In recent years, significant progress has been made in learning-based VSLAM (Visual Simultaneous Localization and Mapping). Cloud-based VSLAM is a promising solution for meeting the computational demands of learning-based methods in mobile robot applications. However, existing cloud-based VSLAM systems face high transmission demands. To address this issue, we propose a cloud-based VSLAM system, offloading the heavy cost of reconstructing challenging images to the cloud using the learning-based method and leaving the light realtime tracking in the edge using the model-based method. By combining the cloudedge transmission and a multiple submap VSLAM framework, we introduce a rumination-inspired mechanism for asynchronous and distributed submap building. The submap-based framework and proposed down-sampling method help reduce transmission frequency and data volume. We present experimental results that demonstrate the robustness and precision of our cloudbased multiple submap VSLAM system. We also evaluate the runtime performance of communication and computation on a real robot platform, which suggests that the multiple submap VSLAM framework can effectively release computation load while satisfying both robustness and realtime requirements.