This paper analyzes the computing resource management implications of SDR base stations implemented as SDR clouds. SDR clouds describe distributed antennas that connect to a data center for digital signal processing. The data center employs cloud computing technology, providing a virtualized computing resource pool. The service area of a single SDR cloud may be a metropolitan area with a high user density. Hence, the data center will execute thousands of SDR applications in parallel, providing wireless communications services to several radio cells. Whenever a user initiates or terminates a wireless communications session, computing resources need to be allocated or deallocated in real time. We therefore propose a hierarchical resource management. This paper justifies such an approach and analyzes different resource management strategies. The results indicate the need for strategies that can dynamically adapt to the given user traffic distribution.