$P_D^{*}$ 的取值范围

D₁的取值

$\text{0}\le P_D^{*}<\frac{2k+1}{{\left(k+1\right)}^2}$

$\frac{k^2+k-\sqrt{2k+2-P^{*}\left(k^2+2k+2\right)}}{k^2+2k+2}$

$\frac{2k+1}{{\left(k+1\right)}^2}\le P_D^{*}<\frac{2k+2}{k^{\text{2}}+2k+2}$

$\frac{k^2+k\pm \sqrt{2k+2-P^{*}\left(k^2+2k+2\right)}}{k^2+2k+2}$

$P_D^{*}=\frac{2k+2}{k^2+2k+2}$

$\frac{k^2+k}{k^2+2k+2}$

$P^{\text{*}}>\frac{2k+2}{k^{\text{2}}+2k+2}$

$\left(k+1\right)\sqrt{\frac{\text{1}-P^{*}}{k^2+2k+2}}$