## 1 Introduction
### Survivability and Resilience in C-RAN Backhaul Networks  
In case of failures or unexpected events, a C-RAN is supposed to both continue basic operations and deliver some degree of quality in doing so. That is, the nature of C-RAN backhauling demands that a BBU is both able to communicate with its associated RRHs and that it does so in accordance with the radio protocols employed at the RRH. A basic definition of resiliency would simply require that the backhaul of a C-RAN includes a set of paths that support communication between every BBU and RRH pair after \(f\) failures. Instead, we prefer the notion of resilience, which requires that after \(f\) failures there is a \"good\" set of paths that enables communication between every pair. We conjecture that the notion of resilience better captures the survivability requirements of C-RAN backhaul than the more basic formulation.  
Given this notion of survivability for C-RAN backhauls, we also distinguish between the properties of basic survivability and resilience in backhaul networks. Here, we describe these properties in the case that \(f=1\), but the concept extends to any number of failures. Basic network survivability is guaranteed by 2-connectivity between nodes, which means that the graph remains connected even in the case of a single link or node failure. Noting that latency provides the primary requirement for the goodness of C-RAN backhaul, we consider a network to be resilient if it has two disjoint paths of limited length connecting any pair of nodes. Thus, the survivability is guaranteed by the 2-connectivity and the operation in accordance with radio protocols after failure is guaranteed because the diameter and the average distance (and, consequently, the latency) are bounded after a failure.  
Survivability in C-RAN and resiliency in 5G networks have been investigated in literature (see [3; 9; 10; 11]). Existing models tend to include this notion into the consideration of other problems, such as: (i) a BBU placement problem; or (ii) a control function split problem. In the former, proposals highlight that a better positioning of BBUs in the network would enable a distribution of the processing capabilities of a C-RAN to tackle latency and scalability issues, as well as achieve better survivability in the case of unexpected delay occurrence. In the latter, the radio protocol functionalities are split between BBUs and RRHs, based on the trade-off between the rate required by the underlying infrastructure and the degree to which processing may be inserted at the edge of the C-RAN. As a secondary effect of optimizing this split of functionalities, both the link capacity and the latency requirements are eased, in turn improving the margin for absorption of failures. Consequently, the survivability of C-RAN networks optimized in such a manner is improved. Finally, it is worth mentioning that, to the best of our knowledge, the existing works reduce the C-RAN backhaul topology planning to a cost optimization problem, as explained in the next section, and do not exploit resilience and survivability properties of the underlying topologies. Extending beyond such works, we assume a broader perspective on survivability by examining the properties intrinsically associated to the topology planning and refining of backhauling to achieve increased survivability in C-RANs.