Centralized radio access network architectures consolidate the baseband operation towards a cloud-based platform, thereby allowing for efficient utilization of computing assets, effective inter-cell coordination, and exploitation of global channel state information. This paper considers the interplay between computational efficiency and data throughput that is fundamental to centralized RAN. It introduces the concept of computational outage in mobile networks, and applies it to the analysis of complexity constrained dense centralized RAN networks. The framework is applied to single-cell and multi-cell scenarios using parameters drawn from the LTE standard. It is found that in computationally limited networks, the effective throughput can be improved by using a computationally aware policy for selecting the modulation and coding scheme, which sacrifices spectral efficiency in order to reduce the computational outage probability. When signals of multiple base stations are processed centrally, a computational diversity benefit emerges, and the benefit grows with increasing user density.