If your Hypervisor System is running on an intel Xeon CPU newer than 2009 or AMD Opteron newer than 2010 it should comply to the Zing System requirements. At least 2 vCores are needed and adding more improves the throughput. As guest system on the hypervisor you can use any of the supported Linux distributions.
On paravirtualized systems Zing cannot be run as the required Zing Systems Tools do not support this mode.
Zing on Docker is supported: Installing Zing on Docker
Zing is also offered for direct use without previous registration on Amazon AWS (HVM only, not PV) as EC2 Marketplace Image on RHEL, SLES, Ubuntu and Amazon Linux. Read more about this in Zing User Guide / Using Zing on AWS.
On the virtualization system the Balloon Driver should be switched off: How to disable the Balloon Driver