# Towards Deterministic-Delay Data Delivery Using Multi-Criteria Routing over Satellite Networks
## 2 System Model
### Spatiotemporal Distribution Model of Service Traffic  
The distribution of network traffic across the Earth's surface is closely related to population distribution. Therefore, in densely populated areas such as major cities like Shanghai and New York, network traffic is high, while in sparsely populated regions, such as the Sahara Desert in Africa and the Amazon Rainforest in Brazil, network traffic is low. To characterize the geographical distribution of service traffic, the Earth's surface can be divided into \(K\) regions based on the coverage area of low Earth orbit (LEO) satellites, where each satellite corresponds to a ground region directly beneath it. In fact, the traffic in satellite networks primarily originates from the ground (e.g., mobile Internet traffic) and from the satellites themselves (e.g., remote sensing, navigation, and space experiment data). In this study, we mainly consider satellite-to-ground traffic. The traffic transmission demand index \(R\) between satellite \(u\) and satellite \(v\) is related to the static equipment density index \(\rho\) and the distance \(d\) between the two satellites. The distance between satellite \(u\) and satellite \(v\) (in meters) is denoted by \(d_{u,v}\). According to the literature [28], when the satellite-to-ground traffic coefficients are \(\alpha=0.5\) and \(\beta=1.5\), the traffic demand between satellite \(u\) and satellite \(v\) can be expressed as:  
\[R_{u,v}=\frac{\left(\rho_{u}*\rho_{v}\right)^{\alpha}}{d_{u,v} ^{\beta}} \tag{1}\]  
The distribution of network traffic is influenced not only by geographical location but also by the time of day [18]. It is assumed that users in different regions of the world exhibit similar Internet usage patterns throughout the day, with less network activity at night and more during the daytime. Additionally, the frequency of Internet access varies across different times of the day. According to the literature [29], the trend in network traffic proportions at each hour of the day across global regions is shown in Figure 2. As expected, human network activity is higher during the day than at night, with traffic proportions peaking between 9 AM and 5 PM. At 10 AM, network traffic can account for up to 11% of the total daily traffic, while nighttime traffic is much lower, with an average hourly traffic proportion of around 1%. Based on this time characteristic, a time traffic ratio parameter \(p_{\tau}\) can be defined to represent the proportion of traffic during a specific time period \(\tau\) relative to the total daily traffic. \begin{table}
\begin{tabular}{c c} \hline
**Symbol** & **Symbol Description** \\ \hline \(S\) & Set of all satellite nodes in the satellite network \\ \(G\) & Network topology \\ \(\mathcal{E}_{T}\) & Set of links in the snapshot graph \\ \(B_{u,v}^{\tau}\) & Maximum transmission rate of link \((u_{\tau},v_{\tau})\) \\ \(R\) & Satellite-to-ground traffic demand index \\ \(\rho\) & Static equipment density index \\ \(d\) & Distance between satellites \\ \(p_{\tau}\) & Time traffic ratio \\ \(A\) & Total daily traffic \\ \(\lambda\) & Average data generation rate of a satellite, in bit/s \\ \(\lambda_{\tau,u,v}^{s}\) & Spatiotemporal traffic factor \\ \(C\) & Capacity of inter-satellite links \\ _load_ & Load on inter-satellite link \\ \(\mu\) & Link load ratio \\ \(Q\) & Set of satellite nodes sorted in descending order of traffic arrival rate \\ \(pts\) & Path for time-sensitive services \\ \(puts\) & Path for non-time-sensitive services \\ \(\delta\) & Link load accumulation factor \\ \hline \end{tabular}
\end{table} 
Table 1: Symbol definitions. Therefore, the traffic between any two satellites in the satellite network is related to both time and space.