Algorithm 1: Service Caching Algorithm based on Gibbs Sampling

Input:$\mathcal{N}$, $ℳ$, $\mathcal{S}$, $D_s\left(s\in \mathcal{S}\right)$, $K_m(m\in ℳ)$, $w$

Output:$\mathcal{C}$, $\mathcal{X}$, $ℱ$, $\tau$, ${\tau }^{ave}$

1: Initialize ${\mathcal{C}}^0\leftarrow 0$, $L$

2: for $l=1:L$ do

3: Randomly select an MEC server $m\in ℳ$ and a feasible caching strategy $C_m^{*}\in \mathcal{C}$;

4: Based on the previous round caching strategy $\left\{C_1^{l-1},C_2^{l-1},\dots C_M^{l-1}\right\}$, compute the task offloading strategy $\mathcal{X}$ and resource allocation strategy $ℱ$ and objective function value $\tau$ and ${\tau }^{ave}$;

5: Based on the current round caching policy $\left\{C_1^l,C_2^l,\dots C_m^{*},\dots C_M^l\right\}$, compute the task offloading strategy ${\mathcal{X}}^{*}$ and resource allocation strategy ${ℱ}^{*}$ and objective function value ${\tau }^{*}$ and ${\tau }^{*ave}$;

6: Let $C_m^l=C_m^{*}$ with the probability $\rho =\frac{1}{1+e^{\left({\tau }^{\ast }-\tau \right)/w}}$;

7: Let $C_m^l=C_m^{l-1}$ with the probability $1-\rho$;

8: end for