1. A method of optimizing virtual graphics processing unit utilization, the method comprising: assigning a computing intensity level to each virtual machine of a plurality of virtual machines; assigning a priority level to each virtual machine of the plurality of virtual machines; determining for each server of a plurality of servers whether the server includes a virtual graphics processing unit (VGPU) that is available to perform compute intensive tasks for the plurality of virtual machines; and assigning one or more VGPUs to a virtual machine of the plurality of virtual machines in dependence upon the computing intensity level and the priority level of the virtual machine and the number of VGPUs available to perform the compute intensive tasks.