# Towards Deterministic-Delay Data Delivery Using Multi-Criteria Routing over Satellite Networks
## 1 Introduction  
The satellite Internet, with its extensive coverage, is a crucial component of next-generation mobile communication systems, providing network access services to space-based vehicles, airborne aircraft, maritime users, and users in remote terrestrial areas [1, 2, 3]. Due to the Earth's rotation and the relative motion between satellites and the Earth, low and medium Earth orbit satellites operate along predetermined orbits, resulting in a uniform distribution of satellite constellations [4]. However, the distribution of ground users, influenced by maritime and geographical factors, is uneven [5, 6]. Efficiently utilizing the uniformly distributed satellite communication resources while ensuring the service quality of differentiated services for unevenly distributed users can help reduce satellite network operating costs and enhance user adhesion to the satellite network [7, 8]. The distribution of land-based users influences the traffic load of the satellite Internet, as illustrated in Figure 1a, which presents a static equipment density index map based on data from the literature [9], with longitude on the horizontal axis and latitude on the vertical axis. The ground is divided into 72 regions, with each grid containing a number representing the static communicationequipment density index for that region (indicating the communication equipment density in the \(i\)-th region). It is assumed that all communication traffic is transmitted via satellite, meaning that the service traffic generated from one grid is routed via satellite to the target grid. The traffic reaching each destination grid is related to the static equipment density index, distance, and time interval between the source node and the destination node. If the satellite network adopts the classic shortest path routing algorithm, the traffic load on inter-satellite links at a given time is as shown in Figure 1b. In this figure, the circles and the numbers on them represent individual satellites, with different circle colors indicating the service load on each satellite: blue, yellow, and red represent low, medium, and high traffic loads, respectively. The lines between circles represent communication links between satellites, where blue, yellow, and red lines represent low, medium, and high link loads, respectively. From Figure 1b, it is evident that unevenly distributed service demand results in significant differences in link loads across the satellite network, with some inter-satellite links becoming bottlenecks that limit the overall capacity of the satellite network. To address the issue of network load balancing, scholars have proposed various load balancing methods. Most load balancing methods aim to reduce the probability of bottleneck links with heavy loads by traffic splitting. For example, the widely used Equal-Cost Multi-Path (ECMP) [10] routing mechanism in terrestrial networks establishes multiple paths between any pair of nodes and randomly selects one path for packet forwarding when a packet arrives at an intermediate node, thereby achieving load balancing. However,  
Figure 1: (**a**) Static equipment density index and Earth’s regional division; (**b**) Load distribution of the satellite network under the shortest path algorithm (total daily traffic of 180 T). the randomness in path selection introduces uncertainty in end-to-end delay, and the long link delay in satellite networks exacerbates the challenge of ensuring end-to-end delay. The traffic-light-based intelligent routing (TLR) strategy proposed in the literature [11] marks the congestion level of candidate paths based on the queue length of pending service traffic at neighboring nodes and selects paths with lower congestion levels for packet forwarding. Compared to the ECMP method, the TLR method considers the load of neighboring links, improving local load balancing but neglecting the load of the entire path.