ZMA ASSOCIATE CTLR WITNESSED CLOSE CONFLICT AT 8000 FT BTWN IFR AND PARACHUTE ACFT DURING BUSY TFC WITH MINIMAL STAFFING.

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I WAS CONDUCTING OJT ON THE RADAR ASSOCIATE POS AT R67 (LAL LO) AT ZMA. THE RADAR CTLR IDENTED A PARACHUTE JUMP ACFT (ACFT X) AND ADVISED HIM TO REMAIN W OF TFC HE CALLED; WHICH WAS ACFT Y; AN SR22 ON AN IFR CLRNC AT 8000 FT. THE SECTOR WAS VERY BUSY AND PROBABLY SHOULD HAVE BEEN SPLIT. WE WERE VERY SHORT STAFFED (I WAS TRAINING FOR CLOSE TO 2 HRS STRAIGHT) AND COULD NOT SPLIT THE SECTOR BECAUSE WE HAD NO PERSONNEL. I BELIEVE IF THE SECTOR WAS SPLIT; THE WORKLOAD AND COMPLEXITY WOULD HAVE DIMINISHED TO THE POINT WHERE IT WOULD HAVE BEEN MANAGEABLE AND THE TFC CALL AND NON READBACK WOULD HAVE BEEN CAUGHT. AS IT WAS; THE R-SIDE DID NOT REALIZE THAT ACFT X DID NOT GET THE TFC CALL AND THE INSTRUCTION TO REMAIN W OF THE TFC. HE ALSO DID NOT HAVE TIME TO CALL THE TFC TO THE IFR ACFT (ACFT Y). THE R-SIDE RECEIVED AN OVERRIDE CALL AFTER ISSUING THE TFC TO ACFT X. I WAS TRAINING AND MY TRAINEE WAS ON THE LINE WITH APCH CTL COORDINATING; SO I WAS TRYING TO PAY ATTN TO BOTH AND DIDN'T HEAR ACFT X ACKNOWLEDGE. I INFORMED MY RADAR CTLR OF THIS; BUT IT WAS TOO LATE; AS THE 2 ACFT MERGED AT THE SAME ALT. THE IFR ACFT (ACFT Y) THEN INQUIRED ABOUT THE TFC; INFORMING US HOW CLOSE IT WAS. HE SAID HE SAW IT ON THE TCASII BUT NOT VISUALLY UNTIL IT WAS TOO LATE. I BELIEVE WE ARE IN A CRISIS SIT AT OUR FACILITY; STAFFING-WISE. WE CANNOT FULLY STAFF ALL THE POS AND; THEREFORE; THEY REMAIN CLOSED DURING BUSY PERIODS. WE ARE ALSO ASKED TO WORK BUSY POS ALONE; WITHOUT A RADAR ASSOCIATE WITH AS MANY AS 20 ACFT AT ONCE. WHEN WE NEED A RADAR TRACKER IF THE SECTOR HAS GOTTEN OUT OF CTL; THEY HAVE TO PULL TRAINERS AWAY FROM TRAINEES TO TRACK; LEAVING THE TRAINEES WORKING A POS THEY ARE NOT QUALIFIED TO WORK ALONE. WE ARE AN AGING WORK FORCE; AND WORKING 2 HR STRETCHES WITH 20-30 BREAKS IN BTWN IS CAUSING FATIGUE AND WILL LEAD TO ERRORS OR WORSE. TFC HAS INCREASED TREMENDOUSLY AND WE HAVE NOT ADAPTED AIRSPACE CHANGES OR STAFFING LEVELS ACCORDINGLY. WE HAVE LESS CPC'S NOW THAN AT ANY TIME SINCE THE STRIKE IN 1981. TRAINEES ARE NOT GETTING CERTIFIED BECAUSE TFC IS SO BUSY AND COMPLEX AND MGMNT IS AT A LOSS TO DO ANYTHING TO HELP.