BE200 HAS DIFFICULTY ESTABLISHING COMS WITH ZMA IN THE CARIBBEAN AIRSPACE DUE TO CTLR WORKING 4 FREQS.

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WE WERE APCHING TADPO INTXN. HAVANA CTR TOLD US TO CONTACT MIAMI ON 132.7. WE CHKED IN WITH MIAMI AND INFORMED THEM WE WERE LEVEL FL280 AND RPTED OUR ESTIMATED TIME TO CROSS TADPO. WE RECEIVED NO ANSWER. IT APPEARED THAT THE CTLR WAS VERY BUSY. THE FREQ WAS VERY CONGESTED. WE ATTEMPTED TO CONTACT MIAMI AGAIN UPON XING TADPO. AGAIN; WE RECEIVED NO RESPONSE FROM MIAMI. SEVERAL OTHER ACFT; INCLUDING AIRLINERS; ALSO TRIED TO CHK ON AT TADPO. THE CTLR RESPONDED THAT ALL ACFT STAND BY. HE SAID WE WERE STEPPING ON EACH OTHER ON THE FREQ AND THAT HE WAS COVERING 4 FREQS. WE ATTEMPTED TO CONTACT MIAMI AGAIN UPON XING MTH NDB; AND AGAIN RECEIVED NO RESPONSE. THERE WAS A VERY LARGE LINE OF TSTMS ON OUR RTE OF FLT. THE WORST OF THE STORMS APPEARED TO BE OVER OR NEAR DHP VOR WHICH BY COINCIDENCE WAS OUR NEXT WAYPOINT. WE THEN CONTINUED MONITORING ZMA ON OUR ASSIGNED FREQ; BUT WE SWITCHED THE XMITTER OVER TO #2 AND TRIED CONTACTING ZMA ON GUARD FREQ (121.5). WE NEVER RECEIVED A RESPONSE. WE THEN SWITCHED THE XMITTER BACK TO #1 AND TOLD ZMA THAT WE NEEDED A W DEV FOR WX. NO RESPONSE. WE THEN XMITTED TO ZMA THAT IF THEY DID NOT ACKNOWLEDGE US WE WERE GOING TO DECLARE AN EMER. THEY THEN RESPONDED AND ASKED IF WE WERE DECLARING AN EMER. WE RESPONDED THAT WE WERE NOT; BUT THAT IF WE DID NOT GET A TURN WE WOULD HAVE NO CHOICE BUT TO DECLARE AND DEV FROM OUR RTE OF FLT. WE TOLD ZMA THAT WE DID NOT EVEN KNOW IF WE WERE RADAR IDENTED AND THAT CONCERNED US. ZMA THEN SAID WE WERE RADAR CONTACT; AND THAT WE NEEDED TO TURN L TO A HDG OF 270 DEGS. WE COMPLIED. FLEW W FOR SEVERAL MI AND MISSED THE WX BY GOING AROUND IT. WHAT CONCERN ME IS THAT CTLR WORKLOAD SEEMS TO BE INCREASING. COVERING MORE THAN 1 FREQ SEEMS TO BE THE NORM; NOT THE EXCEPTION. THIS IS FINE EARLY MORNING IN KANSAS; BUT ON A SATURATED SOUTHERN MIAMI SECTOR; WHEN WX IS PRETTY MUCH EVERYWHERE; AN OVERWORKED CTLR IS A BAD THING. THIS IS A SERIOUS PROB AND CONTINUES TO WORSEN.