Should it be so complex?
Let me separate the problem into two different problems.
1) I have calculated a route. How do I get the time my car will be on each segment. I think if I have the ordered segment collection and the time for each segment �?? it should not be too hard to get it.
2) I have a network and information about the time it takes to cross each segment in a different time in the week. How do I put this information into the network so the routing will take it in to account.
If I solve these two questions and combine them I solve the problem.
There is not to much more into the real problem, it is just a way to make sure two "cars" will not be on the same segment in the same time.