As a developer of ATC safety nets equipment and a sometime pilot, it's also important to point out that normally the pilot is following ATC instructions while in controlled airspace. If a TCAS RA is indicated the pilot should report it and report when the TCAS RA encounter is completed - clear of conflict. Downstairs, ATC are hopefully watching their radar display. They may already be noticing the potential conflict and be about to issue avoidance instructions that are contradictory to the sense (climb/descend) of the RA instructions. Hence by notifying ATC, the pilot should not be given instructions by ATC, in order to avoid a conflicting set of instructions being given.
Remember also, that Short Term Conflict Alert (STCA) is fitted in many ATC units. This is a ground based conflict prediction system that uses radar derived positions and flight levels, calculated tracks and ground speeds, as opposed to TCAS, which is airborne. STCA may also be predicting the loss of separation and this is unknown to the pilot, until an instruction is given by ATC. On most systems, ATC do not know that the pilot is experiencing an RA. Some later systems have the capability to downlink the TCAS RA indication and sense and display this on the radar display, on the label information for the target. This requires a TCAS equiped aircraft, a Mode S equipped aircraft, a Mode-S radar, and a Mode-S capable ground surveilliance system. When the TCAS RA label is displayed, perhaps even at the same time as a STCA warnings, ATC now know that the pilot has been given an RA to follow, even if the pilot has not reported it.
All the information I can find is quite simple.
If the pilot is given an RA, he follows it, deviating from ATC clearance if necessary. He/She informs ATC. ATC monitor the situation. After encounter pilot reportes RA over and ATC will then manage the situation, since it's likely that the aircraft has departed from the assigned flight level.
Presumably airlines write these instrucitons into their operating procedures - not being a commercial pilot I don't know.
There's no need to call PAN PAN PAN, MAYDAY or whatever. The TCAS system is designed to give appropraite avoidance instructions. Obviously, if ATC, pilots, and systems never made mistakes, or took their eye of the ball, we wouldn't need such a system. It's just another safety net, like the height between you and mountains below.
