Algorithm to determine the fastest route passing in all points

Since you brought congestion into the picture, be careful you don't get caught by Braess' Paradox. If everyone chooses the optimal path, it results in worse travel time for everyone.

Basic Algorithm

Maintain two sets of the nodes you can reach from the start and end node. In alternating fashion, go three steps from both sides. Each time replacing your set with nodes you can reach through one more step. After each step you check the two sets for common nodes.

Optimizations

Make sure you can iterate the sets as sorted so that you can search for common nodes in a single sweep: an O(n+m) operation. Lists will be up to a million nodes each.

To extend a set with one step, you have query all connections of the nodes in the original set and merge them into a new sorted set. Merging 2 sorted lists can again be done in a single sweep. So you also want to make sure that you can query the connections of a node as sorted. (This could be preprocessed).

In the last two steps each new set is the result of merging up to 10000 of these query results. It is best to do this merge adaptive (merging equally sized chunks). In that way, the sorted set data structure can be a simple linked list.

That way the whole algorithm becomes O(6*n + 6*n*log n) where n is max. 1,000,000.