will yield larger power savings, since more exponents (i.e., $c_l^m, c_{l+1}^m, \cdots, c_{l'-1}^m$) will assume smaller values. Therefore, we should let these two subsets be empty whenever possible, i.e., either $\mathcal{U}_l^0=\emptyset$ or $\mathcal{U}_l^1=\emptyset$. According to this policy, all the users requesting the level $l$ packet will connect to the same BS. We only need to make the optimal connection decision for each subset of users requesting the same level of packet, rather than for each individual user.

Since not transmitting a lower level packet yields more power savings for a BS, we calculate the power from the lowest to the highest level, and decide whether connecting to the MBS or the FBS for users in each level. Define $G_l^0 = \max_{k\in\mathcal{U}_l} \left\{ 1/H_0^k \right\}$ and $G_l^1 = \max_{k\in\mathcal{U}_l} \left\{ 1/H_1^k \right\}$. The algorithm for solving Problem OPT-Power in this case is given in Table \[tab:Case2Algo\]. In Steps $2$–$10$, the decision on whether connecting to the MBS or the FBS is made by comparing the expected increments in the total power. The user subsets $\mathcal{U}_l^0$ and $\mathcal{U}_l^1$ are determined in Steps $4$ and $7$. In Steps $11$–$14$, $Q_l^m$’s and the corresponding $P_l^m$’s are computed in the reverse order, based on the 