$$\begin{array}{c}\hfill \mathbb{E}[A{T}_p]=\sum _{d=0}^{D-1}\sum _{y=1}^{\infty }\frac{{\sum }_{j={\overline{S}}_{\mathit{dp}}(y)+1}^{\infty }(j-{\overline{S}}_{\mathit{dp}}(y))P(A_{\mathit{dp}}=j)}{{\sum }_{j=0}^{D-1}\mathbb{E}[A_{\mathit{jp}}]}·{\mathit{\pi }}_{\mathit{dpq}}.\end{array}$$ (A2)