Resource allocation: Realizing mean-variability-fairness tradeoffs

Network Utility Maximization (NUM) provides a key conceptual framework to study reward allocation amongst a collection of users/entities in disciplines as diverse as economics, law and engineering. In network engineering, this framework has been particularly insightful towards understanding how Internet protocols allocate bandwidth, and motivated diverse research efforts on distributed mechanisms to maximize network utility while incorporating new relevant constraints, on energy, power, storage, stability, etc., e.g., for systems ranging from communication networks to the smart-grid. However when the available resources and/or users´ utilities vary over time, reward allocations will tend to vary, which in turn may have a detrimental impact on the users´ overall satisfaction or quality of experience. This paper introduces a generalization of the NUM framework which incorporates the detrimental impact of temporal variability in a user´s allocated rewards. It explicitly incorporates tradeoffs amongst the mean and variability in users´ reward allocations, as well as fairness across users. We propose a simple online algorithm to realize these tradeoffs, which, under stationary ergodic assumptions, is shown to be asymptotically optimal, i.e., achieves a long term performance equal to that of an offline algorithm with knowledge of the future variability in the system. This substantially extends work on NUM to an interesting class of relevant problems where users/entities are sensitive to temporal variability in their service or allocated rewards.