Not sure management can really do anything about a 56k satellite connection. In this particular case, the once-an-hour check via script instead of having to open Outlook sounds like a viable solution to this specfic problem.
BTW,one reason I sometimes don't leave message is because I rotate through two or three different people to get an urgent answer that require some one-to-one information exchnage that might not be doable as efficiently via email.
BTW2, we have an official 24 hour response window for most regular requests and communications, unless it is something urgently timed. However, we have times where we require response times within minutes/hour due to the criticality of the issue at hand. You don't want to derail a $100M deal just because you didn't answer your email and a ratings agency is now trashing your bond ratings 
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There are two types of vessels, submarines and targets.
