To say that R is tied to CPUs is a vague guesstimate at best. It is true that if R=0, CPU's are unlikely to clear the gate, but having R space (any amount) doesn't necessarily mean CPUs will clear.

At best R space being open is a good indication that there is (or more appropriately 'may be', given the problems with instrument sweeps) no one waiting for an instrument upgrade, so the odds of clearing a CPU are higher.

R (even R9) doesn't guarantee a CPU being given until doors are about to close. If you want to guarantee the seat, use miles or an instrument. Otherwise, you'll have to wait until UA decides it's appropriate to clear the list (in whatever form it deems appropriate, including TOD's). The TOD thing stinks, but it is what it is...