This study proposes a dynamic traffic engineering method to improve network resource utilization efficiency without affecting important services in an integrated service network where multiple grades of service are accommodated. Network resource utilization is biased over time because future fluctuations in traffic demand are unpredictable. Although a service network provider prefers to re-optimize network resource utilization using a dynamic traffic engineering, it is often superfluous for users who do not want their mission-critical communications, for example, executive web meetings or online surgery, to be affected. Therefore, we classified traffic into very important packets and commoners, and only commoners were dynamically optimized. To classify traffic, we assigned the identifier to a packet on the application side. In this approach, only the application and edge nodes of the network required modification; the core network routers were unaffected. Furthermore, we established the architecture of the edge node using a software-defined network controller and P4 switch. We also provided an algorithm for optimization based on linear programming and demonstrated that it is possible to improve network resource utilization efficiency without affecting very important packets and that the computational and memory costs are practical.