Algorithm 1. Resource Allocation Algorithm for GACK Transmission

Input: U

Output: ${\theta }_r^{*}$, ${\tau }_r^{*}$, ∀r

Initialization: $N_{\theta }^{*}$← 0, r ← 1

1: for t ← 1 to k

2:    if there is an idle gateway on the timeslot t

3:       Generate ${\theta }_r$ and compute $N_{\theta }^r$

4:       if $N_{\theta }^r$ >${N_{\theta }^r}^{*}$ then

5:          ${N_{\theta }^r}^{*}$ ← $N_{\theta }^r$, ${\theta }_r^{*}$ ← ${\theta }_r$

6:          ${\tau }_r^{*}\left(i\right)$ ← $(t,t+{\theta }_r^{*}\left(i\right)-min\left(\mathbf{S}\right))$, ∀i

7:       end if

8:      Repeats 3-9 until all ${\theta }_r$ are considered

9:   end if

10:   r ← r+1

11:   Update U

12:end for