1. An apparatus comprising a computer processor, a computer memory operatively coupled to the computer processor, the computer memory having disposed within it computer program instructions that when executed by the computer processor cause the apparatus to carry out steps of: assigning a computing intensity level to each virtual machine of a plurality of virtual machines, wherein the computing intensity level for each virtual machine is based on a ranking of a number of computing intensive tasks of each virtual machine relative to the number of computing intensive tasks of each of other virtual machines in the plurality of virtual machines; assigning a priority level to each virtual machine of the plurality of virtual machines; prior to moving each of the plurality of virtual machines to one of a plurality of servers for execution, determining that each of the plurality of servers includes a virtual graphics processing unit (VGPU) that is available to perform compute intensive tasks for the plurality of virtual machines including receiving, from each of the plurality of servers, information indicating available resources at the server, examining the available resources for the VGPU, and determining a workload of the VGPU; and moving each of the plurality of virtual machines to one of the plurality of servers for execution including assigning one of the VGPUs of the plurality of servers 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 a number of VGPUs available to perform the compute intensive tasks.