of transmissions is $3$. We can go through all the $(t+1)-$ element subsets of the users and identify for each of them the minimum cover. We note that in the successive transmission scenario, the total latency does not depend on the server transmitting each subsegment, since the contribution to the total latency is the same. In the above example servers $S_1$ and $S_6$ could also deliver the two coded subsegments to users $U_1$ and $U_2$. The selection of the servers matters in the case of parallel transmissions.

Performance analysis {#performance_analysis}
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In this section, we derive an analytical expression for the expected delivery latency in the asymptotic regime, i.e., when $P \rightarrow \infty$, while $\alpha$ and $\hat{\alpha}$ are fixed. Consider a particular subset $\mathcal{H}$ of $t+1$ users. Define $\beta_i$ as the fraction of servers serving $i$ users in $\mathcal{H}$, $i=0,1,\ldots,t+1$. Thus, we have $$\begin{aligned}
 \label{beta_def}
\beta_i = \frac{1}{P}\sum_{p=1}^{P} \mathbbm{1}_{\{ \vert \mathcal{H} \cap \mathcal{K}_p\vert = i\}}.\end{aligned}$$ Taking expectation on both sides of Eq. , we have $$\begin{aligned}
\mathbb{E}[\beta_i]&=\frac{1}{P} \sum_{p=1}^{P} \mathbb{E}[\mathbbm{1}_{\{ \vert \mathcal{H} \cap \mathcal{K}_p\vert = i\}}] \\
&= \frac{1}{P}  \sum_{p=1}^{P} \mathrm{Pr}( \vert \mathcal{H} \cap \mathcal{K}_p\vert = i)\\
&= \mathrm{Pr}( \vert \mathcal{H} \cap \mathcal{K}_p\vert = i) \label{exp_beta_1}\end{aligned}$$ $$\begin{aligned}
= {t+1 \choose i} 