Algorithm 1 StealRM.

Require: the flow set F

Ensure: the scheduling results $\forall s_a$ and $\forall r_a$

1: the schedulable transmission set $R\leftarrow \{{\tau }_{i1}^{*},{\tau }_{i1}^{\prime },{\tau }_{i1}^{\prime \prime }|\forall f_i\in F\}$;

2: for $\forall t\in [1,\mathcal{T}]$do

3:  $R^{\prime }\leftarrow R$;

4:  sort $R^{\prime }$ according to the decreasing order of priorities;

5:  for each a from 1 to $|R^{\prime }|$ do

6:   $i\leftarrow \mathcal{F}\left({\tau }_a\right)$

7:   if ${\chi }_i==H$ and ${\tau }_a\in {\Gamma }_i^{\prime }\cup {\Gamma }_i^{\prime \prime }$ then

8:    $Y^{\prime }\leftarrow \underset{\forall h\in [0,\frac{\mathcal{T}}{T_i\left(H\right)})}{\cup }(Y_{t+T_i\left(H\right)\times h}^H\cup Y_{t+T_i\left(H\right)\times h}^{HL})-\{\forall {\tau }_{ig}^{*}\}$;

9:   else if ${\chi }_i==H$ and ${\tau }_a\in {\Gamma }_i^{*}$ then

10:    $Y^{\prime }\leftarrow \left(\underset{\forall h\in [0,\frac{\mathcal{T}}{T_i\left(L\right)})}{\cup }{Y}_{t+T_i\left(L\right)\times h}^L\right)\cup \left(\underset{\forall h\in [0,\frac{\mathcal{T}}{T_i\left(H\right)})}{\cup }(Y_{t+T_i\left(H\right)\times h}^H\cup Y_{t+T_i\left(H\right)\times h}^{HL})\right)-\{\forall {\tau }_{ig}^{\prime },{\tau }_{ig}^{\prime \prime }\}$;

11:   else

12:    $Y^{\prime }\leftarrow \left(\underset{\forall h\in [0,\frac{\mathcal{T}}{T_i\left(L\right)})}{\cup }{Y}_{t+T_i\left(L\right)\times h}^L\right)\cup \left(\underset{\forall h\in [0,\frac{\mathcal{T}}{T_i\left(H\right)})}{\cup }{Y}_{t+T_i\left(H\right)\times h}^{HL}\right)$;

13:   if ${\displaystyle \underset{\forall {\tau }_b\in Y^{\prime }}{\bigwedge }}({\tau }_a\cap {\tau }_b\ne \varnothing )$ and $|\Theta (Y^{\prime }\left)\right|<M$ then

14:    if t exceeds the deadline of $f_i$ then

15:     return unschedulable;

16:    $s_a\leftarrow t$; $r_a\leftarrow$ a random channel that is not in $\Theta \left(Y^{\prime }\right)$;

17:    $R\leftarrow R-\left\{{\tau }_a\right\}+$ the next transmission of ${\tau }_a$;

18:    if ${\chi }_i==H$ and ${\tau }_a\in {\Gamma }_i^{\prime }\cup {\Gamma }_i^{\prime \prime }$ then

19:     $\forall h\in [0,\frac{\mathcal{T}}{T_i\left(H\right)}),Y_{t+T_i\left(H\right)\times h}^H\leftarrow Y_{t+T_i\left(H\right)\times h}^H+\left\{{\tau }_a\right\}$;

20:    else if ${\chi }_i==H$ and ${\tau }_a\in {\Gamma }_i^{*}$ then

21:     $\forall h\in [0,\frac{\mathcal{T}}{T_i\left(L\right)}),Y_{t+T_i\left(L\right)\times h}^{HL}\leftarrow Y_{t+T_i\left(L\right)\times h}^{HL}+\left\{{\tau }_a\right\}$;

22:    else

23:     $\forall h\in [0,\frac{\mathcal{T}}{T_i\left(L\right)}),Y_{t+T_i\left(L\right)\times h}^L\leftarrow Y_{t+T_i\left(L\right)\times h}^L+\left\{{\tau }_a\right\}$;

24: return $\forall s_a$ and $\forall r_a$;