High throughput satellites (HTSs) outpace traditional satellites due to their multi-beam transmission. The rise of low Earth orbit mega constellations amplifies HTS data rate demands to terabits/second with acceptable latency. This surge in data rate necessitates multiple modems, often exceeding single device capabilities. Consequently, satellites employ several processors, forming a complex packet-switch network. This can lead to potential internal congestion and challenges in adhering to strict quality of service (QoS) constraints. While significant research exists on constellation-level routing, a literature gap remains on the internal routing within a single HTS. The intricacy of this internal network architecture presents a significant challenge to achieve high data rates. This paper introduces an online optimal flow allocation and scheduling method for HTSs. The problem is presented as a multi-commodity flow instance with different priority data streams. An initial full time horizon model is proposed as a benchmark. We apply a model predictive control (MPC) approach to enable adaptive routing based on current information and the forecast within the prediction time horizon while allowing for deviation of the latter. Importantly, MPC is inherently suited to handle uncertainty in incoming flows. Our approach minimizes the packet loss by optimally and adaptively managing the priority queue schedulers and flow exchanges between satellite processing modules. Central to our method is a routing model focusing on optimal priority scheduling to enhance data rates and maintain QoS. The model's stages are critically evaluated, and results are compared to traditional methods via numerical simulations. Through simulations, our method demonstrates performance nearly on par with the hindsight optimum, showcasing its efficiency and adaptability in addressing satellite communication challenges.