📝 SummarXiv

Abstract

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.