AN MD11 IN OCEANIC AIRSPACE FAILED TO MEET A XING RESTR BECAUSE OF OVER RELIANCE ON FMC AND A STRONG TAILWIND.

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IN CRUISE AT FL310 PRIOR TO COAST OUT FIX; WHICH WAS 51N/050W; WE RECEIVED THIS CLRNC FROM GANDER CTR: DSND AND MAINTAIN FL290 AT PLT'S DISCRETION; BE LEVEL BY 51N/050W; RPT LEAVING FL310. WE WERE FILED TO CROSS THE OCEAN AT FL290. I PUT 290 IN THE ALT WINDOW AND READ THE FMA'S: HOLD 31000/PROF TO 29000. (THE CAPT WAS ON A SCHEDULED REST BREAK. I WAS THE FO; BUT THE PF AND THE PIC IN THE CAPT'S ABSENCE.)(PER OUR FOM.) THE RELIEF FO INSERTED 290 IN R2 ON THE MCDU. WE PLANNED TO CROSS 5150N AT FL290. AT 20 MI FROM THE FIX WE NOTED THAT THE FMA'S READ PROF 29000 AND THE SPD WAS DECREASING TO 290 KTS (OUR DEFAULT SPD FOR DSCNT). WE SHOULD HAVE STARTED DOWN. THE RELIEF FO TRIED TO RPT LEAVING FL290 BUT HE GOT NO RESPONSE FROM GANDER CTR ON VHF. HE INSERTED 290 IN THE CRUISE LEVEL ON THE INIT PAGE. HE THEN GOT A CHART OUT TO LOOK FOR AN ALTERNATE FREQ FOR GANDER. MEANWHILE; I NOTICED THAT THE ACFT WAS NOT DSNDING SO I ROLLED THE VERT SPD DOWN APPROX 800 FPM DOWN AND NOTED THAT WE HAD ABOUT 13 MI TO GO BEFORE 50W. I PUSHED THE PROF TILE AND CHANGED MY FOCUS TO THE SPD WHICH WAS STILL DECREASING TO 290 KTS. I MANUALLY CHANGED THE SPD TO A BUG SPD. THEN I NOTICED THAT WE WERE 5 MI FROM THE FIX AND WERE PASSING APPROX FL303. THE RELIEF FO SAID 'WE'RE NOT GOING TO MAKE IT.' I INCREASED THE RATE OF DSCNT WITH VERT SPD AGAIN; BUT IT WAS TOO LATE. WE CROSSED THE FIX AT A LEVEL ABOVE FL290. WE ALSO HAD A TAILWIND OF 100+ KTS. LESS THAN A MIN LATER WE WERE LEVEL AT FL290. WE WERE CPDLC SO WE DID NOT MAKE A POS RPT. WE DID CALL GANDER RADIO TO RECEIVE A SEL-CALL CHK. 10 MINS LATER THEY SEL-CALL'ED US TO PASS THIS MESSAGE FROM GANDER CTR: 'WHEN WE GIVE YOU A CLRNC WITH A XING RESTR WE EXPECT YOU TO COMPLY.' WHAT WE LEARNED IS THAT THIS SITUATION MIGHT HAVE BEEN AVOIDED IF WE HAD DSNDED EARLIER INSTEAD OF TRYING TO CROSS AT FL290 AT THE FIX. I COULD HAVE BEEN MORE AGGRESSIVE ABOUT MAKING THE RESTR BY USING A LEVEL CHANGE. THERE WAS AN ELEMENT OF COMPLACENCY IN WAITING FOR THE AUTOMATION TO DO WHAT MIGHT HAVE BEEN DONE MANUALLY. SUPPLEMENTAL INFO FROM ACN 713487: WE HAVE RECENTLY SWITCHED FROM ONE COMMERCIAL CHART TO ANOTHER COMMERCIAL CHART AND ARE STILL LEARNING WHERE THINGS ARE IN COMMERCIAL CHART.