There is also the sliding shortest path algorithm[2].
[1] https://www.nsa.gov/research/_files/publications/inevitabili...
[2] https://www.nsa.gov/research/_files/publications/sliding_sho...
I'm thinking about what this scenario means for road networks and if it makes sense there at all (not considering the algorithm's assumptions). I guess it would answer the question of how bad traffic jams have to be on certain roads in the shortest path in order to force the route over a specific road.
On a sidenote: in the caption for figure 2, it has to be "link ef is cut" instead of "link eg is cut" in b) if I understand it correctly.