In recent years, there has been a significant increase in the demand for high-bit-rate live broadcast services, which has led to the widespread use of edge transcoding technology. Edge transcoding can effectively reduce the throughput of streaming media transmission, making it a popular and extensively researched technology. However, due to the real-time requirements of live broadcasting, the edge server needs to have the sufficient computing power to ensure low-latency calculations, which makes computing power allocation and traffic distribution become quite difficult. Inspired by the real-time and flexible computing power scheduling ability of the Computing Power Network, this paper explores reasonable edge task offloading and efficient traffic routing path planning to ensure overall low latency. This paper proposes a live stream transmission architecture based on the computing power network to solve the problems mentioned above to some degree. The paper first models the computing power network in the scene and then designs a task offloading algorithm based on Deep Reinforcement Learning (DQN) to determine the device for executing the computing task. Furthermore, a hybrid Simulated Annealing Genetic Algorithm (SAGA) is proposed for routing decisions. The effectiveness and superiority of the scheme are validated through simulation experiments.