Objective: The combination of service function chain (SFC) and edge cloud environments presents a promising technical architecture. Edge computing, being close to data sources, can quickly process data locally, while cloud computing provides robust computational power and storage capacity. Therefore, the integration of edge and cloud computing ensures the efficient execution of real-time tasks and sufficient computing support for large-scale data processing. This setup is applicable to a variety of complex scenarios. However, deploying SFC in the edge cloud environment presents several challenges. First, VNF instances in SFC requests from different users require computing and communication resources during deployment. Second, during SFC deployment, meeting the computing and communication requirements of the SFC requests is essential, along with ensuring that computing, communication and queuing delays—from arrival to processing—satisfy the SFC's end-to-end delay requirements. Finally, the resource capacity of edge devices is limited. Therefore, given capital expenditures and operating costs, it is crucial to balance resource capacity with latency requirements to ensure the revenue of network service providers. As SFC requests arrive dynamically, the edge cloud environment must make immediate, irreversible deployment decisions for these requests. Methods: We address the problem of maximizing revenue from the online deployment of SFCs in an edge cloud environment, subject to constraints on latency, computing resources, and communication resources (SDRM-EC). To solve this problem, an algorithm based on deep reinforcement learning, SDRM-EC-PRP, is designed. First, we comprehensively modeled the physical network, SFC request, and deployment cost. In particular, the deployment cost model incorporates market supply and demand principles, accurately assessing the costs of each request based on the real-time remaining computing power of devices and available communication resources of the links. This approach eliminates device heterogeneity and helps evaluate whether the request is worth accepting. Subsequently, we formulated a Markov decision process for these models and integrated them with the dueling double deep Q-network (D3QN) algorithm to manage large-scale and complex decision processes. To optimize learning efficiency and improve sample utilization, we introduced a priority experience replay mechanism based on D3QN. Additionally, to achieve faster convergence, better stability, and enhanced adaptability to complex environments, we incorporated the random network distillation technique. Results: Simulation experiments were conducted with varying combinations of device size and SFC request quantity. The results demonstrated that, compared with the optimal offline solution, two deep reinforcement learning algorithms and one heuristic algorithm, the SDRM-EC-DPR algorithm, achieved a total revenue increase of 8.82%-18.95% and a reduction in SFC end-to-end latency by 12.5%-38.8%. Furthermore, the SDRM-EC-DPR algorithm showed significant advantages in improving the request acceptance rate, optimizing runtime, and enhancing load balancing. Conclusions: The SDRM-EC-DPR algorithm is highly effective in addressing the SDRM-EC problem, and this study demonstrates its practical value in efficiently deploying SFCs in complex edge cloud environments. This algorithm offers a practical and feasible solution for deploying service function chains in the current edge cloud landscape.