## 3 Network Model  
The architecture and network model of the IWSSN for emergency communications is depicted in this section. When a disaster occurs, an emergency information system will be established, as shown in Figure 1, which mainly consists of three parts, _i.e._, satellite constellations, sensor devices and a core network in a normal area. Sensor devices and terminals in the remote disaster area transmit large amounts of information (e.g., video, voice and data) back to the core network in the normal area using satellites as relays. Satellites can exchange information with each other utilizing inter-satellite links (ISLs). In order to get a general analytic network model, we use the term arbitrary sensor and satellite network to refer to such a remote sensor and satellite network with a total of \(N\) nodes arbitrarily and deterministically (_i.e._, not randomly) located in orbits (LEO, MEO, geostationary earth orbit (GEO), _etc._) or distributed in remote disaster area (sensor nodes). Obviously, these nodes may be either stationary (sensor nodes) or in motion following arbitrary and fixed (_i.e._, not random) trajectories (satellite nodes), so we use the term arbitrary. Each node in the network can be considered as a source, a relay, a destinationor a mixture. A node may choose an arbitrary and fixed number of other nodes as its destinations. Considering the case that a source has multiple destination nodes, the source node may transmit the same information to its destination nodes, _i.e._, multicast, or transmit different information to different destination nodes, _i.e._, unicast. In emergency scenarios, sensors and satellites in the network generally have the ability to collect great amounts of data. It is assumed that all of the nodes are capable of sourcing and sinking infinite amounts of data, _i.e._, there is always information waiting at the source nodes, and received information can always be processed. This saturated traffic scenario enables us to isolate unique characteristics of sensor and satellite nodes that influence network capacity. Let \(V_{N}\) be the node set, and let \(E\) be the link set. A link in the arbitrary sensor and satellite network is a means of an information channel connecting one node to another for the purpose of exchanging mission-specific data (video, voice, data, _etc._). The establishment of a link may follow either the protocol model or the physical model. As we assess sensor and satellite network capacity, we do not consider links between sensors for three reasons. (1) sensor nodes connected to each other can be taken as one virtual source or destination node, as shown in the following Figure 1; also, the gateway and the satellite can be taken as one virtual source or destination node; (2) links between sensor nodes usually exist, but information in a disaster area cannot go back to the the core network in the normal area without the help of satellites in most emergency scenarios; (3) the analysis of the network capacity between sensors helps us little to provide guidelines for optimizing the IWSSN schedules. Additionally, it will make the network capacity model complicated. Hence, we only consider links between sensor and satellite, satellite and satellite. Additionally, we are interested in the overall ability of the network to move data (bits) and are not concerned with the type of data (control or service). Links between sensor and satellite usually are a Rician fading channel. Additionally, links between satellite and satellite are an AWGN channel. Hence, we assume a line-of-sight must exist between two nodes when the link exists (Links may be feasible without direct line-of-sights, e.g., the satellite telephone service of the Iridium system [38, 39]; however, in most practical space scenarios, line-of-sight is necessary; the special cases are not considered in our current work). The existence and bandwidth of the links between sensor and satellite nodes are time variant, related to the dynamics and constraints of the satellite orbit.