B767 FAILS TO MEET ALT XING RESTR SE OF BYI.

Narrative

WE HAD BEEN CLRED TO PROCEED DIRECT TO BYI; A VOR ON THE RTE SEGMENT WHICH WE HAD BEEN ASSIGNED TO FLY. JUST AFTER WE HAD GONE OVER THE BYI VOR ZLC ASSIGNED US A XING RESTR OF 20 MI SE OF BYI; AT FL310. OUR OPERATING ALT WAS THEN FL370. I ENTERED BYI/117/20 INTO THE FMC; AND SET FL310 ON THE MCP OF THE ACFT. AT THAT TIME; I NOTICED THAT WE WERE 14.4 MI FROM OUR POINT TO BE CROSSED AT FL310. THE CTLR WAS SATURATED; NEVER ANSWERED US; WENT RIGHT ON TO OTHER FLTS. FREQ CONGESTION WAS HIGH; AND I WAS UNABLE TO CONTACT THE CTLR TO ADVISE HIM THAT WE WOULD NOT BE ABLE TO COMPLY WITH THIS ALT RESTR. IF I MIGHT BE ALLOWED TO GIVE SOME FIGURES WHICH ILLUSTRATE OUR PROB; WE WERE ABOUT 420 KTS ON OUR GND SPD; OR 7 MI PER MIN. AT THE TIME WE STARTED DOWN; WE WERE ABOUT 14.0 MI OR LESS FROM OUR RESTR POINT. THIS GIVES 2 MIN OR LESS TO LOSE 6000 FT OF ALT. WHILE THIS MAY BE DONE IN SOME ACFT; IT IS NOT POSSIBLE AND SHOULD NOT BE NECESSARY TO HAVE TO LOSE 3000 FT OF ALT PER MIN TO COMPLY WITH A CLRNC WITH PROPER ANTICIPATION OF THE CTLR/CREW. MY FRUSTRATION WAS BEING GIVEN A CLRNC WITH WHICH I WAS UNABLE TO COMPLY WITH AND THEN NOT BEING ABLE TO CONVEY THIS TO THE CTLR IN A TIMELY MANNER. IN OVER 20 YRS OF AIRLINE FLYING; THIS IS THE FIRST TIME THIS HAS EVER OCCURRED IN MY CAREER. IT IS MY HOPE THAT IT WILL NEVER HAPPEN AGAIN. A PLT HAS TO BE ALLOWED TO RESPOND TO A CTLR'S CLRNC; RATHER THAN BEING GIVEN THE CLRNC BY A CTLR; THEN DETERMINING THAT THE CLRNC CANNOT BE MET BUT NOT BEING ABLE TO CONVEY THIS TO THE CTLR DUE TO FREQ CONGESTION.