# Data Traffic Modeling in RPAS/UAV Networks with Different Architectures
## 3 Calculation Method  
The NetCracker Professional 4.1 software [35] was chosen for traffic modeling in proposed models (Figure 2). It uses an analytical simulator based on mathematical equations to predict network behavior. The essence of the applied algorithm is as follows.  
Let us denote the internal characteristics of the communication channel, which are calculated at the time \(t_{k}\), as \(V_{1}(t_{k})\),..., \(V_{n}(t_{k})\); external characteristics at the same moment of time influencing them as \(W_{1}(t_{k})\),..., \(W_{r}(t_{k})\), and the average rate of change of internal characteristics in the time interval \([t_{k},t_{k}+1]\) as \(F_{i}(t_{k},V_{1}(t_{k}),\)..., \(V_{n}\) (\(t_{k}),W_{1}(t_{k})\)...\(W_{r}(t_{k}))\), \(i=1\)... \(n\). By specifying the values of the internal and external characteristics at the moment \(t_{k}\), it is possible to calculate the values of the internal characteristics at the moment \((t_{k}+1)\). To do this, the segment \([t_{0},T]\) is divided into \(P\) parts by the points \(t_{0}\), \(t_{1}\),..., \(t_{k}\),..., \(t_{P}=T\). If the values of internal characteristics at time \(t_{0}\) and average rates of the internal characteristics change on each segment \([t_{k},t_{k}+1]\) are known, then using the following relations it is possible calculating the values of internal characteristics for all \(t_{k}\), \(k=1,\)..., \(P\):  
\[V_{i}(t_{k}+1)=V_{i}(t_{k})+\Delta tF_{i}(t_{k},V_{1}(t_{k}),\)..., \(V_{n}(t_{k}),W_{1}(t_{k}),\)..., \(W_{r}(t_{k})), \tag{1}\]  
where \(i=1\), \(n;k=0,1,\)..., \(P-1\). We modeled such internal characteristics of communication channels as Average Utilization (AU), Travel Time (TT), and the number of dropped packets. Transaction Size (TS), Time Between Transactions (TBT), Bit Error Rate (BER), channel bandwidth, and packet failure probability were chosen as external characteristics that influenced the mentioned internal characteristics. If we consider the functions \(Y_{1}(t)\),..., \(Y_{n}(t)\) as continuous and having derivatives, then to describe the process, the equations of the following form are used  
\[dV_{i}/dt=F_{i}(t,V_{1},\)..., \(V_{n},W_{1},\)..., \(W_{r}), \tag{2}\]  
where \(i=1\),..., \(n\). Here, the functions \(F_{i}(t,V_{1},\)..., \(V_{n},\)\(W_{1},\)..., \(W_{r})\) represent the \"instantaneous\" rates of change of the corresponding internal characteristics.  
To calculate the parameters of the RPAS communication channel, it is necessary to specify the statistical distribution laws for the lengths of transmitted packets \(\omega(x)\) and the time intervals (TBT) between them \(\omega(t)\). In the proposed models, the Const probability distribution law was used: \(\omega(x)=Const\) and \(\omega(t)=Const\). Then the average length of transmitted packets and the average time interval between two neighboring packets are found by the Formulas (3) and (4) correspondently.  
\[TS=\int\limits_{-\infty}^{\infty}x\omega(x)dx. \tag{3}\]\[TBT=\int\limits_{-\infty}^{\infty}t\omega(t)dt. \tag{4}\]  
The average utilization of the communication channel is given by the formula:  
\[AU=TS/TBT=TS/\mu, \tag{5}\]  
where \(\mu=1/TBT\) is the packet transmission rate over the communication channel. The utilization of the communication channel depends both on the size of the transmitted packets and on the intensity of their generation. If the value of the AU parameter is greater than the maximum data transmission rate of the communication channel, then some of the transmitted packets will be lost with the probability:  
\[P=1-\frac{AU_{link}}{AU}. \tag{6}\]  
The average packet travel time through the communication channel is determined by the formula:  
\[TT=\frac{TS}{AU_{link}}. \tag{7}\]