AN A320 FLYING NEAR MIA RPTS HVY TFC AND CONGESTED COM FREQ RESULTING IN A TCASII RA.

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I WOULD LIKE TO INFORM YOU THAT ON MY FLT ON THE RTE MANAGUA-MIAMI I HAD TO EXECUTE A TCASII RA WHILE ON CTL OF MIAMI APCH. THE TFC AT THE ARPT WAS VERY HVY. THE MIAMI APCH FREQ WAS ALSO CONGESTED WITH MANY TFC COMING INTO MIAMI ARPT AT THE SAME TIME. SEVERAL TIMES THE ATC INSTRUCTIONS WERE BLOCKED. COMING FROM TADPO INTXN; WE WERE TOLD BY MIAMI ATC TO FLY DIRECT TO WEVER INTXN. SINCE THE WX ON THE ARR WAS FULL OF TSTMS WE WERE VECTORED AROUND THEM AND ALSO FOR SEQUENCING FOR THE APCH TO THE ILS RWY 9R. WE WERE CLRED TO DSND TO 10000 FT. WE WERE AT 10000 FT AND WE STAYED AS INSTRUCTED ON THE ASSIGNED SPD; HEADING; AND ALT. THIS HEADING TOOK US AGAINST THE WIND TO RWY 9R ON A L TFC PATTERN. WE WERE TOLD THAT THIS VECTOR WAS FOR SEQUENCING. ONCE WE WERE ABEAM THE ARPT WE WERE GIVEN A L HEADING THAT TOOK US TO THE N OF THE ARPT. IT IS ON THIS N HEADING VECTOR THAT WE AT 10000 FT DETECTED A TA ON THE TCASII. THIS TFC (EITHER AN AIRBUS 300 OR A B767) WAS COMING AT OUR 2 O'CLOCK POS AT THE SAME ALT (10000 FT); AT ABOUT 6 MI AWAY AND IT WAS CLR THAT WE WERE ON A CONVERGING COLLIDING PATH. WE RPTED TO MIAMI ATC THAT WE HAD THE TA AT THE SAME ALT ON THE TCASII. THE JET ALSO RPTED TO ZMA THAT HE HAD A TFC ON THE TCASII AT THE SAME ALT; BUT ZMA RESPONDED TO THE JET THAT THE TFC WAS NOT A FACTOR BECAUSE IT WAS IN THE PROCESS OF DSNDING. SINCE I KNEW THAT WE WERE NEVER TOLD TO DSND TO ANY ALT (WE WERE GIVEN ONLY HEADING; SPD; AND ALT 10000 FT) I PROCEEDED TO EXECUTE A CLB OUT OF THE DANGER AREA. AS I WAS ON THE INITIAL CLB I GOT THE TCASII RA TO CLB. I RPTED TO ZMA THAT I WAS EXECUTING A TCASII RA COMMAND. ONCE OUT OF THE DANGER AREA I WENT BACK TO MY ASSIGNED ALT; 10000 FT; AS WELL AS HEADING AND SPD. WE WERE VECTORED AROUND ON A L DOWNWIND LEG AND FINALLY LANDED NORMALLY ON RWY 9R. IT WAS OBVIOUS THAT WHEN WE DETECTED THE TFC AT THE SAME ALT COMING IN A CONVERGING PATH TOWARDS US SOMETHING WAS NOT RIGHT. SINCE WE NEVER RECEIVED A CLR INSTRUCTION TO DSND TO A LOWER ALT WE KNEW THEN THAT WE HAD TO GET OUT OF THE DANGER ZONE. CONTRIBUTING FACTORS: MANY ACFT ARRIVING AT THE SAME TIME. MANY ACFT TRYING TO COMMUNICATE AT THE SAME TIME. BLOCKING OF ATC INSTRUCTIONS BY OTHER ACFT THAT ARE TRYING TO COMMUNICATE WITH ATC. TOO MANY ACFT FOR MIAMI APCH CTLR TO HANDLE AT THE SAME TIME. WX AROUND THE TFC PATTERN. MY PERCEPTION WAS THAT SINCE THE TFC WAS SO HVY AND SINCE ATC TOLD ME THAT THE VECTORS WERE FOR SEQUENCING FOR THE APCH; THAT IT WAS REASONABLE TO BE FLYING AROUND THE ARPT AT 10000 FT. MY JUDGEMENT TOLD ME THAT IT WAS NOT OK FOR 2 ACFT TO BE FLYING AT THE SAME ALT AND IN A CONVERGING PATH. MY DECISION AS A PIC WAS TO TAKE THE NECESSARY ACTIONS TO GET MYSELF OUT OF THE DANGER AREA. THE ACTION TAKEN WAS A CORRECTIVE ONE. I BEGAN TO CLB OUT OF THE DANGER AREA AND THEN THE TCASII BEGAN TO GIVE ME RA'S. ONCE CLR OF THE TFC I DSNDED BACK TO MY ORIGINAL ALT.