## 1 Introduction  
Densely deployed ground communication infrastructures can provide access services for mobile and Internet of Things (IoT) users in urban areas, with the advantages of high data rates and small propagation delay. However, deploying infrastructures in remote areas such as the ocean and desert is challenging and expensive. Various applications in remote areas, such as forest monitoring, desert communication, and maritime logistics, are difficult to serve [1, 2]. There are still approximately three billion people all over the world living without Internet access, presenting an obstacle for 6G in realizing seamless connectivity and ubiquitous access [3, 4]. How to achieve user access and traffic backhaul for mobile and IoT users in remote areas has become crucial [5]. Satellite communication makes up for the shortage of terrestrial networks and provides users with large-scale access services with wide coverage. The utilization of low earth orbit (LEO) satellites for global Internet access and traffic backhaul has garnered attention due to their lower development and launch cost and transmission latency compared with geostationary earth orbit (GEO) and medium earth orbit (MEO) satellites [6]. The use of inter-satellite links (ISLs) enables the traffic generated by ground IoT users to be relayed among LEO satellites and transmitted back to the terrestrial traffic center [7]. However, the severe path loss between LEO satellites and ground IoT users makes it difficult for users to directly access LEO satellites due to limited transmission power. In order to reduce the demand for user-side transmission power, the space-air-ground integrated network has attracted a lot of attention from academia and industry in 6G [8; 9]. Compared to the orbital altitude of hundreds or thousands of kilometers of LEO satellites, the altitude of drones is much lower, thus needing lower transmission power from ground IoT users [10]. In the space-air-ground integrated network, drones in the air are utilized to support user access with lower transmission energy costs, and satellites in space are used to provide traffic backhaul with global coverage [11]. They work together with communication infrastructures on the ground to provide users with various application services. In recent years, a category of drone that can provide users with more stable access, namely high altitude platform (HAP) drone, has become a research hotspot. Different from traditional drones, HAP drones hover at an altitude of about 20 km in the stratosphere, with base stations deployed on them to provide users with ubiquitous and stable access. HAP drones can extend communication capabilities across the space, air, and ground domains. Specifically, aerial networks composed of HAP drones are utilized to support user access and collect traffic generated by users in remote or inaccessible areas lacking communication infrastructures. Then, LEO satellites are used to support traffic backhaul to the terrestrial traffic center, thus supplying stable access and traffic backhaul [12]. Due to the advantages of low deployment cost, flexible on-demand deployment, and reliable line-of-sight communication link, HAP drones have been employed in the satellite-ground network for user access, traffic backhaul, and task execution. However, practical issues in the space-air-ground integrated network have been overlooked in existing research. For instance, due to the high mobility of LEO satellites, HAP drones need to be switched between different LEO satellites. Therefore, the calculation of the available traffic transmission time of HAP drones must jointly consider the remaining visible time and handover latency. Furthermore, different traffic types generated at HAP drones hold varying values, suggesting a preference for establishing matching for high-value traffic types first.