Algorithm 3: Preference-Based Bilateral Matching Offloading Algorithm

Input: $ℐ$, $\mathcal{C}$

Output: $\mathcal{X}$

1: Initialize ${ℳ}_n^{candidate}$, ${\mathcal{N}}_m^{req}$, ${\mathcal{N}}_m^{candidate}$, ${\mathcal{N}}_m^{no}$, ${\mathcal{N}}_m^{rec}$, ${\mathcal{N}}_m^{off}$, ${\mathcal{N}}_m^{exe}$ equal to $\mathsf{Ø}$;

2: User side: each user sends an offloading request to its associated BS;

3: MEC side: BSs mutually forward the users offloading requests;

4: Initial task offloading:

5: for $m\in ℳ$ do

6: ${\mathcal{N}}_m^{req}\leftarrow$ received offloading requests;

7: ${\mathcal{N}}_m^{candidate}$, ${\mathcal{N}}_m^{no}$$\leftarrow {\mathcal{C}}_0$;

8: Initial offloading strategy ${\mathcal{X}}_0$: ${\mathcal{N}}_m^{candidate}\to x_{nm,I_n}=1$, ${\mathcal{N}}_m^{no}\to$ according to user preferences, with full acceptance of offloading requests;

9: Initial resource allocation strategy: ${ℱ}_0\leftarrow {\mathcal{X}}_0$, according to Algorithm 2;

10: end for

11: for $n\in \mathcal{N}$ do

12:  Computing $T_n\leftarrow$ Equation (7);

13:  ${\mathcal{N}}_m^{exe}\leftarrow m\leftarrow \mathcal{X}$;

14: if $T_n\le t_n^{\max }$ and $\underset{n\in {\mathcal{N}}_m^{exe}}{\Sigma }{f}_{mn}\le f_m\left(\forall m\in ℳ, \forall n\in {\mathcal{N}}_m^{exe}\right)$

15:   ${\mathcal{N}}_m^{exe}={\mathcal{N}}_m^{exe}$;

16:   $x_{nm,I_n}=1$;

17: else

18:  Computing ${\gamma }_{nm}(\forall n\in {\mathcal{N}}_m^{exe})$;

19:  Sort ${\gamma }_{nm}$ in descending order, select a task with the smallest value to offload in turn, let ${\mathcal{N}}_m^{exe}={\mathcal{N}}_m^{exe}\backslash \left\{n\right\}$ and ${\mathcal{N}}_m^{off}={\mathcal{N}}_m^{off}\cup \left\{n\right\}$ until and ${\displaystyle \sum _{n\in {\mathcal{N}}_m^{exe}}{f}_{mn}\le f_m}$$\left(\forall n\in {\mathcal{N}}_m^{exe}\right)$;

20: end if

21: end for

22: for $n\in {\mathcal{N}}_m^{off}$ do

23: Computing offloading preference $x_{m,I_n}\left(k\right)$($\forall k\in {ℳ}_n^{candidate}$);

24: Sort $x_{m,I_n}\left(k\right)$ in descending order, select a collaborative BS $k$ with the biggest value to send the offloading request preferentially.

25: if $k=0$ do

26:  Accept the offloading request of $I_n$, let ${\mathcal{N}}_m^{off}\backslash \left\{n\right\}$, $x_{n0,I_n}=1$;

27: else

28:  if $k$ accepts the offloading request of $I_n$, let ${\mathcal{N}}_m^{off}\backslash \left\{n\right\}$, $x_{nk,I_n}=1$;

29:  else send the offloading request of $I_n$ to the suboptimal collaborative BS $k$, until it is accepted, let $x_{nk,I_n}=1$;

30:  end if

31: end if

32: end for