ZHU CTLR TURNED ACFT IN I90'S AIRSPACE WITHOUT COORD TO MAINTAIN SEPARATION.

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ACFT #1 DEPARTED IAH. HE CAME TO MY FREQ CLBING TO FL180 RESTR TO 250 KIAS BY HOU APCH. I CLBED HIM TO FL230 AND ASKED HIM HIS SPD. WHEN HE TOLD ME THAT HE WAS RESTR TO 250 KIAS; I INCREASED HIM TO 300 KIAS. RIGHT AFTER THIS ACFT #2 CHKED ON MY FREQ LEVEL AT 15000 FT. I ASKED HIM HIS SPD AND HE RESPONDED 290 KIAS. AT THIS TIME; THE CONFLICT ALERT ACTIVATED. ACFT #2 WAS LESS THAN 6 NM BEHIND ACFT #1 WHO WAS LEAVING 14700 FT CLBING TO FL230. I ISSUED AN IMMEDIATE TURN TO ACFT #2 WHILE HE WAS STILL WITHIN HOU APCH AIRSPACE. BECAUSE OF THE TURN; RADAR SEPARATION WAS NOT LOST. AT THE TIME OF THIS INCIDENT AS WELL AS AT LEAST 1 HR BEFORE AND 1/2 HR AFTERWARDS; THE SECTOR WAS EXTREMELY BUSY AND COMPLEX. THE HOU LRR WAS OTS CAUSING A DISRUPTION OF THE NORMAL WAY IN WHICH WE WORK THIS BUSY DEP SECTOR. NO TFC MGMNT RESTRS WERE PUT IN PLACE TO MANAGE THE INCREASED COMPLEXITY OF THE SECTOR. SUBSEQUENT TO THIS INCIDENT; I BECAME SO BUSY THAT I WAS NOT ABLE TO KEEP UP WITH TAKING HDOFS FROM I90 IN A TIMELY FASHION AND I90 ENDED UP 'SPINNING' 1 ACFT.