  Cache-aided content delivery is studied in a multi-server system with $P$
servers and $K$ users, each equipped with a local cache memory. In the delivery
phase, each user connects randomly to any $\rho$ out of $P$ servers. Thanks to
the availability of multiple servers, which model small base stations with
limited storage capacity, user demands can be satisfied with reduced storage
capacity at each server and reduced delivery rate per server; however, this
also leads to reduced multicasting opportunities compared to a single server
serving all the users simultaneously. A joint storage and proactive caching
scheme is proposed, which exploits coded storage across the servers, uncoded
cache placement at the users, and coded delivery. The delivery \textit{latency}
is studied for both \textit{successive} and \textit{simultaneous} transmission
from the servers. It is shown that, with successive transmission the achievable
average delivery latency is comparable to that achieved by a single server,
while the gap between the two depends on $\rho$, the available redundancy
across servers, and can be reduced by increasing the storage capacity at the
SBSs.
