This article addresses path selection problems that arise in a large-scale media server. In particular, the problem on a distributed server with two tiers of server nodes connected by a VC-enabled interconnection network is considered. To serve each incoming request, a pair of server nodes should be selected to handle the request. In addition, a network path in the interconnection network should be arranged to pipe the program stream between the pair of server nodes for the request. The problem is modeled as a network flow problem. A two-pass flow (TPF) algorithm is proposed to solve the flow problem that involves multiple types of flow. The proposed algorithm allocates system resources effectively to maximize the number of admitted requests without violating resource constraints. Unlike some other works, the algorithm does not need to rely on assumptions about any particular configuration of the underlying interconnection network.