its request.

Note that each transmitted message $X_p(\mathcal{H}_i)$ by a server is of length $\left. F \right/ \rho {K\choose t}$ bits. The number of messages transmitted by $\mathrm{S}_p$ is $$\begin{aligned}
    \left| \left\{ i\in \left[{K\choose t+1}\right]: \mathcal{K}_p \bigcap \mathcal{H}_i \neq \phi \right\} \right|&= {K\choose t+1}-\left| \left\{ i\in \left[{K\choose t+1}\right]: \mathcal{K}_p \bigcap \mathcal{H}_i = \phi \right\} \right|\\
    &={K\choose t+1}-{K-q_p\choose t+1}.\end{aligned}$$ That is, server $\mathrm{S}_p$ transmits a total of $R_p=\sfrac{F}  {\rho {K\choose t}}\left[{K\choose t+1}-{K-q_p\choose t+1}\right]$ bits.

The delivery latency performance of this proposed coded storage and delivery scheme with both successive and parallel SBS transmissions will be studied in the following two sections.

Due to the symmetry in the network across servers and users, the delivery latency of this scheme depends only on the $\mathbf{q}$ vector, not the particular network topology, i.e., what matters is the number of users served by each server, not the identity of the users. More specifically, all permutations of a $\mathbf{q}$ vector, and the associated users, result in the same latency. Hence, we define the “type" of a network topology as a vector of dimension $K+1$, $\mathbf{g}$, where $g_i$ denotes the number of servers serving $i$ users, for $i=0,1,\ldots, K$. We have $0\leq g_i \leq P$, $\sum_{i=0}^{K} g_i 