Abstract: Collaborative optimization of “cloud-edge-end” resource collaboration optimization is one of the key challenges in the deployment of computing power networks. Effectively integrating heterogeneous computing resources, such as high-performance cloud computing, low-latency edge computing, and low-cost user devices, is of great significance for the construction of computing first networks. Based on this, we propose a joint optimization scheme for computing and transmission in “cloud-edge-end” computing first networks, aiming to provide a systematic solution from three aspects: application service model, network state awareness, and resource collaboration optimization. Firstly, according to the characteristics of general application services, the traditional network service chain representation model is improved, and a generalized graph structure-based universal service model is proposed. Secondly, to characterize the dynamic rules of heterogeneous network states, a dual virtual queue structure for modeling time-varying computing and transmission loads is proposed. Thirdly, to reduce the complexity of joint optimization of computing and transmission resources in large-scale computing first networks, an augmented graph model based on graph concepts is proposed. This model can transform the joint optimization problem of computing and transmission into a routing problem of the augmented graph, simplifying the formal representation difficulty of heterogeneous resource joint optimization problems. To solve this problem in practice, a heterogeneous resource collaboration optimization algorithm based on the Polyak Heavy-Ball Method is designed, and the algorithm complexity and related theoretical performance analysis are provided. Finally, through numerical simulations and prototype system experiments, the correctness of the algorithm's theoretical performance is verified, as well as the performance advantages in terms of service utility and resource cost compared to three contemporary relevant solutions.