# Designing a Softwarized Network Deployed on a Fleet of Drones for Rural Zone Monitoring
## 4 Computational Model of the Backbone Node Drones
### Edge Streamers  
According to (3), let us derive the computational load due to the edge streamer chain, as represented in Figure 5b. In order to evaluate the computational load of the load balancer, let us observe that this block is loaded by a traffic bit rate given by the sum of two terms, the first related to the live streaming flows coming from the acquirers, and the second related to the stored flows requested by the clients connected to the considered edge streamer. The first term is the aggregated bit rate of all the live streaming flows directed to the clients accessing the platform through the edge streamer running in the considered drone \(\wp\). In order to calculate it, for a generic live streaming flow \(f_{L}\) encoded at a quality level \(q_{OUT}\), let us define the indicator function \(I_{\wp}^{(VDT)}(f_{L},q_{OUT})\) of the fact that the considered edge streamer in the drone \(\wp\) is on the VDT \(T_{[f_{L},q_{OUT}]}\), that is, some clients connected to the platform through the drone \(\wp\) have requested to receive the flow \(f_{L}\) at quality \(q_{OUT}\). Thus, this function is defined as follows:  
\[I_{\wp}^{(VDT)}(f_{L},q_{OUT})=\left\{ \begin{array}{ll}1&\text{if the drone $\wp$ belongs to the VDT $T_{[f_{L},q_{OUT}]}$}\\ 0&\text{otherwise}\end{array} \right. \tag{14}\]  
On the other hand, the second term can be calculated as the sum of the bit rates of the stored flows requested by clients connected to the platform through the drone \(\wp\). To this purpose, for a generic stored flow \(f_{S}\), let us define the following indicator function:  
\[I_{\wp}^{(St)}(f_{S})=\left\{ \begin{array}{ll}1&\text{if some Client connected to the drone $\wp$ has requested the stored flow $f_{S}$}\\ 0&\text{otherwise}\end{array} \right. \tag{15}\]  
The total input bit rate of the ES node in the drone \(\wp\) is:  
\[\lambda_{IN}^{(ESn)}=\sum_{f_{L}=1}^{N_{F}}\sum_{q_{OUT}=0}^{Q_{L}}I_{\wp}^{(VDT )}(f_{L},q_{OUT})\cdot\gamma_{q_{OUT}}+\sum_{f_{S}\in\aleph^{(S)}}\lambda_{f_{S }}I_{\wp}^{(St)}(f_{S}) \tag{16}\]  
where \(\aleph^{(S)}\) is the set of stored flows, and \(\lambda_{f_{S}}\) the bit rate of the stored flow \(f_{S}\). Now, we can calculate the computational load of the load balancer block as follows:\[\Omega_{LB}^{(ESn)}=\varphi_{LB}+\xi_{LB}\lambda_{IN}^{(ESn)} \tag{17}\]  
The computational load of the DPI block can be calculated as in (5), taking into account that in this case the input bit rate is \(\lambda_{IN}^{(ESn)}\). Therefore, we have:  
\[\Omega_{DPI}^{(ESn)}=N_{S}\cdot\varphi_{DPI}+\xi_{DPI}\lambda_{IN}^{(ESn)} \tag{18}\]  
In order to calculate the computational load of the edge streamer (ES) blocks, we note that we have one ES for each live streaming flow crossing the drone \(\wp\), and an additional ES for each client that has requested to watch a stored video stream. Therefore, we have:  
\[\Omega_{ES}^{(ESn)}=\sum\limits_{f_{L}=1}^{N_{F}}\sum\limits_{q_{IN}=0}^{Q_{L} }I_{\wp}^{(VDT)}(f_{L},q_{IN})\cdot\left[\varphi_{ES}+\xi_{ES}\gamma_{q_{IN}} \right]+\sum\limits_{f_{S}\in\mathbb{N}^{(S)}}I_{\wp}^{(St)}(f_{S})\cdot\left[ \varphi_{ES}+\xi_{ES}\lambda_{f_{S}}\right] \tag{19}\]  
Let us now derive the computational load for the point-to-multipoint (PM) blocks in the edge streamer of the drone \(\wp\). It is the sum of two terms: the first one considers the PMs used to send the video flows to the transcoding blocks and, for a given flow \([f_{L},q_{IN}]\), it is present if this flow has to be transcoded to at least two quality levels; the second term accounts for the point-to-multipoint transmission of each flow to more than one client. Therefore, if we indicate the number of clients connected to the VDT \(T_{[f_{L},QUT]}\) through the edge streamer in the drone \(\wp\) as \(N_{[f_{L},QUT]}^{(Cl,\wp)}\), and define the following indicator function:  
\[I_{>1}^{(Cl,\wp)}\Big{(}T_{[f_{L},QUT]}\Big{)}=\left\{ \begin{array}{ll}1& \text{if the number of Clients connected through the ES $\wp$}\\ &\text{on the tree $T_{[f_{L},QUT]}$ is greater than 1}\\ \\ 0&\text{otherwise}\end{array}