Lower Bounds for the Fair Resource Allocation Problem

by   Zaid Allybokus, et al.

The α-fair resource allocation problem has received remarkable attention and has been studied in numerous application fields. Several algorithms have been proposed in the context of α-fair resource sharing to distributively compute its value. However, little work has been done on its structural properties. In this work, we present a lower bound for the optimal solution of the weighted α-fair resource allocation problem and compare it with existing propositions in the literature. Our derivations rely on a localization property verified by optimization problems with separable objective that permit one to better exploit their local structures. We give a local version of the well-known midpoint domination axiom used to axiomatically build the Nash Bargaining Solution (or proportionally fair resource allocation problem). Moreover, we show how our lower bound can improve the performances of a distributed algorithm based on the Alternating Directions Method of Multipliers (ADMM). The evaluation of the algorithm shows that our lower bound can considerably reduce its convergence time up to two orders of magnitude compared to when the bound is not used at all or is simply looser.


page 1

page 2

page 3

page 4


Multi-Path Alpha-Fair Resource Allocation at Scale in Distributed Software Defined Networks

The performance of computer networks relies on how bandwidth is shared a...

Real-Time Fair Resource Allocation in Distributed Software Defined Networks

The performance of computer networks relies on how bandwidth is shared a...

On the performance of an integrated communication and localization system: an analytical framework

Quantifying the performance bound of an integrated localization and comm...

Playing games against nature: optimal policies for renewable resource allocation

In this paper we introduce a class of Markov decision processes that ari...

Courtesy as a Means to Anti-coordinate

In this paper, we investigate the problem of anti-coordination under rat...

Width-Independence Beyond Linear Objectives: Distributed Fair Packing and Covering Algorithms

In network routing and resource allocation, α-fair utility functions are...

A Polynomial Time Algorithm for Fair Resource Allocation in Resource Exchange

The rapid growth of wireless and mobile Internet has led to wide applica...

Please sign up or login with your details

Forgot password? Click here to reset