Algorithm 1 Thermal aware workload scheduling

Input:$D{C}_{Distributed}$, $N$ the number of distributed servers, $M$ the number of workload tasks, $T_{Room}$ the temperatures in the rooms where the servers are distributed, $T_{set-point}$ the desired temperature in the rooms. Output: $W_{scheduling}$ matrix keeping the tasks scheduling on servers $\mathit{O}\mathit{p}\mathit{t}\mathit{i}\mathit{m}\mathit{i}\mathit{z}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{G}\mathit{o}\mathit{a}\mathit{l}:determine{W}_{scheduling}toMIN\left({\displaystyle \sum _{k=1}^N}distance\left(T_{Room}^k,T_{set-point}^k\right)\right)$ Considering the following constraints for each server $k=1\dots N$ $C1:W_{alocation}^k=\left\{Tas{k}_j\right|j\in \left\{1\dots M\right\}and{W}_{scheduling}\left(k\right)\left(j\right)>0\}$ $C2:Q_{generated}^k\left(T\right)={\displaystyle \sum _{i=1}^{nc}}\omega \left(i\right)\ast f_{schedule}\left(W_{alocation}^k\right)$ $C3:T_{Room}^k(\nabla )=f_Q^k\left(T_{Room}^k\left(0\right),Q_{server}^k(\nabla )\right)$ $C4:t_{start}^{kj}+t_{execution}^j\le t_{deadline}^j$ $C5:\forall t\in \left[0\dots T\right],CP{U}_k\left(t\right)\ge {\displaystyle \sum _{j=1t_{start}^{kj}\le t\le t_{start}^{kj}+t_{execution}^j}^M}CP{U}_j\left(t\right)$ $C6:\forall t\in \left[0\dots T\right],RA{M}_k\left(t\right)\ge {\displaystyle \sum _{j=1t_{start}^{kj}\le t\le t_{start}^{kj}+t_{execution}^j}^M}RA{M}_j\left(t\right)$ $C7:\forall t\in \left[0\dots T\right],HD{D}_k\left(t\right)\ge {\displaystyle \sum _{j=1t_{start}^{kj}\le t\le t_{start}^{kj}+t_{execution}^j}^M}HD{D}_j\left(t\right)$