Examples allocate and schedule use of graphics processing unit (GPU) resources among a plurality of users executing virtual machines (VMs) or processes. During initialization, shares representing proportional access to the GPU resources are assigned and then adjusted based on graphics command characteristics. Quantum is allocated among the VMs based on the shares. At runtime, graphics commands from the VMs are queued and iteratively sent to the GPU based on a comparison between allocated quantum and a threshold quantum. In this manner, the GPU resources are fairly shared among the VMs.