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Fair allocation has been studied intensively in both economics and computerscience, and fair sharing of resources has aroused renewed interest with theadvent of virtualization and cloud computing. Prior work has typically focusedon mechanisms for fair sharing of a single resource. We provide a newdefinition for the simultaneous fair allocation of multiplecontinuously-divisible resources. Roughly speaking, we define fairness as thesituation where every user either gets all the resources he wishes for, or elsegets at least his entitlement on some bottleneck resource, and therefore cannotcomplain about not getting more. This definition has the same desirableproperties as the recently suggested dominant resource fairness, and alsohandles the case of multiple bottlenecks. We then prove that a fair allocationaccording to this definition is guaranteed to exist for any combination of userrequests and entitlements (where a user's relative use of the differentresources is fixed). The proof, which uses tools from the theory of ordinarydifferential equations, is constructive and provides a method to compute theallocations numerically.

No justified complaints: On fair sharing of multiple resources