Computer networks require sophisticated control mechanisms to realize fair resource allocation among users in conjunction with efficient resource usage. To successfully realize fair resource allocation in a network, someone should control the behavior of each user by considering fairness. To provide efficient resource utilization, someone should control the behavior of all users by considering efficiency. To realize both control goals with different granularities at the same time, a hierarchical network control mechanism that combines microscopic control (i.e., fairness control) and macroscopic control (i.e., efficiency control) is required. In previous works, Aida proposed the concept of chaos-based hierarchical network control. Next, as an application of the chaos-based concept, Aida designed a fundamental framework of hierarchical transmission rate control based on the chaos of coupled relaxation oscillators. To clarify the realization of the chaos-based concept, one should specify the chaos-based hierarchical transmission rate control in enough detail to work in an actual network, and confirm that it works as intended. In this study, we implement the chaos-based hierarchical transmission rate control in a popular network simulator, ns-2, and confirm its operation through our experimentation. Results verify that the chaos-based concept can be successfully realized in TCP/IP networks.