I believe the opposite is the more likely outcome: I think we can expect much lighter traffic the more autonomous vehicles there are.
Most traffic is caused by humans doing really irrational things, like following each other too closely, making unnecessary lane changes, and driving at inconsistent speeds. It's very rare that traffic congestion is actually caused by roads' lack of bandwidth.
Anything that will increase the amount of cars will quickly dominate inefficient driving behaviors, and self driving cars will massively increase the amount of cars on the road, as it would drive down the cost of driving and enable many many people who currently can’t drive to get onto the road (eg. Disabled, elderly, unlicensed, children).
I mean in some sense this is always going to be true, and removing cars will always help alleviate traffic. But it's not true that driving behaviour is not a significant cause of traffic congestion: it's the cause in most cases. [1]
For an extreme illustration, there's a well-known phenomenon where adding extra lanes of traffic to a highway or freeway actually worsens traffic: the added bandwidth interacts in weird/subtle ways with driver behaviour. [2]
[1] https://www.vox.com/2014/11/24/7276027/traffic-jam
[2] https://www.wired.com/2014/06/wuwt-traffic-induced-demand/
Roads are fixed in size, cars are very big and take up too much space.
Fundamentally baked into the design this is an inefficient way to move people around and there's no fix to be found working within a car oriented framework. The only solution is in removing cars from the road. This is why self driving cannot fix traffic as it will only add more cars.
Self driving buses, now that would be an improvement, but self driving cars no.
This is obviously largely ruined by one single human driver acting unpredictably, so it's a very "all or nothing" resolution.
The road will be full to the point where the cars automatically slow down for safety, and then it will be a heavy traffic, mostly stopped road