A BE400A ON TEXNN3 STAR TO HOU FAILED TO SLOW TO CHARTED 250 KT RESTR AT QTRBK. APCH CTLR ASKED THEIR SPD; AND VECTORED THEM TO RWY.

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I WAS FLYING AS SIC ON A BEECHJET 400A; FLYING THE TEXNN3 ARR TO HOU ARPT. WE WERE CLRED TO CROSS COACH AT 11000 FT WHICH WAS DONE. THE FIX AFTER COACH IS QTRBK WHICH HAS NOTE ON THE ARR CHART TO CROSS AT 250 KTS. THIS SPD WAS MISSED WHILE FLYING THE ARR/STAR. WE WERE QUESTIONED BY HOUSTON APCH AFTER PASSING QTRBK AS TO OUR SPD (WHICH WAS 270 KTS) AND GIVEN VECTORS TO THE FINAL APCH AT HOU AS WE WERE TOLD WE HAD INTERRUPTED THE TFC FLOW; WE WERE GIVEN A PHONE NUMBER AND ASKED TO CALL HOUSTON APCH UPON ARR AT HOU. HOUSTON APCH WAS CONTACTED AFTER LNDG; THE SITUATION WAS DISCUSSED WITH THE CTLR AND THE CAPT; THE SPD RESTRS ON THE ARR WERE EXPLAINED BY THE CTLR; SO THAT THIS SITUATION COULD BE PREVENTED IN THE FUTURE. CONTRIBUTING FACTORS TO THIS OCCURRENCE WERE: 1) CONSISTENT EARLY WAKE-UP CALLS BY THE COMPANY FLT OPTIONS FOR 4 DAYS PREVIOUS; CREW DAYS -- LONG DUTY. 2) BUSY WORKLOAD; AN ARR TO HOU. 3) SPD RESTR NOT DISPLAYED ON FMS SCREEN IN ACFT. THIS SITUATION WILL NOT OCCUR AGAIN AS CHARTS; SIDS; STARS; AND APCH WILL BE REVIEWED IN GREATER DETAIL IN FUTURE.