B757 FLC BELIEVE ZKC LATE DSCNT AND T75 FREQ CONGESTION ON COM XFER ARE CONTRIBUTING FACTORS TO A TCASII TA-RA.

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APCHING STL TERMINAL AREA. KANSAS CITY GAVE A LATE DSCNT CLRNC TO SEVERAL ACFT INCLUDING OURS. THE CLRNC REQUIRED A DSCNT FROM FL350 TO FL270 IN 15 MI. WE THEN RECEIVED A SIMILAR LATE CLRNC TO CROSS QBALL INTXN AT 11000 FT. CTR WAS INFORMED THAT WE COULD NOT COMPLY AND AN OFF COURSE VECTOR WAS ISSUED. AFTER WE COULD MAKE THE XING RESTR; WE WERE CLRED DIRECT QBALL AND SWITCHED TO STL APCH. THE FREQ WAS VERY BUSY AND OUR CHK-IN WAS DELAYED. 2 MI FROM QBALL; A TCASII TA APPEARED FOR AN ACFT AT 11 O'CLOCK POS; OUR ALT. THE TA QUICKLY CHANGED TO AN RA; REQUIRING A 500 FT DSCNT. THE ACFT PASSED OFF TO THE L ABOUT 1 MI. APCH'S RESPONSE TO RA 'DIDN'T SEE ACFT.' WE DON'T KNOW IF THE ACFT WAS BEING CTLED. POSSIBLE CAUSE: CTR CTLR UNDERSTANDING OF DISTANCE REQUIRED FOR A NORMAL DSCNT AND/OR ACFT POS RELATIVE TO FIX. WORKLOAD PREVENTED CTR OR APCH CTLR FROM SEEING OR CALLING TFC. FREQ CONGESTION ALSO A FACTOR ON APCH. POSSIBLE TRAINING TAKING PLACE. CORRECTIVE ACTIONS: TIMELY CLRNCS TO AVOID DELAYING VECTORS; FREQ CONGESTION; AND DISRUPTION OF SMOOTH TFC FLOW.