ZID CTLR EXPERIENCED OPERROR AT FL310 AS ACFT IS SLOW IN DSCNT AND CONFLICTS WITH XING TFC.

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ACFT WAS SLIGHTLY N OF COURSE 100 NM SE WHEN ZID CTLR ASKED PLT TO VERIFY ON THE HMV TRANSITION FOR THE SWEED 6 STAR. PLT STATED 'NO; PROCEEDING DIRECT FLM.' CTLR #1 ASSIGNED HDG 280 DEGS FOR SEQUENCE. ACFT CHKED ON WITH CTLR #2 WITH FREQ AT FL310. CTLR #2 CLRED ACFT 'DIRECT DRESR; CROSS DRESR AT AND MAINTAIN FL240.' PLT SAID 'WE WILL NEED A HDG; DON'T HAVE THE EQUIP FOR THAT.' CTLR #2 ASSIGNED 'HDG 310 DEGS; JOIN THE SWEED 6 ARR; CROSS DRESR AT AND MAINTAIN FL240.' PLT SAID 'WE DON'T SEE DRESR ON THAT ARR CTR.' I ASSUMED THE RADAR POS AND ISSUED 'FLY PRESENT HDG; INTERCEPT THE VXV 012 DEG RADIAL OR 015 DEG RADIAL (I'M NOT CERTAIN WHICH) FOR THE SWEED 6 ARR; DRESR WILL BE 15-20 MI N OF YOUR POS ON THE ARR.' PLT; 'SO YOU WANT US BACK OVER ON THE VXV RADIAL?' ME; 'AFFIRMATIVE; IT'S RIGHT OFF YOUR NOSE ABOUT 2 MI; TURN R TO JOIN THE RADIAL FOR THE SWEED 6.' PLT; 'ROGER.' I ASKED HIM TO VERIFY IN THE TURN FOR THE RADIAL AND HE ACKNOWLEDGED 'ESTABLISHED.' APPROX 8 MI S OF DRESR; ACR X MODE C SHOWED STILL LEVEL AT FL310. I ASKED IF THEY HAD STARTED THEIR DSCNT TO MAKE THE XING. PLT; 'WE'RE STARTING DOWN NOW...UH; WHAT ALT DID YOU WANT US AT DRESR? WE MUST HAVE MISSED IT.' MY QUESTION WAS PROMPTED BY THE PRESENCE OF TFC 2 MI N OF DRESR IN THE ADJACENT SECTOR IN A DSCNT OUT OF FL305 FOR FL290. I COORDINATED TO HAVE THAT TFC TURNED E; THEN TURNED ACR X 30 DEGS L (W) AND EXPEDITED HIS DSCNT TO FL240 SEPARATION WAS LOST.