## 2 Network Architecture and Model  
In this section, SD-EOSN architecture and an EOSNV-ETL model are proposed. Figure 1 shows the model composites of satellite and ground networks. Among them, the satellite network mainly comprises LEO satellites, intra and inter-orbit satellite links form inter-satellite links (ISLs). The ground network includes ground stations (GSs), routers, and satellite network management centers (SNMCs). The data plane is composed of LEO nodes and ground routers. All forwarding nodes request data forwarding rules from the controller after receiving optical path connection requests, receive and parse the requirements issued by the controller, perform forwarding operations according to the corresponding laws of the controller, and report resource status information of nodes and links to the control plane. The control plane is also essential in achieving optical satellite network virtualization. We have divided the controller into two components because of its strong computing ability [24]. One part is used to compute and update the virtual topology, and another is used to collect information and perform related routing and resource allocation calculations. When the request arrives, the controller calculates and generates a virtual topology. The management plane is used to formulate and distribute routing and resource allocation strategies. Under the SD-EOSN architecture, utilizing optical network virtualization technology and adding a virtual topology model to solve the difficulty of traffic grooming establishes an EOSNV-ETL model, which generates a virtual optical network topology based on link and node information in the elastic optical satellite network, complete routing and resource allocation for incoming requests, thereby achieving dynamic traffic grooming and reducing issues such as business congestion, resource fragmentation, and limited network resource utilization in traditional elastic optical networks due to business allocation. Figure 1: SD-EOSN network architecture. It shows the process of generating a virtual topology from the EOSNs in Figure 1, which includes the same node number as the EOSNs. In the initial generation stage of virtual topology, there are no links between network nodes that are connected to it [25]. Optical links are established between nodes in the virtual layer when requests arrive. In the proposed twin-layer network model, the physical topology and virtual topology are represented by \(G^{S}\) and \(G^{V}\); \(N^{S}\), and \(E^{S}\) represent satellite nodes and links in the physical topology; \(N^{V}\) and \(E^{V}\) represent satellite nodes and links in the twin-layer network. Among them, \(|N|\) and \(|E|\) denote the number of satellite nodes (\(N\)) and links (\(E\)) in the twin-layer network, respectively, where \(|N^{S}|=|N^{V}|\) and \(|E^{S}|\geq|E^{V}|\). Due to the dynamic of the topology structure, the discrete-time strategy is adopted in this paper [26]. The information transmitted by the synchronous digital hierarchy (SDH) technology, widely used in satellite communication, is fixed in size. The schematic diagram of the logical connection between nodes in EOSNs and the optical path switching of the internal wavelength routing device is shown in Figure 2. Among them, a synchronous transfer module (STM) is a device that realizes branch signal division and multiplexing without photoelectric and optical conversion and can decompose the signal into a time-slot frame structure. It can integrate the information of different time slots at the input and output end through cross-interconnection. The integration mode between various time-slot resources is independent of each other. The working principle of the onboard forwarding service is as follows: each receiving antenna on the satellite receives all the laser signals in its link, packages each wavelength signal on different links into time-slot resources through STM, multiplexes the resources that need to be transmitted into one signal, and switches them to the corresponding transmitting antenna.