A packet network architecture called “functionally distributed transport networking” is being studied, where control elements (CEs) are separated from the forwarding elements (FEs) of all routers in a network, and a centralized CE manages the control functions for all FEs. A crucial issue to be addressed in this network architecture is the occurrence of bottlenecks in the CE performance, and rapid network restoration after failures is the main problem to be solved. Thus, we propose here a fast backup route determination method suitable for this network architecture, and we also show the practicality of this architecture. Most failures can be categorized as single-node or single-link failures. The proposed method prepares backup routes for all possible single-node failures in advance and computes backup routes for single-link failures after the failure occurs. The number of possible single-node failures is much less than that of possible single-link failures, and the preparation of backup routes for single-node failures is practical under the memory requirements. Two techniques are used in computing backup routes for single-link failures in order to reduce the computation time. One is to calculate only the routes affected by the link failure. The other is to use an algorithm to compute backup routes for single-link failures based on preplanned backup routes for single-node failures. To demonstrate the practicality of our method, we evaluated the amount of memory and computation time needed to prepare backup routes for all single-node failures, and we carried out simulations with various network topologies to evaluate the route computation time required for a single-link failure.