Yes, of course, its an interesting research topic in the cloud, and some papers have benn published : look at this one for example : https://www.cs.berkeley.edu/~alig/papers/drf.pdf
It depends what you mean by resource: is it a VM or a physical machine running a VM? Depending on the choice, provider (for PM allocation in the datacenter and VM-to-PM provisioning) or client (task-to-VM scheduling) objectives can be considered. The answer is not simple as it depends on your objective(s): energy, load balancing, resource utilization, execution time, throughput, latency. Fairness is a vaguely defined term: for instance it can refer to "all users have the same experience in terms of response times". You can take a look at the numerous resource scheduling and allocation papers dealing with clouds. They all address fairness in terms of the objective(s).
By the way, are you conducting research works on this subject ? It sounds interesting for me. Dont hesitate to contact me if you want to collaborate with my team.
There are many available articles on resource allocation in cloud computing environments.
However, I would consider checking work with elasticity in cloud computing as they often load balancing situations and better resources allocation, both considering infrastructure aspects (CPU, memory, network, etc.) or applications/systems aspects (throughput, response time, etc.), helps in achieving fairness.