A Framework for Stochastic Fairness in Dominant Resource Allocation with Cloud Computing Applications

Allocation of limited resources under uncertain requirements often necessitates fairness considerations, with applications in computer systems, health systems, and humanitarian logistics. This paper introduces a distributionally robust (DR) stochastic fairness framework for multi-resource allocation, leveraging rough estimates of the mean and variance of resource requirement distributions. The framework employs a sampled approximation DR (SA-DR) model to develop the concept of stochastic fairness, satisfying key properties such as stochastic Pareto efficiency, stochastic sharing incentive, and stochastic envy-freeness under suitable conditions. We show the convergence of the SA-DR model to the DR model and propose a finitely convergent algorithm to solve the SA-DR model. We empirically evaluate the performance of our moment-based SA-DR model -- which uses only rough estimates of the mean and variance of the resource requirement distribution -- against alternative resource allocation models under varying levels of information availability. We demonstrate that our moment-based partial-information SA-DR model can achieve performance closer to the full-information model than the worst-case information model. Convergence of the sampled approximation model and comparisons across models are illustrated using data from cloud computing applications.