The suction level in a regulator in equilibrium (i.e. with the boards
not moving) is determined solely by the strength of springs that are
trying to push open the reservoir.  It's basic physics: with the board
not moving, the air suction inwards must exactly equal the spring
pressure outwards.  Even when the board is moving the analysis is
pretty similar, although you do have to allow a bit for the spring
action of the air itself.

A player piano needs to have a very non-linear spring strength for
the reservoir, so that when you push hard on the pedals for an accent
it causes the suction level to rise rather than be mopped up by the
reservoir springs.

Because you want an accent to last only a short while, the amount of
air involved with these high suction periods is very low.  Just how
much reserve is provided at high suction was a design decision for the
maker: Aeolian made it quite low, so that accents were easy to add with
a tap of the foot at exactly the right time.  Some other makers chose
to provide more reserve at high suction so that you didn't need to be
as accurate with your pedalling, but this also prevented fine-control
of dynamic levels because the reservoir would smooth them our more.

On the other hand, the reservoir also needs to keep the wind motor
running when you're not pedalling, or between pedal strokes.  To do
this it needs to provide a fairly substantial amount of air at a fairly
low suction.  This suction level shouldn't be quite strong enough to
operate notes, because if it did you would never be able to play more
quietly than that level.

To meet this rather complex design requirement you find that all
player piano reservoirs have two springs, or an equivalent design.  One
is a weakish linear spring that operates for about half the travel of
the reservoir: this is for the wind-motor reserve.  Being linear it
provides a suction level that doesn't vary much across its whole range.
At about half-travel another spring cuts in.  This is much stiffer, and
is highly non-linear so that the strength of the spring rises very
rapidly with compression.  Examples include Aeolian's strip of wood, or
Standard's tapering coil spring whose diameter decreases with
compression therefore raising its spring rate.

The exact strength of the springs depends on the design of the
player action and wind motor.  Players with small pneumatics working
with low travel, but having higher leverage on the piano action, will
need higher suction than actions with large long-travel pneumatics.
Both will (all else being equal) deliver the same energy to the piano
action and take the same effort to pedal.

A similar consideration can be made for the wind motor.  If you
encounter a player whose wind motor stutters at quiet playing it's
worth asking whether it's the original motor or whether the weaker
reservoir springs are the right ones.  Most makes got this right when
they were new, but some have been fiddled with over the years by folks
who don't understand the consequences of doing so.

This behaviour is vital to the operation of the foot-operated player
piano, yet rather oddly it is completely omitted from every one of the
rebuilding books I've ever seen!

Julian Dyer