virtual machine with dedicated GPU - is it possible? Private GPU Cloud

You might want to take a look at Xen, it supports VGA passthrough if your hardware supports VT-d. E.g. Setting Up A Xen Graphics Card Pass-Through.

However, if you want to use CUDA, OpenCL etc... (this is what I assume, since you're talking about a "GPU cloud"), you are looking at a very big problem. See those discussions:

• on Stack Overflow: CUDA / OpenCL within a Virtual Machine / Hypervisor
• on Unix&Linux SE: GPGPU/CUDA in KVM or Xen