Update: the project described in this post no longer works due to Twitter API changes.
At some point last week, I realized that I could measure roughly how busy I was based on the inverse of the frequency of my posts to Twitter. Based on that, I've created the Twitter Busyness Average (similar to the familiar UNIX load average).
This measurement shows how busy somebody was in the last 2 days. The average = (k) / (hourly frequency of Tweets during the last 2 days).
The constant k is unique to each person; this should be adjusted to match the user's Twitter usage pattern. A target value for "standard", not particularly stressful, busyness is around 2. (For me, k ~= 0.75.)
To avoid division by zero, if you haven't Tweeted in the last 2 days, calculate the frequency as if you had Tweeted once.
This should require sufficiently few requests to the Twitter API that calculating it client-side is appropriate. I've created a quick jQuery plugin for this, and when I have some time, I'll also whip up a PHP script.