In Software defined networking (SDN), distributed control plane is becoming a promising solution to tackle with scalability and performance. We propose a tree-like hierarchical routing architecture which employs the divide-and-conquer strategy to enhance routing performance on the distributed control plane. To evaluate and optimize the performance of the hierarchical architecture, we apply queuing theory to modeling routing request arrival and processing, and derive an explicit expression of the routing response time. Then we formulate the resource allocation problem in the hierarchical architecture as an optimization problem whose objective is to minimize the response time subject to queue stability and resource constraints. Using the Karush- Kuhn-Tucker (KKT) condition we obtain the optimal resource allocation policy. Based on that, we theoretically prove that the response time under the hierarchical routing architecture is strictly less than that under the Peer to peer (P2P) architecture. Finally, we perform numerical analyses to confirm the conclusions.