As the UK's grossly overcrowded trains and (quite frankly antique rails) attempt to make it through yet another century...it becomes obvious that the easiest way is to get the trains to balance on one rail.
Then, even a single-track line is capable of carrying two trains going in opposite directions*
at the same time. Huzzah!
This could be done gyroscopically, but that would be boring.
Best would be to put the heaviest commuters at the bottom corner of the carriage, so lowering the centre of mass, with the rest of the commuters (having gained government sponsored black belts in surfing, riding unicycles, tight-rope walking and other pursuits likely to foster a good sense of balance) go at the top corner of the carriage.
Perhaps they can be offered discounts on train tickets, or might just do the balancing bit out of being public spirited?
Anyway, you're thinking, "yes, but what happens when the train stops?" Well, I'm glad you asked that question...err..obviously the platforms will need to altered to a v-shape to take the now diamond cross-section trains and all new tunnels will also be diamond-shaped so saving on kneepads. And cheese.
Equally obviously, only riding on one set of wheels, will be a net saving.
I leave it up to the train companies to decide whether to ditch the wheels or use them on alternate days, perhaps having the carriage windows facing south on winter days, and facing north in the winter?
* if they are on the other rail**
** or going in the same direction***
*** Huzzah, again.