# Flying Real-Time Network to Coordinate Disaster Relief Activities in Urban Areas +
## 4 Network Deployment Model  
During the deployment of the network, the initial locations of the nodes must be defined as described in Section 3.2. The network topology should contain the minimum number of TWUs, and the total length of the network links must be short enough to guarantee a low communication delay between the SAR teams and the IC. At run-time, the power consumption of all mobile units (which is directly related to the network deployment) becomes an important aspect to consider, since it allows the communication service to be kept active for longer time periods--hopefully for the whole golden relief time, although this would typically involve the exchange of units.  
In order to represent a realistic scenario for studying disaster relief activities, we consider a set of \(N_{f}\) nodes, each one with a fixed location. One of these nodes plays the role of IC and the rest are SAR teams. The teams and the IC have a communication range defined by \(Pf_{i}\), for \(i=1,...,N_{f}\). Each team must communicate with the IC, but eventually the communication range between them is not short enough to perform a direct interaction, and therefore the signal must be repeated by TWUs (particularly, by meta-TWUs) or eventually the information should be transported to the IC and vice versa using males.  
Formally, let \(X\) be a matrix of \(N_{m}\) rows by three columns containing the positions of \(N_{m}\) mobile nodes (SAR teams). \(X_{i}\) is the position of the \(i\)-th node of the set. The third component of \(X\) represents the altitude of the node location. Because the mobile nodes are on ground, the altitude of its location is assumed as a function of the first two components of \(X\). Let \(Z\) be a matrix containing the elevation map of the terrain where the network must be deployed. Because \(Z\) is discrete and the mobile nodes can be located in any position within the area, bi-linear interpolation is used to calculate the altitude of each node position.  
We consider that each node has a maximum communication range defined by \(Pm_{i}\), with \(i=1\),..., \(N_{m}\). To establish a link between two nodes, they must be in range and in line of sight. For a node \(i\) to be linked to a different node \(j\), this distance can be expressed as follows:  
\[\text{dist}(X_{i},X_{j})<\min(Pm_{i},Pm_{j})\wedge\log(X_{i},X_{j},Z), \tag{1}\]  
where \(\text{dist}(v,w)\) is the Euclidean distance between \(v\) and \(w\), and \(\log(v,w,z)\) computes the line-of-sight visibility of points \(v\) and \(w\) according to elevation map \(z\). Taking these conditions into account, if random allocation of mobile nodes is used, \(N_{m}\) must be a sufficiently large number such that the communication between the SAR teams and the IC can be achieved.  
We further extend this network model to consider a communication protocol using a simple routing algorithm that determines the path of minimum length between each SAR team and the IC. Each path is enumerated as \(path_{i}\) with \(i=1,...,N_{f}-1\). Figure 4 illustrates two network deployment situations. For each team, there must be a route that allows communication with the IC. Discarding nodes that are not part of any of the \(N_{f}-1\) routes, we obtain the minimum number of nodes for the \(X\) distribution, which is named \(N_{opt}\). Therefore, it is necessary to determine \(X\) such that \(N_{opt}\) is minimum, and the sum of the distances of each path that links the SAR teams with the IC is also minimal. Then, the optimization problem is formulated as follows:  
\[\text{minimize}f(X)=\alpha\cdot\sum_{i=1}^{N_{f}-1}\text{length}(path_{i})+ \beta\cdot N_{opt}, \tag{2}\]where \(\alpha\) and \(\beta\) allow us to weigh the importance of minimizing the number of TWUs or maximizing the speed of the network by reducing the distance of each path. Although the terms of Equation (2) are independent, it is assumed that the smaller the number of nodes, the less flexible the network is to allow direct paths from the SAR teams to the IC, and therefore the length of each path is greater.