Variability Aware Network Utility Maximization

Network Utility Maximization (NUM) provides the key conceptual framework to study resource allocation amongst a collection of users/entities across 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 on distributed mechanisms to maximize network utility while incorporating new relevant constraints, on energy/power, storage, stability, etc., for systems ranging from communication networks to the smart-grid. However when the available resources and/or users' utilities vary over time, a user's allocations will tend to vary, which in turn may have a detrimental impact on the users' utility or quality of experience. This paper introduces a generalized NUM framework which explicitly incorporates the detrimental impact of temporal variability in a user's allocated rewards. It explicitly incorporates tradeoffs amongst the mean and variability in users' allocations. We propose an online algorithm to realize variance-sensitive NUM, which, under stationary ergodic assumptions, is shown to be asymptotically optimal, i.e., achieves a time-average 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.