No justified complaints: On fair sharing of multiple resources

TL;DR

This paper introduces a new fairness definition for allocating multiple resources simultaneously, ensuring fair sharing in virtualized and cloud environments, with a proven existence and a constructive method for computation.

Contribution

It proposes a novel fairness concept for multiple resources, extending existing ideas, and provides a proof of existence along with a numerical computation method.

Findings

Existence of fair allocations for any user requests and entitlements.

The fairness concept handles multiple bottlenecks effectively.

A constructive proof using differential equations is provided.

Abstract

Fair allocation has been studied intensively in both economics and computer science, and fair sharing of resources has aroused renewed interest with the advent of virtualization and cloud computing. Prior work has typically focused on mechanisms for fair sharing of a single resource. We provide a new definition for the simultaneous fair allocation of multiple continuously-divisible resources. Roughly speaking, we define fairness as the situation where every user either gets all the resources he wishes for, or else gets at least his entitlement on some bottleneck resource, and therefore cannot complain about not getting more. This definition has the same desirable properties as the recently suggested dominant resource fairness, and also handles the case of multiple bottlenecks. We then prove that a fair allocation according to this definition is guaranteed to exist for any combination of user requests and entitlements (where a user's relative use of the different resources is fixed). The proof, which uses tools from the theory of ordinary differential equations, is constructive and provides a method to compute the allocations numerically.