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The cellular industry is evaluating architectures to distribute the signal processing in radio access networks. One of the options is to process the signals of all base stations on a shared pool of compute resources in a central location. In this centralized architecture, the existing base stations will be replaced with just the antennas and a few other active RF components, and the remainder of the digital processing including the physical layer will be carried out in a central location. This model has potential benefits that include a reduction in the cost of operating the network due to fewer site visits, easy upgrades, and lower site lease costs, and an improvement in the network performance with joint signal processing techniques that span multiple base stations. Further there is a potential to exploit variations in the processing load across base stations, to pool the base stations into fewer compute resources, thereby allowing the operator to either reduce energy consumption by turning the remaining processors off or reducing costs by provisioning fewer compute resources. We focus on this aspect in this paper. Specifically, we make the following contributions in the pa- per. Based on real-world data, we characterise the potential savings if shared homogeneous compute resources are used to process the signals from multiple base stations in the centralized architecture. We show that the centralized architecture can potentially result in savings of at least 22% in compute resources by exploiting the variations in the processing load across base stations. These savings are achievable with statistical guarantees on successfully processing the base station's signals. We also design a framework that has two objectives: (i) partitioning the set of base stations into groups that are simultaneously processed on a shared homogeneous compute platform for a given statistical guarantee, and (ii) scheduling the set of base stations allocated to a platform in order to meet their real-time processing requirements. This partitioning and scheduling framework saves up to 19% of the compute resources for a probability of failure of one in 100 million. We refer to this solution as CloudIQ. Finally we implement and extensively evaluate the CloudIQ framework with a 3GPP compliant implementation of 5 MHz LTE. [ABSTRACT FROM AUTHOR]