This paper proposes a system to provide cycle-based traffic load balancing method for a clustered network managed by multiple SDN controllers. The system adopts a layered control plane in which local controllers are responsible for managing each administrative domain and a federation controller coordinates some local controllers. Previous studies have proposed a traffic load balancing algorithm utilizing multiple cycle structures that must cover the entire network. The algorithm performs traffic load balancing in each cycle so that it can achieve fast calculation and parallelization. In order to verify the feasibility of the cycle-based traffic load balancing method in a pragmatic situation, our study implements the algorithm in a network managed by multiple SDN controllers. This paper focuses on a method to grasp the amount of traffic to detect congestion and alleviate the congestion by switching paths along cycles.