FLC OF AN MLG ACR ACFT OVERSHOT CLB ALT IN RESPONSE TO A TCASII RA.

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ON CLBOUT OF 10000 FT CTR REQUESTED 320 KT SPD FOR THE DTW ARR GATE; AND MAINTAIN 11000 FT. JUST PRIOR TO LEVEL OFF; FO ACKNOWLEDGED A CLB CLRNC FROM ZAU TO CLB TO 16000 FT. I NOTICED A TCASII TFC AT ABOUT 2 O'CLOCK; 6 MI AT 2400 FT ABOVE US. I LOOKED OUT AND SAW AN ACFT AT ABOUT THAT POS. WE WERE CLBING AT ABOUT 2000 FPM AT 320 KTS. WE GOT A TA THEN AN RA AND A 2000 FPM DSCNT. I EXECUTED A PITCH OVER AND DSCNT TO 2000 FPM AND ABOUT THAT TIME ZAU ASKED US TO MAINTAIN 13000 FT AND SAID THAT WAS OUR CLRED ALT. I LEVELED OFF AT 13000 FT AND TOLD CTR THAT WE HAD NEVER HEARD OR ACKNOWLEDGED THE 13000 FT ALT ASSIGNMENT. WE THEN GOT A FREQ CHANGE TO ZID. SOLUTION: AS MLG CAPT FOR MAJOR AIRLINE IN AND OUT OF THE DTW AREA; I FEEL THAT THE ATC SYS IS TOO BUSY. THE CTLRS HAVE TOO MANY AIRPLANES TO WORK WITH FREQ CONGESTION AND COORDINATED ARR SEQUENCING. TOO MANY HUBS IN SUCH A SMALL AREA OF THE CTR (I.E.; DTW; CVG; PIT; CLE; ORD) FOR THE PRESENT SYS TO HANDLE WHEN WX OR EQUIP FAILURE HAPPENS -- NOT MENTIONING JUST DAY IN; DAY OUT OPS.