Hypervisors’ smooth operation and efficient performance has an immediate effect in the supported Cloud services. We investigate scheduling algorithms that match I/O requests originated from virtual resources, to the physical CPUs that do the actual processing. We envisage a new paradigm of virtualized resource consolidation, where I/O resources required by several Virtual Machines (VMs) in different physical hosts, are provided by one (or more) external powerful dedicated appliance(s), namely the I/O Hypervisor (IOH). For this reason I/O operations are transferred from the VMs to the IOH, where they are executed. We propose and evaluate a number of scheduling algorithms for this hypervisor model, concentrating on providing guaranteed fairness among the virtual resources. A simulator has been built that describes this model and is used for the implementation and the evaluation of the algorithms. We also analyze the performance of the different hypervisor models and highlight the importance of fair scheduling.