Your windows service is watching an email inbox.

How often should it poll?

Once every 5 minutes? Every 10? Then of course you realise that it should be different for every customer… or maybe every mailbox. You need more config!

Or not.

The real answer, of course, is something completely different: it should poll a lot when a lot of emails are arriving, and not very much when they aren’t.

It took a lot longer than it should have done to get my maths brain back on, but with the help of my wife I eventually settled on this code for deciding the intervals between polls:

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let interval i =
    let x = float i
    let maxWait = 60. * 10.
    let raisePower x = pown (x /10.) 4
    (maxWait * (raisePower x)) / (raisePower x + 1.)
    |> (*) 1000. |> int

The ‘i’ in this function is the number of times we’ve polled since the last time a new email was received (if one is received, we reset i to 0).

If you plot this out on a graph, you get something that looks like this:

You can play with the shape of the graph at Wolfram|Alpha if you're feeling really geeky :).

This gives us very aggressive polling for the first few minutes after discovering an email, then dropping off rapidly to close to the one every ten minutes mark that I decided was a reasonable background polling rate.

It's not truly adaptive in the machine learning sense, but it gives a very good first cut that is an awful lot better than any fixed value could be.