Wireless networks have faced increasing demand to cope with the exponential growth of data. Conventional architectures have hindered the evolution of network scalability. However, the introduction of cloud technology has brought tremendous flexible and scalable on demand resources. Thus, cloud radio access networks (C-RANs) have been introduced as a new trend in wireless technologies. Despite the novel advancements that C-RAN offers, remote radio head (RRH)-to-base band unit (BBU) resource allocation can cause significant downgrade in efficiency, particularly the allocation of computational resources in the BBU pool to densely deployed small cells. This causes an increase in power consumption and wasted resources. Consequently, an efficient resource allocation method is vital for achieving efficient resource consumption. In this paper, the optimal allocation of computational resources between RRHs and BBUs is modeled. This is dependent on having an optimal physical resource allocation for users to determine the required computational resources. For this purpose, an optimization problem that models the assignment of resources at these two levels is formulated. A decomposition model is adopted to solve the problem by formulating two binary integer programming subproblems; one for each level. Furthermore, two low complexity heuristic algorithms are developed to solve each subproblem. Results show that the computational resource requirements and the power consumption of BBUs and the physical machines decrease as the channel quality worsens. Moreover, the developed heuristic solution achieves a close to optimal performance while having a lower complexity. Finally, both models achieve high resource utilization, cementing the efficiency of the proposed solutions.