MD81 CREW RECEIVES TCAS RA WEST OF PIE AT FL350.

Narrative

HVY ATC WORKLOAD DUE TO NUMEROUS ACFT BEING CTLED WITH ZMA NOT TAKING HDOFS. DURING RADAR VECTORING DUE TO ZMA UNABLE TO TAKE HDOF FROM ZJX AN RA FROM TCAS COMMANDED A DSCNT. WE DSNDED TO FL340 AND HEARD ON THE FREQ AN ACR Y FLT ALSO HAD AN RA WHICH COMMANDED A CLB. WHEN WE QUERIED ZJX AS WELL AS ACR Y XMITTING THEY HAD AN RA. ZJX GAVE ACR Y A CLRNC TO DSND TO FL340 (OPPOSITE THE RA COMMAND FROM THEIR TCAS). FORTUNATELY; ACR Y FOLLOWED THEIR TCAS RA. THIS EVENT OCCURRED JUST OFF THE COAST FROM ST PETERSBURG; FL. SUBSEQUENT TO THIS EVENT AND AFTER BEING GIVEN A HOLDING CLRNC AT THE PIE VOR; WE RESPONDED WE COULDN'T HOLD DUE TO INSUFFICIENT FUEL. WE NOTIFIED DISPATCH AND AGREED TO DIVERT TO RSW ALONG WITH A HOST OF OTHER FLTS DUE TO ZMA DELAYS INTO SOUTH FLORIDA DUE TO WX. DURING THE RA FROM OUR TCAS; WE VISUALLY SIGHTED THE ACR Y B757 IN A PRONOUNCED NOSE-UP ATTITUDE DIRECTLY IN OUR PATH. ONBOARD TCAS ISSUED AN RA. AFTER HEARING ON THE RADIO THE EVENT UNFOLDING AS WELL AS VISUALLY SIGHTING OTHER ACFT WE DETERMINED AN EVENT OCCURRED. AFTER CONCLUSION OF EVENT WE QUERIED ATC TO WHAT TOOK PLACE. EXTRA VIGILANCE ON THE PART OF ATC WHEN OPERATING/CTLING DURING PERIODS OF HVY TFC/HIGH WORKLOAD.