ALT DEV ALT OVERSHOT ON DSCNT. TCASII RA WAS ACTIVATED BY PROX TO OPPOSITE DIRECTION TFC.

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AT FL310 ATC ISSUED CLRNC TO WHAT WAS HEARD FL240. AT THE TIME WE WERE TALKING TO FLT ATTENDANT CONCERNING GATE INFO AND FLT CONDITIONS. PNF ANSWERED CALL. VERIFICATION OF FL240 WAS MADE WITH HIM AND OUR DSCNT PROGRESSED. THERE WAS HVY CONGESTION ON THE FREQ AND THE CTLR WHO APPEARED TO BE A TRAINEE (AS WE COULD HEAR BACKGND INSTRUCTIONS) WAS VERY BUSY. WE WERE CLRED DIRECT THE VOR AS THERE ALSO WAS WX IN THE AREA AND OUR CLRED ALT WAS QUITE HIGH FOR THE NORMAL ARR. PASSING APPROX 24800 TCASII ISSUED A TA. I BEGAN TO LEVEL OFF AND WE OBSERVED THE SCOPE TO LOCATE OUR TFC. THIS WAS DIFFICULT AS WE WERE IN WX MODE AND PAINTING; AND THE TFC WAS BUNCHED AT THE BOTTOM OF THE SCREEN. ATC THEN CALLED TO VERIFY FL250. SHORTLY THEREAFTER TCASII ISSUED A CLB RA WHICH WE IMMEDIATELY DID. ALTHOUGH LOOKING FOR; WE NEVER SAW TFC AND DIDN'T BELIEVE FROM THE SCOPE THAT IT WAS CLOSER THAN 1-2 MI AND CORRECTION WAS MADE BY APPROX 24650. ATC SAID THEY HAD ISSUED FL250 WITH DISCRETION OUT OF FL290; WHICH NEITHER PLT HEARD AND WAS CERTAIN WASN'T ISSUED. THE TRAINEE CTLR WAS RELIEVED BY THE OTHER CTLR AND HDOF TO APCH WAS MADE. APCH GAVE AN EXPEDITED DSCNT AND LARGE HDG CHANGE TO GET US CLOSER TO NORMAL PROFILE AND ARR GATE. (WE WERE APPROX 7000-8000 FT HIGH AND S OF THE NORMAL ARR. AT NO TIME DID ATC ISSUE ANY IMMEDIATE INSTRUCTIONS OR ADVISE OF TFC CONFLICT.) SEVERAL FACTORS I FELT WERE CONTRIBUTING: THE FREQ CONGESTION ALONG WITH COCKPIT DISTR COULD HAVE AFFECTED COM AS ONLY 1 PLT CLRLY HEARD THE CLRNC. ALSO THE WORKLOAD FOR AN ATC TRAINEE WAS QUITE HIGH AND COULD HAVE AFFECTED WHAT CLRNC THEY FELT WAS ISSUED. THEIR OVERLOAD WAS APPARENT BY OUR RTE AND ALT POS ON THE ARR. MISCOM WAS OF COURSE THE OVERRIDING CAUSE. TCASII WAS VALUABLE IN ALERTING US TO POSSIBLE CONFLICT; ALTHOUGH DIFFICULT TO ASSIMILATE INFO QUICKLY WITHIN SECONDS NEEDED THE FINAL RESULT MADE ME A BELIEVER IN THE SYS.