= P$ and $\sum_{i=0}^{K} ig_i=K\rho$.

Successive SBS Transmissions {#s:Successive}
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In this section we assume that the SBSs share the same communication resources, and hence, transmit successively to avoid interference. When the SBSs transmit successively in time, the normalized delivery latency is given by $$\begin{aligned}
   T_{sd} \triangleq \sum_{p=1}^P R_p &= \frac{1}{\rho {K\choose t}} \sum_{p=1}^{P} \left[{K\choose t+1}-{K-q_p\choose t+1} \right] \\
    &=\frac{1}{\alpha} \frac{(K-t)}{(t+1)} - \frac{1}{\rho {K\choose t}} \sum_{p=1}^{P}  {K-q_p \choose t+1} \label{eq:sumrate1} \\
    &= \frac{1}{\alpha} \frac{(K-t)}{(t+1)} - \frac{1}{\rho {K\choose t}} \sum_{i=0}^{K} g_i {K-i \choose t+1}.\label{eq:sumrate}\end{aligned}$$

To characterize the “best” and “worst” network topologies that lead to the minimum and maximum delivery latency, respectively, we present the following lemma without proof.

\[convexity\] For $n_1, n_2 , r \in \mathcal{Z}^{+}$ satisfying $r \leq n_1$ and $n_1 + 2 \leq n_2$, we have $$\begin{aligned}
    {n_1 \choose r} + {n_2 \choose r} \geq {n_1+1 \choose r} + {n_2-1 \choose r}.\end{aligned}$$

The lemma above indicates the “convex” nature of the binomial coefficients in ; that is, the points $(r, {r \choose r})$, $(r+1, {r+1 \choose r})$, …, $(n_1+n_2-r, {n_1+n_2-r \choose r})$ form a convex region. From Lemma \[convexity\], it can be deduced that the second summation term in takes its minimum when $\max_{p}(q_p) \leq \min_{p}(q_p) + 1$, 