So if you want to see terrible traffic jam...
I can get several conditions:
1. Place as much buildings producing, not consuming as possible
2. End the road with bottleneck
3. Wait till all flags are fully occupied.
With my last game I even USED this idea. (Why? If you have bottleneck in production place, you won't have bottleneck somewhere else.):
I was producing fish in one place, far away from my main production centre. 18 fisher's huts were at 100% production. All of them connected to one single road. The road had two bottlenecks at once: first was because not every part of the road was with a donkey helping the carrier with moving fish; second, because (at least) one of the distance between flags was 3-units long. So considering that road, all the traffic was concentrated on a single road with limited capacity. The capacity was only 50% less than perfect (or perfect one was 33% far from target one).
So answering to your question, I will make a chain of thesis:
There is no full congestion
In a perfect world (without any bugs!) every ware has its own destination and route. So if we consider no changes on routes, there is no logic way of complete stop of moving the wares. But the world is not perfect. So probably this thesis is not 100% accurate, but 99.99% will be ok.
There are terrible traffic jams
My sub-thesis for this is that: every participant of last tournament had at least one traffic jam. And traffic jam definition here can be: at least 27 wares concentrated on 3 neighbour flags with 3 carriers. Most complex traffic jam I had was with my port building and my short calculations says that it should be about 1500 wares there. It is possible, but unbelievable.
Traffic jams happen just before bottleneck
Bottleneck is: a piece of road with lower capacity than (previous) neighbour(s). So if you have a 2-units road system, the bottleneck will be a piece of road 3-units long. Of course the longest road is, the more visible bottleneck is. Also bottleneck can happen when you have at least 2 roads which are narrowed to 1-road system. Of course those roads should be used.
The bottlenecks aren't the same
As it was told above, the bottleneck can differ. But the mathematical difference is a factor of capacity. If we take 2 equal roads that are narrowed to one, the factor will be 2. So the narrowed road is 2-times less efficient. If we take 2-units length into 3-units one, the factor is 1.5.
Capacity depends on road lengths
Total capacity of a single road can be calculated. Known data is that every unit has velocity equals to 1 unit per 1.8 seconds of gametime. Every minute the carrier walks through 33.3 units. That means... 8.3 full walks between flags in range of 2 units. And 4.16 full walks between flags in range of 4 units. And almost 1 unit per minute in 17-units length road.
The worst traffic system
- Build as long roads as possible
- Build as less flags as possible
- Consider making real bottleneck of bottlenecks of ...
Is this a partly mathematical view on your problem