# Designing a Softwarized Network Deployed on a Fleet of Drones for Rural Zone Monitoring
## 4 Computational Model of the Backbone Node Drones
### Acquiers  
Let us consider the service chain related to the acquirer running in the generic drone \(\wp\). Let \(N_{F}\) be the number of VTs attached to \(\wp\). Referring to Figure 5a, the whole acquirer computational load is the sum of the loads related to all the blocks highlighted in that figure, as expressed in (2). According to the linear model of the computational load, the computational load of the load balancer is:  
\[\Omega^{(ACh)}_{LB}=\wp_{LB}+\xi_{LB}\sum_{f=1}^{N_{F}}\lambda_{f} \tag{4}\]  
where \(\lambda_{f}\) is the bit rate of the flow \(f\). The computational load for the deep packet inspectors can be calculated taking into account that we have one DPI for each computation unit that is active in the drone \(\wp\), and the whole traffic coming from the VTs is distributed to the DPI blocks of the active computation units. Therefore, the overall computational load due to the DPI blocks is:\[\Omega_{DPI}^{(ACh)}=N_{S}\cdot\varphi_{DPI}+\xi_{DPI}\sum_{f=1}^{N_{F}}\lambda_{f} \tag{5}\]  
where \(N_{S}\) is the number of computation units in the considered drone \(\wp\). In order to calculate the computational load due to the acquirer blocks, notice that we have an instance of the acquirer block for each entering flow, and therefore:  
\[\Omega_{A}^{(ACh)}=N_{F}\cdot\varphi_{A}+\xi_{A}\sum_{f=1}^{N_{F}}\lambda_{f} \tag{6}\]  
Let us now derive the computational load due to the point-to-multipoint (PM) blocks. For this purpose, let us note that we have two sets of PM blocks. The first set is constituted by PM blocks that replicate flows to be sent to the transcoders if they have to be transcoded. More in depth, we have one PM block for each flow \(f\) that has to be transcoded in the considered drone \(\wp\), event represented by the indicator function \(I_{\wp}^{(\text{CO})}(f)\) defined as follows:  
\[I_{\wp}^{(\text{CO})}(f)=\left\{ \begin{array}{ll}1&\text{if the flow $f$ has to be transcoded in the drone $\wp$}\\ 0&\text{otherwise}\end{array} \right. \tag{7}\]  
The generic PM block of this set, the one that manages the generic flow \(f\), is loaded by a bit rate \(\lambda_{f}\), and has a computational load per unit of flow, \(\xi_{PM}\), that depends on the number of replicas it has to do, that is equal to the number \(N_{\wp}^{(\text{CO})}(f)\) of transcodings that the drone \(\wp\) has to do on the flow \(f\), plus one if it has been requested the storage of the flow. In order to represent this last event, let us define the following indicator function:  
\[I^{(Ss)}(f)=\left\{ \begin{array}{ll}1&\text{if some user has requested to store the flow $f$}\\ 0&\text{otherwise}\end{array} \right. \tag{8}\]  
The second set is constituted by the PM blocks that create replicas of the flows for the edge streamers in the related VDTs. To this purpose, for the generic flow \(f\) that has to be forwarded by the drone \(\wp\) to some edge streamers at an output quality \(q_{OUT}\), we indicate its bit rate as \(\gamma_{q_{OUT}}\), and define the indicator function \(I_{>1}^{(ESn)}\Big{(}T_{[f_{OUT}]}\Big{)}\) as follows:  
\[I_{>1}^{(ESn)}\Big{(}T_{[f_{OUT}]}\Big{)}=\left\{ \begin{array}{ll}1&\text{ if the number of ES nodes on the tree $T_{[f_{OUT}]}$ is $>1$}\\ 0&\text{otherwise}\end{array} \right. \tag{9}\]  
Each of these last PM blocks has to manage a flow bit rate \(\gamma_{q_{OUT}}\) and has a computational load per unit of flow, \(\xi_{PM}\), that depends on the number of replicas it has to do, that is equal to the number \(N_{f_{OUT}}^{(ESn)}\) of edge streamers nodes on the related VDT \(T_{[f_{OUT}]}\). Therefore, we have:  
\[ \begin{split}\Omega_{PM}^{(ACh)}&=\sum\limits_{f=1}^{N_{F}} \Big{\{}\Big{[}I_{\wp}^{(\text{CO})}(f)\text{ or }I^{(Ss)}(f)\Big{]}\cdot\varphi_{PM}+\xi_{PM}\Big{(}N_{\wp}^{(\text{CO})}(f)+I ^{(Ss)}(f)\Big{)}\cdot\lambda_{f}+\\ &\quad+\sum\limits_{q_{OUT}=0}^{Q_{L}}I_{>1}^{(ESn)}\Big{(}T_{[f_{OUT} ]}\Big{)}\cdot\Big{[}\varphi_{PM}+\xi_{PM}\Big{(}N_{f_{OUT}}^{(ESn)}\Big{)} \cdot\gamma_{q_{OUT}}\Big{]}\Big{\}}\end{split}