Algorithm 1 Proposed dynamic resource allocation and ACB scheme in a slot

1: $N$: number of DS devices attempt to access

2: $p_{ACB}$: ACB factor

3: $L_{DS}^{*}$: optimal number of preambles allocated to DS devices

4: $p_{ACB}^{*}$: optimal value of ACB factor for DS devices

5: $L_{avail}$: number of available preambles

6: if $N\le L_{avail\_DS}$ then

7:   Set $p_{ACB}^{*}=1$;

8:   Compute $L_{set}$ through Equation (9);

9:     if $L_{set}=\varnothing$ then

10:     $L_{DS}^{*}=N$;

11:     else

12:     Compute $L_{DS}^{*}$ through Equation (10);

13:     end if

14: else if $N>L_{avail\_DS}$ then

15:   Set $L_{DS}^{*}=L_{avail\_DS}$

16:   Compute $p_{set}$ through Equation (12);

17:     if $p_{set}=\varnothing$ then

18:      $p_{ACB}^{*}=\raisebox{1ex}{$L_{avail\_DS}$}\!\left/ \!\raisebox{-1ex}{$N$}\right.$;

19:     else

20:      Compute $p_{ACB}^{*}$ through Equation (13);

21:     end if

22: end if