An air carrier Captain reported taking evasive action when numerous vehicles entered the safety parking zone as the aircraft was approaching its parking spot.

Narrative

During safe-gate parking; approximately 50 FT from the final stopping position; while the aircraft was in forward motion an one of our air carrier's vehicle towing two baggage carts in front of the aircraft drove from outside of the safe-gate clear zone into the clear zone completely and traveled under the right wing. I stopped the aircraft immediately; if not abruptly; when this vehicle first entered the clear zone. Moments later about a dozen vehicles began streaming in both directions in front of the aircraft; approaching from behind and from under the wingtips. Our Operations was called with the vehicle number of the first offending vehicle and a ground. Ramp Supervisor was requested. After a nine minute delay I was finally able to park the aircraft. For more then TEN YEARS I have identified these types of ramp safety issues at MIA; phone calls to Miami Ramp Supervisors; field debriefs with ramp Supervisors and meetings with former Miami Chief pilots. Written reports respond by saying they will 'track' the problem. Supervisors say the ramp workers 'know better.' Behavior remains unacceptable; putting the safety of the aircraft at risk as well as that of those working on the ramp. Since none of this has remedied the problem I can only hope that by contacting the FAA with their threat of enforcement action might lead to a safe resolution. I am requesting your assistance in this process.