# Towards Deterministic-Delay Data Delivery Using Multi-Criteria Routing over Satellite Networks
## 3 Problem Modeling
### Routing Algorithm
The simulation was conducted using Xi'an local time as a reference, with the local time set to 15:00 to generate service traffic for each region. The packet size was set to 1000 bits, and the inter-satellite link capacity was configured at 200 Mbit/s. The ratio of time-sensitive to non-time-sensitive services was set at 1:4, and the traffic arrival rate was determined by equation (2). The simulation duration was 30 min, running on hardware with an Intel(R) Core(TM) i7-14700 HX 2.10 GHz processor and 32 GB of memory. Figure 4 shows the network load distribution under the satellite Internet service scheduling algorithm based on the spatiotemporal distribution of traffic. Similar to Figure 1b, the traffic arrival rate and link status of satellites at a given time can be calculated based on the ground population distribution and the relative position of satellites to the ground. In Figure 3, there are 40 lightly loaded links, 13 heavily loaded links, and 59 moderately loaded links. Compared to Figure 1b, which has 62 lightly loaded links, 12 heavily loaded links, and 38 moderately loaded links, the satellite Internet service scheduling algorithm based on the spatiotemporal distribution of traffic results in most network links being in a moderately loaded state, improving link utilization in the network. Figure 4: Load distribution of the satellite network under the satellite Internet service scheduling algorithm based on spatiotemporal distribution of traffic (total daily traffic of 180 T). Figure 5 shows the packet loss rate for time-sensitive services under different algorithms. When the network load is light, the packet loss rate for the satellite Internet service scheduling algorithm based on the spatiotemporal distribution of traffic is similar to that of the shortest path algorithm. However, as the network load increases, the packet loss rate for the satellite Internet service scheduling algorithm becomes gradually lower than that of the shortest path algorithm. Specifically, when the network load is 120 Tbit, the packet loss rate for time-sensitive services in the shortest path algorithm is 22%, while it is 5.1% in the satellite Internet service scheduling algorithm based on the spatiotemporal distribution of traffic. The lower packet loss rate of the proposed algorithm is due to its design, where, under high inter-satellite link load conditions, time-sensitive services are transmitted via the shortest path while non-time-sensitive services are routed through less loaded links, even if it means taking a longer path. This strategy fulfills non-time-sensitive service transmission requirements while reserving the remaining bandwidth for time-sensitive services, thereby reducing the contention for transmission resources and lowering the packet loss rate for time-sensitive services. In comparison with the optimized method, when the total daily traffic is less than or equal to 85 Tbit, both the spatiotemporal distribution-based satellite Internet service scheduling algorithm and the optimized method have zero packet loss. However, when the total daily traffic is 150 Tbit, the packet loss rate for the optimized method is 6.47%, while the packet loss rate for the proposed method is 12.37%, showing a performance difference of approximately double. From Figure 6, it can be observed that when the network load is 50 Tbit, the throughput of time-sensitive services in both the traffic distribution-based satellite Internet scheduling algorithm and the shortest path algorithm is nearly identical. This is because, under a low network load, most links are in a light load state. During routing calculations, the link cost in the traffic distribution-based satellite Internet scheduling algorithm is nearly the same as the initial link cost (i.e., the propagation delay between two satellites), resulting in almost identical throughput for both algorithms under a light load. However, as the overall network load increases, the satellite network load becomes increasingly imbalanced.