PLTDEV RESULTING IN A LOSS OF SEPARATION BTWN ACR X AND ACFT Y.

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ENRTE TO DTW-DCA; ZOB CALLED; GAVE INSTRUCTIONS TO 'DSND TO FL350; BE OUT OF FL370 IN 2 MINS.' (NOTE: WE WERE AT FL410.) FO WAS ON #2 RADIO WITH DEST STATION. I ACKNOWLEDGED THE DSCNT CLRNC BUT MISTOOK THE CTLR'S CLRNC AS INSTRUCTIONS TO BEGIN OUR DSCNT WITHIN 2 MINS. AS WE DSNDED THROUGH FL395; I ASKED THE FO TO GET CLARIFICATION FROM ZOB AS TO OUR CLRNC. WHEN QUERIED; THE CTLR ADVISED WE HAD 20 SECONDS TO BE OUT OF FL370; THAT IT DIDN'T LOOK LIKE WE'D MAKE THAT. HE THEN ADVISED/DIRECTED A L TURN; FROM OUR 105 DEG HDG; TO 050 DEGS; THEN 010 DEGS. WHILE IN OUR TURN; THE TCASII WARNING ANNOUNCED 'TFC; TFC' FOLLOWED BY AN RA OF 'CLB; CLB.' WE WERE IN A 2000-3000 FPM DSCNT AT THE TIME. I IMMEDIATELY DISCONNECTED THE AUTOPLT AND TIGHTENED THE TURN TO THE L WHILE PULLING UP INTO A CLB. THE TCASII DISPLAYED OUR CONFLICTING TFC 300 FT BELOW AND TO THE R. THE FO ADVISED HE WAS PASSING OFF TO OUR R ABOUT 3 MI AWAY; AND THEN ADVISED ATC THAT WE WERE CLBING DUE TO A TCASII RA. ATC ACKNOWLEDGED; 'ROGER; ADVISE WHEN YOU HAVE DSNDED THROUGH FL370....' HUMAN FACTORS: A LONG CREW DUTY DAY COUPLED WITH A VERY SHORT REST PERIOD PRIOR TO THIS DAY MADE FOR A TIRED COCKPIT CREW. THE CTLR CONTINUOUSLY TRANSPOSED OUR CALL SIGN FROM XX324 TO XX234. THE INITIAL CLRNC REQUIRED WHAT I REGARD AS AN EXCESSIVE DSCNT RATE (2000 PLUS FPM) FROM HIGH ALT (FL410). CTLRS DON'T SEEM TO APPRECIATE THAT SUCH HIGH DSCNT RATES ARE DIFFICULT AND UNCOMFORTABLE FOR THE PAX. IN RETROSPECT; I QUESTION THE NEED FOR SUCH A CLRNC GIVEN ITS DIFFICULTY AND THE NEED FOR IMMEDIATE PLT ACTION. SUPPLEMENTAL INFO FROM ACN 281650: THE DSCNT WAS A 2000- 3000 FPM RATE AND THE CTLR ISSUED A R TURN TO 050 DEGS (ACFT WAS ON HDG OF ABOUT 100 DEGS). CTLR WAS ASKED TO VERIFY R TURN; AT WHICH TIME HE SAID L TURN; HDG 010 DEGS. CTLR'S USE OF PROPER CALL SIGN FOR ACFT WAS NOT CLR AND I BELIEVE HE WAS MIXING UP THE NUMBERS ON AT LEAST 1 OF HIS CALLS. ACFT WAS IN THE L TURN AND DSNDING WHEN TCASII GAVE 'TFC; TFC' FOLLOWED BY 'CLB; CLB.' DISPLAY SHOWED ACFT AT 1-2 O'CLOCK CONVERGING; 300 FT BELOW. PF DISCONNECTED AUTOPLT AND BEGAN CLB TO FOLLOW TCASII RA; STILL IN L TURN. CTLR WAS ADVISED BY PNF THAT ACFT WAS IN TURN AND CLBING TO 'FOLLOW TCASII RA.' CTLR ACKNOWLEDGED AND ASKED FOR ADVISORY WHEN WE RESUMED DSCNT THROUGH FL370. VISUAL CONTACT WAS ESTABLISHED WITH INTRUDER ACFT; 2-3 O'CLOCK; 300 FT BELOW; APPROX 3 MI HORIZ. (THAT ACFT THEN ASKED CTR ABOUT TFC AT HIS 2 O'CLOCK.) WE LEVELED FL350 AND RECEIVED CLRNC BACK ON COURSE. REMAINDER OF SEGMENT WAS UNEVENTFUL.