Resource Allocation: Realizing Mean-Variability-Fairness Tradeoffs

TL;DR

This paper extends the Network Utility Maximization framework to explicitly account for and optimize the tradeoffs between mean, variability, and fairness in reward allocations over time, addressing user satisfaction concerns.

Contribution

It introduces a generalized NUM framework that incorporates temporal variability and fairness, along with an online algorithm that achieves asymptotic optimality under stationary ergodic conditions.

Findings

The proposed algorithm effectively balances mean rewards and variability.

It achieves asymptotic optimality compared to offline benchmarks.

The framework applies to diverse systems like communication networks and smart-grids.

Abstract

Network Utility Maximization (NUM) provides a key conceptual framework to study reward 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 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 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' reward allocations, as well as fairness. 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.