I have been working on a project that turns out to be a special case of the directed version of the survivable network problem.Iterative rounding gives a 2-approximation of the undirected case. I'm wondering if the directed case has been studied at all and if so, what approximations can be guaranteed.
Survivable networks, directed case
reference request;network modeling
The directed versions are much harder. A survey by Nutov available on his web page is a good starting point. http://www.openu.ac.il/home/nutov/Survivable-Network.pdf