Due to integrated high-speed networks accommodating various types of services and applications, the quality of service (QoS) requirements for those networks have also become diverse. The network resources are shared by the individual service traffic in the integrated network. Thus, the QoS of all the services may be degraded indiscriminately when the network becomes congested due to a sudden increase in traffic for a particular service if there is no traffic engineering taking into account each service's QoS requirement. To resolve this problem, we present a method of controlling individual service traffic by using an overlay network, which makes it possible to flexibly add various functionalities. The overlay network provides functionalities to control individual service traffic, such as constructing an overlay network topology for each service, calculating the optimal route for the service's QoS, and caching the content to reduce traffic. Specifically, we present a method of overlay routing that is based on the Hedge algorithm, an online learning algorithm to guarantee an upper bound in the difference from the optimal performance. We show the effectiveness of our overlay routing through simulation analysis for various network topologies.