Algorithm 3: Carbon-Aware Security Job Scheduling

Job queue $\mathcal{J}$, nodes $\mathcal{N}$, Sforecast horizon $\mathrm{H}$, Scheduling interval $\Delta \mathrm{t}$ Job-to-node-time assignments $\mathrm{x}$ Initialize carbon intensity forecasts ${\widehat{\gamma }}_{\mathrm{n}}\left(\mathrm{t}\right)$ for all $\mathrm{n}\in \mathcal{N}$, $\mathrm{t}\in \left[{\mathrm{t}}_{\mathrm{now}},{\mathrm{t}}_{\mathrm{now}}+\mathrm{H}\right]$ Compute renewable energy forecasts ${\widehat{\rho }}_{\mathrm{n}}\left(\mathrm{t}\right)$ for all nodes Update forecasts using LSTM model via (25) Sort jobs by priority: ${\mathcal{J}}_{\mathrm{sorted}}\leftarrow \mathrm{Sort}\left(\mathcal{J},{\omega }_{\mathrm{j}},{\mathrm{D}}_{\mathrm{j}}\right)$ Identify feasible (node, time) pairs satisfying (22), (23) Compute carbon cost ${\mathrm{c}}_{\mathrm{j},\mathrm{n},\mathrm{t}}={\mathrm{E}}_{\mathrm{j}}\cdot {\widehat{\gamma }}_{\mathrm{n}}\left(\mathrm{t}\right)$ for feasible pairs Select $\left({\mathrm{n}}^{*},{\mathrm{t}}^{*}\right)={\mathrm{argmin}}_{\mathrm{n},\mathrm{t}}\left({\mathrm{c}}_{\mathrm{j},\mathrm{n},\mathrm{t}}+{\omega }_{\mathrm{j}}\cdot \left(\mathrm{t}-{\mathrm{t}}_{\mathrm{arrival},\mathrm{j}}\right)\right)$ Assign ${\mathrm{x}}_{\mathrm{j},{\mathrm{n}}^{*},{\mathrm{t}}^{*}}\leftarrow 1$ Update capacity constraints Execute scheduled jobs Collect actual carbon emissions for model refinement End if End for Assignment matrix Return x