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Resource allocation problems are a fundamental domain in which to evaluatethe fairness properties of algorithms. The trade-offs between fairness andutilization have a long history in this domain. A recent line of work hasconsidered fairness questions for resource allocation when the demands for theresource are distributed across multiple groups and drawn from probabilitydistributions. In such cases, a natural fairness requirement is thatindividuals from different groups should have (approximately) equalprobabilities of receiving the resource. A largely open question in this areahas been to bound the gap between the maximum possible utilization of theresource and the maximum possible utilization subject to this fairnesscondition.  Here, we obtain some of the first provable upper bounds on this gap. Weobtain an upper bound for arbitrary distributions, as well as much strongerupper bounds for specific families of distributions that are typically used tomodel levels of demand. In particular, we find - somewhat surprisingly - thatthere are natural families of distributions (including Exponential and Weibull)for which the gap is non-existent: it is possible to simultaneously achievemaximum utilization and the given notion of fairness. Finally, we show that forpower-law distributions, there is a non-trivial gap between the solutions, butthis gap can be bounded by a constant factor independent of the parameters ofthe distribution.

Fairness and Utilization in Allocating Resources with Uncertain Demand