Not sure about the 727, but generally what we are trying to achieve in the 757 is thrust levers closed from TOD all the way down to spooling up on final approach to use as little fual as possible and thus help costs. Operationally this is obviously subject to ATC requirements such as a portion(s) of level flight, spacing regarding other a/c and things like engine and/or wing anti-ice needing to be on (which spools up the engines slightly thus decreasing the rate of descent for the same speed. Wind is another factor like a/c weight. A strong headwind gives a lower groundspeed and therefore your descent will start later than with a strong tailwind.
We work on a rule of thumb to cross-check the automatics and that is number of track miles required to reach a defined point (such as final fix or touchdown point) is roughly 3xheight to lose to that point(in thousands of feet), plus 1nm for each 10kts of airspeed to lose to min. clean speed. So if I wanted to know when to descend from 30,000' to touchdown at sea level with a min. clean speed of 210kts and I wanted to descend at 300kts that would take 3x30+9=99nm, say 100nm for simplicity. Operationally we keep updating the our mental model using this rule of thumb to ensure we are still in the ballpark. There are a number of ways to correct any error either way, say if ATC shortcut you and you lose track miles. If possible, when high on profile you could increase rate of descent by increasing speed (with the thrust levers still shut) and dive back onto your ideal profile (or in reality get a bit below your previous ideal as you are now going faster and will need a few more miles to bleed of this speed), or you could increase drag by using speedbrake or even taking the gear down early if you are really high.
If ATC hold you high due traffic for instance, as you fly level away from your ideal descent profile you can slow down(if permissable) and then speed up when given further descent to again dive back onto the profile. That way you may be able to fly level at idle thrust descellerating and keep the levers shut when further clearance is given.
If below your ideal profile at some stage it is better to decrease your rate of descent sooner (and therefore higher) by adding some thrust rather than later (and lower) where you will burn more fuel.
So you can see, it's all about energy management, playing with speed and thrust and drag to balance out track miles and wind components with required height loss and speed reduction.
Hope that was of some help.
PP
ps we would normally descend at ECON speed of about 0.8M/300kts in the 757, but in the real world this will often need to be adjusted for the reasons above.