Silly Dilbert, the first thing you should do in that sort of environment is book out blocks of time in your calendar for yourself. For instance I knew a guy who had 12-1 booked every single day (I noticed this when I tried to book a meeting with him) so that he could have lunch and wouldn't have to worry about people booking him in meetings throughout the whole day. I also set a start and end time in the hated Lotus Notes so that people could book meetings with me before 8:30 or after 5. If you've got a project due, book out the day as a meeting so no one can bother you with meeting requests. Easy.
I remember attending nine different one-hour meetings in a single day. A PHB who was in our 8:00 a.m. meeting asked me at a 4:00 p.m. meeting "Did you take care of the action items from this morning?"