AN ARTCC RADAR CTLR ISSUED A CLB TO ONE ACFT AND A DSCNT TO ANOTHER BELIEVING THAT SEPARATION COULD BE MAINTAINED. THE CTLR WAS NOT ABLE TO DEVOTE THE ATTN NEEDED DUE TO HVY TFC LOAD. WHEN SEPARATION BTWN THE 2 ACFT BECAME QUESTIONABLE; THE CTLR ISSUED TURNS; BUT NOT SOON ENOUGH.

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ACR Y WAS VECTORED OFF COURSE AND CLBED TO FL310 TO GET ON TOP OF A HOLDING PATTERN AT HOPEWELL THAT HE WAS GOING TO BE JOINING AS SOON AS HE GOT TO FL310. (WE WERE PUT INTO A HOLD FOR EWR AND HE WAS #5 TO GO INTO HOLD.) ACR X WAS GOING TO PHL AND DSNDED TO FL290. AT THE TIME; I DID NOT THINK THEY WERE GOING TO BE A FACTOR FOR ONE ANOTHER. ACR Y WAS CLBING VERY SLOWLY (LESS THAN 500 FPM) AND THIS WAS MISSED ON THE SCAN. SECTOR WAS VERY BUSY TRYING TO GET OTHER ACFT ESTABLISHED IN HOLD. WHEN I NOTICED THAT THE VECTOR AND CLB WAS NOT GOING TO WORK; I TURNED BOTH ACFT; BUT THE TURNS WERE NOT SOON ENOUGH TO AVOID THE ACFT FROM COMING WITHIN 5 MI OF EACH OTHER. THE WHOLE PROB STARTED WHEN I WAS SUDDENLY SLAMMED INTO HOLD FOR EWR BY THE SECTOR I WAS FEEDING. THIS MORE THAN TRIPLED MY WORKLOAD IN SECONDS. OUR FLOW CTL UNIT DID NOTHING TO HELP THE SIT EVEN THOUGH WE HAD BEEN IN AND OUT OF HOLD FOR THE LAST 2 HRS. NO PREWARNING OF GOING BACK INTO HOLD HAD BEEN GIVEN. IF THE FAA IS GOING TO CONTINUE TO HAVE A TFC MGMNT SYS; THEN THEY SHOULD START DOING THEIR JOB.