We discuss the design of robust protocols that despite poor knowledge about network connectivity achieve consistent performance. Optimal routes and schedules are obtained to (i) maximize a social network utility subject to a variance constraint; and (ii) minimize a variance cost subject to a minimum yield. Corresponding optimization problems are formulated and shown to be convex under mild conditions usually satisfied in practice. Protocols are obtained relying on dual decomposition algorithms that compute the solution of these optimization problems in a distributed manner. The resulting protocols yield utilities that come close to the prescribed requirement even when channel estimates are rough.