 59, 60$ second mark, and in the second minute you have emails coming in at $61, 62, 63$ mark. All these emails will be processed by the email server, and all these emails are also within a 10 second interval, contradict the premise. Am I missing something here?

If my aside is incorrect, and it's the latter where you have a rolling 1 minute window, then I think the premise may be correct, though there should be a stricter condition? It seems the stricter condition is that the person can't receive more than 3 messages every 10 seconds, otherwise it violates the 3 emails every minute criteria.

roulette01
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    I think the rolling window is the best assumption. I think that then the person can't get more than three messages per minute in their rolling window. So you might be misremembering some details from the statement you saw a while ago. Without more precise information I don't think your question has an answer. – Ethan Bolker Dec 08 '23 at 15:53
  • Do you have a link? Because it sounds very implementation-specific. If it were based on clock reading of each minute, I'd expect 6 to be the max as in your example. If it were based on a rolling window I'd expect 3 to be the max. To get 5 would seem to require a strange algorithmic-implementation-specific combination of the two. – DotCounter Dec 08 '23 at 15:56
  • I agree with your analysis that if every minute is disjoint, then the person can receive $~6~$ emails in 10 seconds. If the rolling window interpretation is correct, then the comment of @EthanBolker holds. – user2661923 Dec 08 '23 at 15:56

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