Algorithm 2 DT-MILP Task Offloading

Require:  ${\mathbf{z}}_t,{\mathcal{S}}_t$, task i at m, $\{f_{\mathrm{edge}}^{n,j},c_{\mathrm{edge}}^{n,j}\}$, $\mathit{\lambda },\rho$ Ensure:  $({\beta }_i^{t,m},{\gamma }_i^{t,m},{\delta }_i^{t,m})$   1: Formulate MILP objective: $$J={\lambda }_1{T}_i^{t,m}+{\lambda }_2{E}_t^m+{\lambda }_3{\delta }_i^{t,m}+{\lambda }_4(1-\mathrm{FI})+{\lambda }_5{\mathcal{S}}_t$$   2: Subject to constraints: $$\left(28\right)–\left(36\right)$$   3: Warm-start using DT predictions: $${\mathbf{z}}_t\to \{U_{\mathrm{CPU}},E_t,\mathrm{fairness}\mathrm{indicators}\}$$   4: Solve MILP: $$({\beta }_i^{t,m},{\gamma }_i^{t,m},{\delta }_i^{t,m})\leftarrow \mathtt{intlinprog}\left(J\right)$$   5:if  ${\gamma }_i^{t,m}=1$ then   6:       Select destination: $$(n^{🟉},j^{🟉})\leftarrow \arg \max x_{ij}^{t,m}$$   7:      Offload task to CPU $j^{🟉}$ at server $n^{🟉}$   8: end if   9:return optimal decision variables