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Every patch has a different scope, and every environment requires a different set of tests. If i'm reading your question properly, as in "how long does it take to test patch changes", its not possible to answer. If you're just asking how long it takes to run the patch, then the answer is under 1 minute.
You may find that this is not the root cause of your issue, but I personally wouldn't try to troubleshoot that type of behavior until its over, since you have no easy way of knowing if the DDos is causing your issue. I've seen some strange paypal functionality today that i've never seen in years working with it.
