Algorithm 3 DVFS and Virtual Task Injection

1:${\mathbf{T}}_{cur}\leftarrow$ current temperature sensor values; 2:Calculate ${\mathbf{P}}_{cur}$ with ${\mathbf{T}}_{cur}$ using Equation (1); 3:${\mathbf{P}}_{th}=(\mathbf{G}+\mathbf{K})·{\mathbf{T}}_{th}-\mathbf{K}·{\mathbf{T}}_{amb}$; 4:$i\leftarrow 0$; 5:for$m=1$ to M do                        ▹ For each core 6:    while ${\mathbf{P}}_{th}\left[m\right]>{\mathbf{P}}_{cur}\left[m\right]$ do 7:        if $fa(p{e}_m)\ne f_L$then                   ▹ Frequency scaling 8:           when $fa(p{e}_m)=f_l$, $fa(p{e}_m)$ to $f_{l+1}$; 9:        else                          ▹ Virtual task injection 10:           if $u_m+\frac{v\_e{x}_{}}{v\_p_{}·f_L}\le 1$ then 11:               $V\leftarrow V\cup \{v_i\}$; 12:               set $map(v_i)=p{e}_m$ and update $u_m$; 13:               $i\leftarrow i+1$; 14:           else 15:               break; 16:           end if 17:        end if 18:        update ${\mathbf{P}}_{cur}\left[m\right]$; 19:    end while 20: end for