ZMA CTLR VOICED CONCERN REGARDING ACR'S FAILURE TO CONTACT ENROUTE FACILITIES AS REQUIRED AFTER WX DEV RTE WAS FILED BY COMPANY.

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ACR X FLYING FROM SAN JUAN; PR (TJSJ) RE-FILED THE FLT PLAN THROUGH SANTO DOMINGO AND PORT AU PRINCE'S AIRSPACE FOR WX AVOIDANCE. PLT NEVER CALLED SANTO DOMINGO ATC NOR PORT AU PRINCE CTRS. THE MAP CLRLY SHOWS THE FIR BOUNDARIES; RADIO CONTACT INSTRUCTIONS AND XFER POS. ACR X CHKS IN WITH ZMA ABOUT 20 MI FROM THE BOUNDARY ON THE CORRECT FREQ SO THERE APPEARS TO BE A MAP IN THEIR FLT BAG. ZMA SECTORS FOR THE LAST 3 DAYS HAVE HAD NUMEROUS ACFT VIOLATE THEIR AIRSPACE BECAUSE PLTS OR COMPANIES WERE CHANGING FLT PLANS; BUT NOT ADVISING CTRS -- SANTO DOMINGO OR PORT AU PRINCE -- THEN FLYING THROUGH THEIR AIRSPACE AND TRYING TO HAVE ZMA PERFORM THE REQUIRED FLT DATA FUNCTIONS OF RTE CHANGES AND NOTIFICATIONS. MIAMI FSS AT GRAND TURK WAS EXPERIENCING SIGNIFICANT DELAYS IN PROVIDING SVC THE ENTIRE WKEND AND THE ACFT CREWS WERE CALLING ZMA TO ATTEMPT TO RESOLVE THE ISSUES. A NOTAM SHOULD BE DISTRIBUTED ADVISING ALL ACFT FLYING IN THE REGION BTWN HAVANA CTR (MUHA); ZMA; PORT AU PRINCE; SANTO DOMINGO; JAMAICA; AND ARUBA TO CALL THE APPROPRIATE CTR 10 MINS PRIOR TO THE BOUNDARY.