Algorithm 1. Core function for computing transmission probabilities and throughput calculation.

Require: Input parameters x

Ensure: Computed values for tap, $t_{he\mathrm{\_}sta}$, $p_{coll\mathrm{\_}cont\mathrm{\_}ap}$, $p_{coll\mathrm{\_}cont\mathrm{\_}he\mathrm{\_}sta}$

1: # Initialize core function for computing transmission probabilities

2: $t_{ap},t_{he\mathrm{\_}sta},p_{c\mathrm{\_}ap},p_{coll\mathrm{\_}cont\mathrm{\_}he\mathrm{\_}sta}\leftarrow x$

3: $nu{m}_{he\mathrm{\_}sta}\leftarrow NumHe$

4: function E( $Cont{W}_{min},m,p_c$)

5:     return ${\displaystyle \frac{(1-p_{coll\mathrm{\_}cont}-p_{coll\mathrm{\_}cont}\cdot {(2\cdot p_{coll\mathrm{\_}cont})}^m)}{(1-2\cdot p_{coll\mathrm{\_}cont})}}$

6: end function

7: ${\displaystyle p_{coll\mathrm{\_}cont\mathrm{\_}ap}\leftarrow 1-(1-t_{he\mathrm{\_}sta}{)}^{nu{m}_{he\mathrm{\_}sta}}}$

8: if $nu{m}_{he\mathrm{\_}sta}>0$ then

9:     $p_{coll\mathrm{\_}cont\mathrm{\_}he\mathrm{\_}sta}\leftarrow 1-(1-t_{ap})$

10: else

11:     $p_{coll\mathrm{\_}cont\mathrm{\_}he\mathrm{\_}sta}\leftarrow 0$

12: end if

13: $t_{ap}\leftarrow {\displaystyle \frac{1}{E(Cont{W}_{min\mathrm{\_}ap},ma{x}_{ap},p_{coll\mathrm{\_}cont\mathrm{\_}ap})+1}}$

14: if $nu{m}_{he\mathrm{\_}sta}>0$ then

15:     ${\displaystyle t_{he\mathrm{\_}sta}\leftarrow \frac{1}{E(Cont{W}_{min\mathrm{\_}he\mathrm{\_}sta},ma{x}_{he\mathrm{\_}sta},p_{coll\mathrm{\_}cont\mathrm{\_}he\mathrm{\_}sta})+1}}$

16: else

17:     $t_{he\mathrm{\_}sta}\leftarrow 0$

18: end if

19: $outcome\leftarrow [t_{ap},t_{he\mathrm{\_}sta},p_{coll\mathrm{\_}cont\mathrm{\_}ap},p_{coll\mathrm{\_}cont\mathrm{\_}he\mathrm{\_}sta}]$

20: return outcome

21: # Fixed Point Iteration

22: $initial\mathrm{\_}guess\leftarrow$ array of zeros with size 4

23: $result\leftarrow$ scipy.optimize.fixed_point(core_function, initial_guess)

24: ${\displaystyle probability\leftarrow \frac{(1-p_{coll\mathrm{\_}cont\mathrm{\_}ap}-p_{coll\mathrm{\_}cont\mathrm{\_}ap}\cdot {(2\cdot p_{coll\mathrm{\_}cont\mathrm{\_}ap})}^{ma{x}_{ap}})}{(1-2\cdot p_{coll\mathrm{\_}cont\mathrm{\_}ap})}}$

25: # Transmission times

26: $T{r}_{su}\leftarrow (T{r}_{su\mathrm{\_}Du}+T{r}_{SIFS}+T{r}_{BACK}+T{r}_{SIFS})$

27: $T{r}_{mu\mathrm{\_}du}\leftarrow get\mathrm{\_}T{r}_{mu\mathrm{\_}du}(nu{m}_{a\mathrm{\_}mu\mathrm{\_}dl},V_u)$

28: $T{r}_{mu\mathrm{\_}u}\leftarrow maxTxopDuration$

29: # Probabilities of having a certain outcome at a given slot

30: $nu{m}_{he\mathrm{\_}sta}\leftarrow NumHe$

31: ${\displaystyle p_{coll\mathrm{\_}he\mathrm{\_}device}\leftarrow \frac{NumHe}{params{[}^{\mathrm{\prime }}nStation{s}^{\mathrm{\prime }}]}}$

32: $a1\leftarrow (t_{ap}\cdot p_{coll\mathrm{\_}he\mathrm{\_}device}\cdot \alpha \cdot (1-p_{coll\mathrm{\_}cont\mathrm{\_}ap}))$

33: $a2\leftarrow (nu{m}_{he\mathrm{\_}sta}\cdot t_{he\mathrm{\_}sta}\cdot (1-p_{coll\mathrm{\_}cont\mathrm{\_}he\mathrm{\_}sta}))$

34: $a3\leftarrow ((1-\alpha )\cdot \beta \cdot t_{ap}\cdot p_{he\mathrm{\_}device})$

35: $a4\leftarrow ((1-\alpha )\cdot (1-\beta )\cdot t_{ap}\cdot p_{he\mathrm{\_}device})$

36: $b1\leftarrow ((1-t_{ap})\cdot (1-t_{he\mathrm{\_}sta}{)}^{nu{m}_{he\mathrm{\_}sta}})$

37: $p_{coll\mathrm{\_}he\mathrm{\_}tx}\leftarrow (1-(1-t_{he\mathrm{\_}sta}{)}^{nu{m}_{he\mathrm{\_}sta}})$

38: # UL and DL throughput

39: $T{h}_{a1}\leftarrow T{h}_{su}$

40: $T{h}_{a2}\leftarrow T{h}_{su}$

41: $T{h}_{a3}\leftarrow T{h}_{mu\mathrm{\_}d}$

42: $T{h}_{a4}\leftarrow T{h}_{mu\mathrm{\_}u}$

43: $T{h}_{c1}\leftarrow T{h}_{cont\mathrm{\_}su}$

44: $T{h}_{c2\mathrm{\_}sta}\leftarrow T{h}_{cont\mathrm{\_}su}$

45: $T{h}_{c2\mathrm{\_}ap}\leftarrow T{h}_{cont\mathrm{\_}mu\mathrm{\_}dl}$

46: $T{h}_{c3\mathrm{\_}sta}\leftarrow T{h}_{cont\mathrm{\_}su}$

47: $T{h}_{c3\mathrm{\_}ap}\leftarrow T{h}_{cont\mathrm{\_}mu\mathrm{\_}ul\mathrm{\_}ap}$

48: $T{h}_{c4}\leftarrow T{h}_{cont\mathrm{\_}su}$

49: # Head-of-line

50: $hol\leftarrow \mathbf{i}\mathbf{f}params{[}^{\mathrm{\prime }}d{l}^{\mathrm{\prime }}]==\mathrm{\prime }s{u}^{\mathrm{\prime }}\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{n}NumHe\cdot (T{h}_{su}+E_{ap}\cdot T{h}_e)\cdot 1000\mathbf{e}\mathbf{l}\mathbf{s}\mathbf{e}\frac{NumHe}{Va{r}_u}\cdot (T{h}_{mu\mathrm{\_}d}+E_{ap}\cdot T{h}_e)\cdot 1000$