OPERROR OCCURRED WHEN COMMUTER FLC DIDN'T DSND FROM 11000 FT TO 10000 FT AS THE CTLR'S XMISSION WAS CUT OUT AND FLC COULD NOT CONFIRM THE CLRNC DUE TO FREQ CONGESTION. RPTR RECEIVED TCASII ALERT ON AN AIRBUS VISUALLY SIGHTED AT THE SAME ALT. RPTR DELAYED A SUBSEQUENT VECTOR TURN UNTIL THE AIRBUS HAD PASSED.

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WHILE ENRTE TO MIA FROM MYGF (FREEPORT; BAHAMAS); ESTABLISHED ON BR68V AND INTERCEPTING V295 TO VKZ; IT WAS BELIEVED THAT WE WERE GIVEN A DSCNT TO 10000 FT FROM OUR PRESENT ALT OF 11000 FT. HOWEVER; THERE WAS EXTREMELY HIGH CONGESTION ON THE FREQ AND PART OF THE CTLR'S XMISSION WAS CUT OUT. WE WANTED TO CONFIRM THE BELIEVED DSCNT INSTRUCTION BUT COULD NOT DO SO; THEREFORE WE STAYED LEVEL AT 11000 FT. SOON AFTER; WE WERE ALERTED BY TCASII OF TFC AT 4 O'CLOCK; SAME ALT; SAME HDG. WHILE GETTING THE TFC IN SIGHT (AN AIRBUS) WE WERE GIVEN A HDG CHANGE TO 270 DEGS -- RIGHT INTO THE TFC. STILL UNABLE TO ADVISE DUE TO CONGESTION; WE PURPOSELY DELAYED OUR TURN SO AS TO PASS BEHIND THE FAST-MOVING TFC. IT WAS LATER LEARNED THAT ONE CTLR WAS TRAINING ANOTHER; WHICH EXPLAINED THE CHANGE OF VOICES ABOUT MIDWAY THROUGH THIS EVENT. IT IS MY FEELING THAT THE AREA WAS FAR TOO BUSY TO BE HANDLED BY JUST 1 PERSON; AS CONFIRMATIONS OR EVEN ACKNOWLEDGEMENTS TO GIVEN INSTRUCTIONS COULD NOT BE EASILY MADE. A SIMILAR PROB IS ENCOUNTERED AT MIA WHEN ON TWR AND/OR GND FREQS DURING CERTAIN PERIODS OF THE DAY.