## 3 Network Model
### Spatial Channel Networks  
As described in Section 1, refs. [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16] have conducted a series of studies on SCNs and demonstrated the practicability, scalability, reliability, and economical efficiency of SCNs.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Network Architecture** & **Network Resource** & **Solutions** \\ \hline \multirow{3}{*}{EONs} & & ILP: [19; 20; 40; 41; 43; 44; 45] \\  & RSA & Intelligent Optimization Algorithms: [21; 22; 23; 24; 25; 42] \\  & RMSA & Heuristic Algorithms: [26; 27; 37; 41] \\  & & Machine Learning: [29; 30] \\  & & ILP: [32; 36] \\  & RCSA & Intelligent Optimization Algorithms: [35; 36; 46; 47] \\  & RMCSA & Heuristic Algorithms: [31; 33; 39; 46; 47] \\  & & Machine Learning: [38] \\ SCNs & RSWA & Heuristic Algorithms: [48] \\  & RSCSA & ILP and Heuristic Algorithms: [49] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Related works on the optical network resource allocation problem.  
In Figure 1, the optical layer can be divided into an SDM layer and a WDM layer, and the optical nodes are considered as HOXCs, consisting of WXCs and SXCs in SCNs. To meet the functional requirements of SCNs, it is necessary to design HOXC architectures that are reliable, growable, and flexibly connected. Four SXC architectures have been designed, namely full-size matrix-switch-based SXCs, sub-matrix-switch-based SXCs, full-size core-selective-switch-based SXCs, and sub-core-selective-switch-based SXCs [12]. The SCNs in this paper use sub-core-selective-switch-based SXCs, the advantages and disadvantages of which are described in detail in the following content. The pros and cons of other types of SXCs are not discussed here.  
The SDM layer consists mainly of SXCs and SDM links, and the SDM links are the transmission medium bypassing the overlaying WDM layer for the SDM layer in Figure 1. Parallel SMFs or uncoupled MCFs are used as SDM links in SCNs. The fiber cores in SDM links are the physical entities of spatial lanes (SLs), which are the spatial resource units for resource allocation in SCNs. Moreover, a spatial channel (SCH) is an ultra-high-capacity optical data stream used to carry optical channels (OCHs) and is allowed to occupy the spectrum of the entire fiber core. SCNs are classified into four types according to the different properties of OChs carried on SCNs.  
Type I: An OCh can occupy a whole SCN or most of the capacity of an SCH;  
Type II: Multiple OChs with the same source and destination nodes are carried on the same SCH;  
Type III: Multiple OChs with different source and destination nodes are carried on the same SCH;  
Type IV: The capacity of an OCh is much larger than that of an SCH, and this OCh needs to be carried by cascaded SCNs.  
Since a single OCh can occupy a Type I SCh, only SXCs are needed to spatially bypass the optical signal, and no spectral grooming is required using WXCs (indicated by the dashed lines in Figure 1). Although the traffic of a single OCh is not large enough to occupy an entire Type II SCh, it is still possible to spatially bypass it using SXCs, since multiple OChs with the same source node and destination nodes could be carried on a single SCH. Switching costs are low for both of the above SCNs due to the utilization of cost-effective SXCs and the fact that no WXCs are deployed. Moreover, there is no need to set a guard band (GB) between OChs carried on these two types of SCNs, which saves  
Figure 1: Spatial channel network (SCN) model.  
spectrum resources. Since the source and destination nodes of each OCh carried on Type III SChs are different, WXCs (indicated by solid lines in Figure 1) must be used to achieve optical add/drop and optical bypass, which increases the switching cost. Furthermore, the occupied spectrum resources will increase because of GB. Therefore, Type I and Type II SChs should be used to carry OChs as much as possible when solving the RMSSA problem of SCNs.