Let’s build another road
Every day, a large number of people commute from city A to D by going through B and C. There are 4 roads
and the travel times are
A-B 40 minutes
C-D 40 minutes
The travel times on the two other roads depend on the proportion of traffic that uses them. Let p be the proportion of the commuters that use a segment.
A-C 30*p minutes
B-D 30*p minutes
For example, if 90% of the traffic goes A-C then it takes them 27 minutes.
An equilibria is reached with p = 50%, and each commute requires a total of 40 + 15 = 55 minutes on both paths A-B-D and A-C-D.
Here is the question: Construction a new road can only help with the traffic flow, right ? What happens after that a road joining B and C is constructed ?
The travel time is
B-C 5 minutes.