  A Fog radio access network is considered as a network architecture candidate
to meet the soaring demand in terms of reliability, spectral efficiency, and
latency in next generation wireless networks. This architecture combines the
benefits associated with centralized cloud processing and wireless edge caching
enabling primarily low-latency transmission under moderate fronthaul capacity
requirements. The F-RAN we consider in this paper is composed of a centralized
cloud server which is connected through fronthaul links to two edge nodes
serving two mobile users through a Z-shaped partially connected wireless
network. We define an information-theoretic metric, the delivery time per bit
(DTB), that captures the worst-case per-bit delivery latency for conveying any
requested content to the users. For the cases when cloud and wireless
transmission occur either sequentially or in parallel, we establish coinciding
lower and upper bounds on the DTB as a function of cache size, backhaul
capacity and wireless channel parameters. Through optimized rate allocation,
our achievability scheme determines the best combination of private, common
signalling and interference neutralization that matches the converse. Our
converse bounds use subsets of wireless, fronthaul and caching resources of the
F-RAN as side information that enable a single receiver to decode either one or
both users' requested files. We show the optimality on the DTB for all channel
regimes. In case of serial transmission, the functional DTB-behavior changes at
fronthaul capacity thresholds. In this context, we combine multiple channel
regimes to classes of channel regimes which share the same fronthaul capacity
thresholds and as such the same DTB-functional. In total, our analysis
identifies four classes; in only three of those edge caching and cloud
processing can provide nontrivial synergestic and non-synergestic performance
gains.
