## 1 Introduction
These low-latency and high-reliability characteristics of satellite communication systems, combined with edge computing and storage resources deployed on satellites, can provide users with strong computing and storage resource support [12; 13; 14]. This can significantly reduce data transmission between the edge and the central cloud, reduce delay, and lower energy consumption. In addition, with the increasing demand for computing and storage resources in new application scenarios, satellite edge computing can provide strong computing and storage resource support for new applications. By integrating MEC technology with LEO satellite communication networks, satellites not only can receive and forward tasks to ground stations but also deploy MEC servers onboard, enabling LEO satellites to possess computing and storage resources. This is crucial for expanding service capabilities. Considering the characteristics of the LEO satellite communication networks and MEC technology, their integration can fully utilize the flexible satellite chain routes of LEO communication networks for efficient transmission [14]. Additionally, by deploying satellite servers, we can meet the needs of end users for faster, better, and safer applications. Therefore, building a LEO satellite edge computing network is an inevitable trend in the development of communication networks [15]. In our initial result [16], integrating edge computing technology with LEO networks can significantly reduce the service response time of LEO satellites, enhance the autonomous task processing capabilities of satellites, and improve network performance. Moreover, dynamic task offloading and transmission scheduling are critical for optimizing performance in satellite networks as they must adapt to various dynamic factors such as fluctuating user demand, the movement of satellites, changes in network topology, and environmental conditions. This adaptability ensures that tasks are efficiently offloaded to the most suitable resources in real time, thereby enhancing overall system performance and responsiveness. The existing challenges of latency issues and bandwidth allocation must be addressed to improve system optimization. Although satellite networks are known for their low latency advantages, certain applications may still experience latency issues, especially when bandwidth is constrained during peak usage periods. Effective bandwidth allocation is crucial as it directly influences task processing speed and response times. Furthermore, optimizing bandwidth is essential in enhancing resource utilization efficiency, which ultimately contributes to better overall system performance. The LEO satellite systems integrated with edge computing need to communicate through satellites and ground stations, and there is a certain signal transmission delay between satellites and ground stations. This delay may adversely affect real-time applications and tasks that require rapid data processing; the bandwidth of satellite communications is relatively limited and insufficient for supporting large-scale data transmission and processing needs. This means that bottlenecks may be encountered when processing large-scale data sets and performing complex computing tasks; the LEO satellite systems integrated with edge computing require a large amount of energy supply to support their computing and communication needs. However, current solar battery technology and battery capacity limitations restrict the energy supply capacity of satellite systems. This may lead to the system being unable to meet the needs of high-intensity computing tasks. Additionally, satellite systems still face difficulties in maintenance and updates, as well as high costs. The major contributions of this paper are as follows:  
* This paper proposes a novel integration of Mobile Edge Computing (MEC) technology with LEO satellite communication networks while comprehensively considering constraints such as onboard computing and transmission, satellite-ground and inter-satellite links, and traffic conservation.