Integrating Software-Defined Networking (SDN) and Edge Computing (EC) technologies becomes a promising approach to harness enormous data traffic in the Internet. Recent studies examined the Quality of Service (QoS) based routing paradigms for different data applications such as IoT, heterogeneous networks, and 5G network slicing in such integrated networks. In this paper, our study formulates the QoS-specific routing optimization as a minimum-cost resource allocation problem, while multi-dimensional factors of bandwidth cost, latency, and packet los are jointly considered. Since we use the fittingness factor to help the problem solving, we propose a path selection scheme based on the measure of fittingness factor, briefly named as FitPath. The FitPath scheme can appropriately adjust network resources to maintain delivery time against various service requirements of user demands. Simulation results show that the FitPath scheme can perform better than the Open Shortest Path First (OSPF) and Greedy heuristic schemes in terms of the total of link costs, delivery latency, and packet loss rate under both of normal and heavy data traffic experiments. The effects by the FitPath scheme can be further enhanced with the top-B% path selection policy in integrated network environments.INDEX TERMS Routing, data delivery, path selection, quality of service (QoS), edge computing, (EC) and software-defined networking (SDN).