Also, if the car is self-driving, people will be want to make more trips. For example, if we send their cars back home once they got to work, we'll save on parking, but get more congestion. I'd love to automatically send my car to a mechanic when needed, what's also more congestion... I'm sure people will find lots of good reasons for sending their cars around.
Anyway, what will probably reduce congestion is a smart bus system. Imagine a small bus that takes you door to door, and takes only slightly more time to get there than your own car, but is way cheaper. I've seen that on the news just recently, I think it's Japan trying it.