One useful way to think about self-driving cars is to imagine them as more perfect than human drivers, eliminating many of the inefficiencies that reduce the throughput of roads. For example, making intersections more efficient or reducing the compounding negative effects of traffic jams.
It's nice to imagine that these efficiency gains will lead to less traffic. Unfortunately, it's also wrong. To understand why, consider a well-studied change has also increased capacity of roads over the past 50 years: the addition of more lanes and new highways. And the conclusion is that more capacity induces more demand such that overall traffic is not reduced.
From this research we should expect self-driving cars to increase total miles traveled by cars but without any noticeable reduction in traffic.
If only that were the end of the story. Alas, self-driving cars not only increase the efficiency of the road, but also make the ride more comfortable for the driver who no longer has to drive.
A quick thought exercise: How much longer are you willing to commute if you could spend that time reading, watching netflix, or with your kids rather than focused on the road? In my own experience, I'm willing to almost double my commute.
This willingness to spend more time will translate directly into more induced demand and longer trips. Get ready for more gridlock.