# Evaluating the Functioning Quality of Data Transmission Networks in the Context of Cyberattacks
## 5 Demonstration of the Efficiency of the Suggested Method
The equivalent function of the stochastic network when there are two types of action is as follows:  
\[Q(s)~{}=~{}w(s)h(s), \tag{29}\]  
where  
\[w(s)~{}=~{}\bigg{(}\frac{\theta}{\theta+s}\bigg{)}^{\eta};~{}~{}h(s)~{}=~{} \frac{\Big{[}1-\Big{(}\frac{r_{1}}{r_{1}+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{[}1 -\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{]}\Big{(}\frac{h}{h+s }\frac{d(d+c+s)}{(d+s)(d+c)}}{\Big{[}1-\Big{(}\frac{h}{h+s}\Big{)}^{\alpha_{ 3}}\frac{d}{(d+s)}\Big{]}\Big{[}\Big{(}\frac{r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_ {1}}+\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{[}1-\Big{(}\frac{ r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{]}\Big{]}}. \tag{30}\]  
Let us calculate the parameters of the scale and shape of the partial distributions:  
\[r_{1(2)}~{}=~{}\frac{t_{r1(2)}}{D_{r1(2)}}~{}=~{}1.5(2.65);~{}\alpha_{r1(2)}~{ }=~{}\frac{t_{r1(2)}}{D_{r1(2)}}^{2}~{}=~{}450\Big{(}1.06*10^{3}\Big{)}; \tag{31}\]  
\[h~{}=~{}\frac{t_{b}}{D_{b}}~{}=~{}5.1*10^{3};~{}\alpha_{h}~{}=~{}\frac{t_{b}}{ D_{b}}^{2}~{}=~{}31.4. \tag{32}\]  
Then, by means of numerical methods, we shall receive the mathematical expectation and dispersion of the service (transmission) time:  
\[M_{1}~{}=~{}T_{h}~{}=~{}-\frac{d}{ds}\bigg{(}\frac{h(s)}{h(0)}\bigg{)}_{s~{}=~ {}0}~{}=~{}0.078~{}(s);~{}D_{h}~{}=~{}\frac{d^{2}}{ds^{2}}\bigg{(}\frac{h(s)}{ h(0)}\bigg{)}_{s~{}=~{}0}-T_{h}^{2}~{}=~{}0.714 \tag{33}\]  
and quadratic coefficient of the variation of the service time is equal to  
\[C_{b}^{2}~{}=~{}\frac{D_{h}}{T_{h}^{2}}~{}=~{}117.3. \tag{34}\]  
Further, by means of (16) and (17), and taking into account (19), we will determine the quadratic coefficient of variation of the data flow, mathematical expectation and dispersion of the waiting time at storage capacity \(K\) = 50:  
\[C_{uw}^{2}~{}=~{}3.36;~{}T_{w}~{}=~{}12.067~{}(s);~{}D_{w}~{}=~{}145.6~{} \Big{(}s^{2}\Big{)}. \tag{35}\]  
Distribution parameters of the service waiting time are equal to:  
\[\theta~{}=~{}\frac{T_{w}}{D_{w}}~{}=~{}0.083;~{}\eta~{}=~{}\frac{{T_{w}}^{2}}{ D_{w}}~{}=~{}0.993. \tag{36}\]  
Now we have the necessary data to calculate the parameters of the shape and scale of the delivery time distribution function in the context of cyberattacks:  
\[\alpha_{n}~{}=~{}\frac{(T_{h}+T_{w})^{2}}{D_{h}+D_{w}}~{}=~{}1.1;~{}\beta_{n}~ {}=~{}\frac{(T_{h}+T_{w})}{D_{h}+D_{w}}~{}=~{}0.083. \tag{37}\]  
The probability of successful delivery, based on (8), is equal to:  
\[P(t\leq T_{z})~{}=~{}F(T_{z}~{}=~{}5~{}s)~{}=~{}0.336, \tag{38}\]meanwhile, the average data delivery time is equal to:  
\[w(s)~{}=~{}\bigg{(}\frac{\theta}{\theta+s}\bigg{)}^{\eta};~{}~{}h(s)~{}=~{} \frac{\Big{[}1-\Big{(}\frac{r_{1}}{r_{1}+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{[}1 -\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{]}\Big{(}\frac{h}{h+s }\frac{d(d+c+s)}{(d+s)(d+c)}}{\Big{[}1-\Big{(}\frac{h}{h+s}\Big{)}^{\alpha_{ 3}}\frac{d}{(d+s)}\Big{]}\Big{[}\Big{(}\frac{r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_ {1}}+\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{[}1-\Big{(}\frac{ r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{]}\Big{]}}. \tag{30}\]0  
Jitter of the delivery time is equal to:  
\[w(s)~{}=~{}\bigg{(}\frac{\theta}{\theta+s}\bigg{)}^{\eta};~{}~{}h(s)~{}=~{} \frac{\Big{[}1-\Big{(}\frac{r_{1}}{r_{1}+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{[}1 -\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{]}\Big{(}\frac{h}{h+s }\frac{d(d+c+s)}{(d+s)(d+c)}}{\Big{[}1-\Big{(}\frac{h}{h+s}\Big{)}^{\alpha_{ 3}}\frac{d}{(d+s)}\Big{]}\Big{[}\Big{(}\frac{r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_ {1}}+\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{[}1-\Big{(}\frac{ r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{]}\Big{]}}. \tag{30}\]1  
The probability of data loss is equal to:  
\[w(s)~{}=~{}\bigg{(}\frac{\theta}{\theta+s}\bigg{)}^{\eta};~{}~{}h(s)~{}=~{} \frac{\Big{[}1-\Big{(}\frac{r_{1}}{r_{1}+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{[}1 -\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{]}\Big{(}\frac{h}{h+s }\frac{d(d+c+s)}{(d+s)(d+c)}}{\Big{[}1-\Big{(}\frac{h}{h+s}\Big{)}^{\alpha_{ 3}}\frac{d}{(d+s)}\Big{]}\Big{[}\Big{(}\frac{r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_ {1}}+\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{[}1-\Big{(}\frac{ r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{]}\Big{]}}. \tag{30}\]2  
The graph of the distribution function of the data delivery time in the context of cyberattacks is shown in \[w(s)~{}=~{}\bigg{(}\frac{\theta}{\theta+s}\bigg{)}^{\eta};~{}~{}h(s)~{}=~{} \frac{\Big{[}1-\Big{(}\frac{r_{1}}{r_{1}+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{[}1 -\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{]}\Big{(}\frac{h}{h+s }\frac{d(d+c+s)}{(d+s)(d+c)}}{\Big{[}1-\Big{(}\frac{h}{h+s}\Big{)}^{\alpha_{ 3}}\frac{d}{(d+s)}\Big{]}\Big{[}\Big{(}\frac{r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_ {1}}+\Big{(}\frac{r_{2}}{r_{2}+b+s}\Big{)}^{\alpha_{2}}\Big{[}1-\Big{(}\frac{ r_{1}}{r_{1}+b+s}\Big{)}^{\alpha_{1}}\Big{]}\Big{]}\Big{]}}. \tag{30}\]3