In the current landscape of online data services, data transmission and cloud computing are often controlled separately by Internet Service Providers (ISPs) and cloud providers, resulting in significant cooperation challenges and suboptimal global data service optimization. In this study, we propose an end-to-end scheduling method aimed at supporting low-latency and computation-intensive medical services within local wireless networks and healthcare clouds. This approach serves as a practical paradigm for achieving low-latency data services in local private cloud environments. To meet the low-latency requirement while minimizing communication and computation resource usage, we leverage Deep Reinforcement Learning (DRL) algorithms to learn a policy for automatically regulating the transmission rate of medical services and the computation speed of cloud servers. Additionally, we utilize a two-stage tandem queue to address this problem effectively. Extensive experiments are conducted to validate the effectiveness for our proposed method under various arrival rates of medical services.