Table 2.

Coefficients for the cost functions involved in the mathematical formulation

Description	Numerical data
$a_{\mathit{gu}}$ and ${\overline{a}}_{\mathit{gu}}$: Coefficients of the transmission cost of services from user g to the controller UAV u both in the first, the second stage under scenario $\omega$ and third stage under scenario $\xi$ ($c_{\mathit{gu}}^1$, $c_{\mathit{gu}}^{2\omega }$, $c_{\mathit{gu}}^{3\xi }$)	$a_{11}={\overline{a}}_{11}=0.1$, $a_{12}={\overline{a}}_{12}=0.2$, $a_{21}={\overline{a}}_{21}=0.1$, $a_{22}={\overline{a}}_{22}=0.2$, $a_{31}={\overline{a}}_{31}=0.1$, $a_{32}={\overline{a}}_{32}=0.2$
$d_{\mathit{uf}}$ and ${\overline{d}}_{\mathit{uf}}$: Coefficients of the transmission cost of the service requests from controller UAV u to any UAV $f\in {\mathcal{F}}_3$ in the first stage, the second stage under scenario $\omega$ and third stage under scenario $\xi$, ($c_{\mathit{uf}}^1$, $c_{\mathit{uf}}^{2\omega }$, $c_{\mathit{uf}}^{3\xi }$)	$d_{1\widehat{1}}=0.2$, $d_{1\widehat{2}}=0.1$, $d_{1\tilde{1}}=0.1$, $d_{1\tilde{2}}=0.2$, $d_{2\widehat{1}}=0.2$, $d_{2\widehat{1}}=0.2$, $d_{2\tilde{1}}=0.1$, $d_{2\tilde{2}}=0.2$, ${\overline{d}}_{1\widehat{1}}=0.2$, ${\overline{d}}_{1\widehat{2}}=0.1$, ${\overline{d}}_{1\tilde{1}}=0.1$, ${\overline{d}}_{1\tilde{2}}=0.2$, ${\overline{d}}_{2\widehat{1}}=0.2$, ${\overline{d}}_{2\widehat{2}}=0.1$, ${\overline{d}}_{2\tilde{1}}=0.1$, ${\overline{d}}_{2\tilde{2}}=0.2$
$g_f$ and ${\overline{g}}_f$: Coefficients of the execution cost of requested services to the UAV $f\in {\mathcal{F}}_3$ in the first stage, the second stage under scenario $\omega$ and third scenario under scenario $\xi$, ($c_f^{(E),1}$, $c_f^{(E),2\omega }$, $c_f^{(E),3\xi }$ )	$g_{\widehat{1}}=0.2$, $g_{\widehat{2}}=0.1$, $g_{\tilde{1}}=0.1$, $g_{\tilde{2}}=0.2$ ${\overline{g}}_{\widehat{1}}=0.2$, ${\overline{g}}_{\widehat{2}}=0.1$, ${\overline{g}}_{\tilde{1}}=0.1$, ${\overline{g}}_{\tilde{2}}=0.2$
$n_{\tilde{f}}$ and ${\overline{n}}_{\tilde{f}}$: Coefficients of the cost due to add new UAVs $\tilde{f}\in \tilde{\mathcal{F}}$ at the highest level of the network in the first stage, the second stage under scenario $\omega$ and third stage under scenario $\xi$ ($c_{\tilde{f}}^1$, $c_{\tilde{f}}^{2\omega }$, $c_{\tilde{f}}^{3\xi }$)	$n_{\tilde{1}}={\overline{n}}_{\tilde{1}}=0.1$, $n_{\tilde{2}}={\overline{n}}_{\tilde{2}}=0.2,$
$r_u$ and ${\overline{r}}_u$: Coefficients of the cost due to add additional capacity to the controller UAV u, both in the first and the second stage under scenario $\omega$ ($c_u^1$, $c_u^{2\omega }$)	$r_1=r_2={\overline{r}}_1={\overline{r}}_2=0.2$
$q_u$ and ${\overline{q}}_u$: Coefficients of the cost due to reduce capacity to the controller UAV u, both in the second stage under scenario $\omega$ and third stage under scenario $\xi$ ($c_u^{(D),2\omega }$, $c_u^{(D),3\xi }$)	$q_1=q_2={\overline{q}}_1={\overline{q}}_2=0.05$