The main benefit to owning your own car is instant access. To retain that a significant portion of these cars will be sitting in parking lots just the same as if their owners had drove them.

Queuing theory forms a mathematical basis for analyzing the problem. So far its been heavily analyzed and applied towards dynamic pricing models. But if you want to replace cars people need to feel confident they are going to have a ride available in a short amount of time and not be price gouged.