I love that style auto valve. I made and animation of it.
That's not any different from a PC/RF20 valve.
The cycle speed will be determined by air pressure, the force exerted by the spring, the diameter of the piston tube, and the size of the air inlet hole.
The main problem with this design is that unless you have a very large tank relative to the volume of the air bursts, or a high pressure tank with a regulator, the pressure will quickly decrease to the point that it will no longer cycle. I guess you could also employ the Nerf solution and use an elastic tank that maintains high pressure even as volume drops.
Along with all those thing the cycle speed will also be determined by the size and strengh of the spring and the distance of the input and output holes.