## 2 Related Works  
Several works on satellite load balancing have been published in recent years. Their current include load balancing based on the distribution of users, load balancing based on satellite ephemeris topology, and load balancing based on Quality of Service (QoS). The schemes of load balancing based on DoU dictate that the users decide which satellites to access by analyzing the density of equipment distributions [20; 21; 22; 23]. [PERSON] etc. proposed a routing algorithm based on segment routing for traffic return of LEO satellite networks [20]. They dynamically divide the surface of the earth into light and heavy load zones according to the relative position between gateways and the reverse slot. They then use a pre-balanced shortest path algorithm in the light load zone and use the minimum weight path defined by congestion index as the routing rule in the heavy load zone. [PERSON] etc. proposed a method for optimizing the layout of satellite beams by applying mixed-integer linear programming (MILP) [21]. They designed two different sizes of spot  
Figure 1: The problems of load balancing for Ser-BH in SIN. beams to cover the area under non-uniform DoU. In their schemes, low user density areas would be covered with large-size beams, and high user density areas would be covered with small-size beams. MILP was exploited to optimize load balancing to achieve well-distributed traffic among the different beams. [PERSON] et al. proposed a load balancing algorithm for a multi-RAT (radio access technology) network including an NTN and a TN [22]. They first offloaded the appropriate edge UEs of an overloaded cell to underutilized neighboring cells in TN. If there were any overloaded cells after the first step, they offloaded the delay-tolerant data flows of UEs to a satellite link. The load balancing schemes based on satellite topology dictate that the users decide which satellites to access by analyzing which planned satellites would be on the services. [PERSON] etc. proposed a load balancing routing scheme by hybrid-traffic-detour [24]. They calculated and designed the shortest path and a long-distance traffic detour path to forward packets and determine which path to use for forwarding to against link congestion [25]. The scheme tried to avoid a situation in which the routing path between a node and its neighbors were directed toward the same destination node. It chose the next hop based on satellite ephemeris prediction and traffic distribution, which increased the effect of load balancing. [PERSON] et al. proposed a load balancing routing algorithm based on extended link states [26]. They keep all the satellite nodes informed of the link congestion state through an active state discovery and automatic congestion state release mechanism. All satellite nodes update the route table according to the link congestion state to achieve a balanced distribution of traffic load. Load balancing schemes based on QoS dictate that the users decide which satellites to access by analyzing the average QoS of the satellite network. [PERSON] et al. proposed a load balancing algorithm under the satellite network with hopping beams [27]. They divided the beams into heavy load beam (HLB) and light load beam (LLB) groups and offloaded the user terminals that had the highest packet loss rate in the HLB to an adjacent LLB. Then they offloaded the remaining user terminals that had the highest packet loss rate in the HLB to a non-adjacent LLB with hopping beams. After reviewing the existing works on the load balancing of satellites, most research institutes were concerned with treating satellite networks as a pure transmission network. Their schemes mainly selected a suitable route to achieve efficient traffic offloading. Usually, they focused on the scenarios of the Sat-Beams without intra-Ser-BH, and the users with unified uniform distribution in the time and space domains.