System virtualization is becoming pervasive and it is enabling important new computing diagrams such as cloud computing. Live virtual machine (VM) migration is a unique capability of system virtualization which allows applications to be transparently moved across physical machines with a consistent state captured by their VMs. Although live VM migration is generally fast, it is a resource-intensive operation and can impact the application performance and resource usage of the migrating VM as well as other concurrent VMs. However, existing studies on live migration performance are often based on the assumption that there are sufficient resources on the source and destination hosts, which is often not the case for highly consolidated systems. As the scale of virtualized systems such as clouds continue to grow, the use of live migration becomes increasingly more important for managing performance and reliability in such systems. Therefore, it is key to understand the performance of live VM migration under different levels of resource availability. This paper addresses this need by creating performance models for live migration which can be used to predict a VM's migration time given its application's behavior and the resources available to the migration. A series of experiments were conducted on Xen to profile the time for migrating a DomU VM running different resource-intensive applications while DomO is allocated different CPU shares for processing the migration. Regression methods are then used to create the performance model based on the profiling data. The results show that the VM's migration time is indeed substantially impacted by DomO's CPU allocation whereas the performance model can accurately capture this relationship with the coefficient of determination generally higher than 90%.