# Towards Deterministic-Delay Data Delivery Using Multi-Criteria Routing over Satellite Networks
## 1 Introduction
The literature [12] introduces an extended localized link state load balancing routing algorithm (LB-ELS), which employs a triggered local congestion notification mechanism and on-demand routing calculation. By assessing the congestion state of all links on each candidate path, it selects the optimal route from a set of candidate paths to mitigate congestion and achieve load balancing. The literature [13] proposes a Distance-based Back-Pressure Routing (DBPR) strategy, which introduces a new metric, destination distance delay, estimated by the Euclidean distance between satellites to predict the propagation delay of packets to the destination. The algorithm dynamically selects non-congested short paths for data transmission by calculating link weights that take into account both queue backlogs and the propagation delay, achieving load balancing by restricting the transmission area. However, due to the lack of a global view, the algorithms proposed in the literature [12; 13] face the issue of local optimality [14; 15]. The literature [16] proposes a load balancing routing algorithm based on extended link state information, which designs a link congestion notification mechanism. When the queue length at a node reaches or exceeds a threshold, the node is considered congested, and the algorithm recalculates the route to avoid that node. Simultaneously, it computes multiple candidate paths using the K Shortest Paths (KSP) algorithm, allowing a quick switch to other available paths when congestion occurs on the current path. Nevertheless, none of these algorithms considers the impact of service arrival rates during their design. Considering the impact of historical service arrival rates on the performance of load balancing algorithms, the literature [17] proposed a hybrid traffic detour load balancing routing strategy (HLBR). This approach predicts regions prone to congestion based on the access traffic load in ground areas and calculates detour paths accordingly to achieve load balancing. The literature [18] introduced a multipath search load balancing a routing algorithm based on regional traffic splitting. This algorithm dynamically calculates transition probabilities using link weight factors, steering factors, and node visibility parameters to achieve regional traffic splitting, ensuring that data transmission prioritizes links with a low congestion risk. Additionally, the algorithm calculates the optimal path and alternative paths under delay constraints, effectively addressing dynamic funnel congestion caused by uneven distribution of ground stations. The literature [19] proposed a load balancing routing algorithm based on deep reinforcement learning, where the relationship between traffic information and routing selection is obtained through machine learning. The algorithm uses the link utilization of the entire network and the traffic matrix as input states and designs output actions to select the optimal routing scheme. Feedback on the impact of the chosen route is provided through a reward function, optimizing the network load distribution. However, the methods proposed in the literature [17; 18; 19] treat time-sensitive and non-time-sensitive services equally, which may result in time-sensitive services choosing longer paths in a satellite network environment, making it difficult to guarantee the QoS requirements for time-sensitive services. The literature [20] proposed a hybrid service-aware routing algorithm based on service scheduling. This algorithm constructs a priority assignment function based on service arrival rates and waiting times, effectively distinguishing and handling services with different QoS requirements. For high-QoS services, the algorithm adopts an intra-orbit priority forwarding strategy, while for low-QoS services, a link-weighted routing algorithm is used.