Algorithm 3 Find optimal ${\lambda }_a^{*}$
1:	Input:${\tau }^{\mathrm{h}}$, $p_0$, $N_0$, W, $g_k$, $h_k$, ${\pi }_k$, $v_k$, ${\gamma }_k$, $D_{max}$, K, T, $\lambda$, ${\lambda }_a^{min}=0$ and ${\lambda }_a^{max}=\frac{\lambda }{K}$, precision ${\epsilon }_{\lambda }$.
2:	Output:${\lambda }_a^{*}$
3:	Compute ${\lambda }_a^{\mathrm{mid}}=\frac{{\lambda }_a^{max}+{\lambda }_a^{min}}{2}$.
4:	Apply Algorithm 1 to find out ${\theta }_{min}$.
5:	Apply Algorithm 2 to find out ${\mathbf{\lambda }}^{\mathrm{mid}}$.
6:	while$|\sum {\mathbf{\lambda }}^{\mathrm{mid}}-\lambda |>{\epsilon }_{\lambda }$do
7:	if $\sum {\mathbf{\lambda }}^{\mathrm{mid}}-\lambda >0$ then
8:	${\lambda }_a^{max}={\lambda }_a^{\mathrm{mid}}$.
9:	else
10:	${\lambda }_a^{min}={\lambda }_a^{\mathrm{mid}}$.
11:	end if
12:	${\lambda }_a^{\mathrm{mid}}=\frac{{\lambda }_a^{max}+{\lambda }_a^{min}}{2}$.
13:	Apply Algorithm 1 to find out ${\theta }_{min}$.
14:	Apply Algorithm 2 to find out ${\mathbf{\lambda }}^{\mathrm{mid}}$.
15:	end while
16:	${\lambda }_a^{*}=({\lambda }_a^{min}+{\lambda }_a^{max})/2$.
17:	END