ACR X TCASII RA DSND HAD NMAC WITH ACFT Y. SEE AND AVOID CONCEPT.

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ACR X ON THE AQN2 ARR TO DFW. WE WERE CLRED TO DSND TO 11000 FT AND TO CUT THE CORNER E OF AQN TO INTERCEPT THE 040 DEG RADIAL OUTBOUND. AT ABOUT 12500 FT AND DSNDING; WE RECEIVED A TCASII TA AT 11 O'CLOCK; ABOUT 7-8 MI (YELLOW INTRUDER) AT 1000 FT BELOW OUR ALT. AT ABOUT 4-5 MI WE GOT THE RED RA AND INSTRUCTIONS TO DSND AT A MINIMUM OF 1500 FPM. WE RESPONDED ACCORDINGLY WHILE LOOKING OUTSIDE. WE GOT A VISUAL ON THE INTRUDING LIGHT ACFT Y AT ABOUT 1 MI. HE PASSED ABOVE US AT ABOUT 500 FT AND MAYBE SLIGHTLY BEHIND US. AT NO TIME WERE WE ADVISED OF THIS TFC BY ATC. ONLY AFTER WE CALLED IT DID THE CTLR ACKNOWLEDGE IT. LATER PHONE CALL WITH SECTOR SUPVR INDICATED THAT THE CTLR WAS EXTREMELY BUSY HANDLING BOTH ACTON AND BOIDS ARRS TO DFW AND ACKNOWLEDGED THAT SHE SIMPLY MISSED THE TFC. OTHERWISE WE WOULD NEVER HAVE BEEN CLRED TO 11000 FT THROUGH THE INTRUDER'S ALT. TCASII SAVED OUR BACON! IT WAS VERY UNCOMFORTABLE BEING DIRECTED TO DSND THROUGH A YET UNSEEN (BUT VERY CLOSE) INTRUDER'S ALT; BUT TCASII OBVIOUSLY HAD IT ALL FIGURED OUT. RECOMMENDATION: PROPERLY STAFF BUSY SECTORS DURING PEAK HRS TO REDUCE CHANCES OF THIS TYPE SIT.