The interesting thing about flying with TCAS, as I do,
is that the skies are far busier than you ever
thought they were when you were flying without
it's assistance.
One part of Andrews's paper I didn't describe was a comparison of the 'unalerted' visual acquisition capability with the TCAS equipped equivalent. The results were, as you would expect, vastly better. 57 of 66 targets were acquired, and 5 were not acquired because avoiding action prevented a visual sighting. Moreover, targets were sighted earlier giving the pilots a much better chance to assess the threat and take avoiding action. In the terms of the paper, the probability of sighting per unit time per unit solid angle of target was increased by a factor of about 9.
The problem with the portable collision avoidance units is that they don't give any azimuthal indication (i.e. relative bearing to the target). It's that that is the main contributor to increasing acquisition probability. Simply knowing that something is out there and getting closer doesn't help much unless you know where to look.