A Novel Framework for Decentralized Dynamic Resource Allocation Using Voronoi Tessellations

TL;DR

This paper introduces a decentralized framework using Voronoi tessellations for dynamic resource allocation among agents, with applications in smart grid power management, emphasizing scalability, robustness, and flexibility.

Contribution

It presents a novel CVT-based approach for static and dynamic resource allocation, including an analytical solution and a decentralized update mechanism with negotiation modeling.

Findings

Effective resource distribution in smart grids demonstrated

Decentralized updates improve scalability and robustness

Civility model enhances negotiation flexibility

Abstract

In this work, we approach the problem of resource allocation in a team of agents through the framework of Centroidal Voronoi Tessellations. CVTs provide a natural way to embed a desired global trend in the team through probability distributions, and in one-dimensional spaces, CVTs offer an inherent line structure allowing for a simple communication graph and scalability. We first consider the amount of resource to be allocated to be a constant and provide an analytical solution to such static resource allocation problem by embedding the allocation constraint within the distribution through a system of nonlinear equations. Using the solution of such a constrained CVT minimization problem as an initialization step, we propose a decentralized dynamic resource allocation solution that employs a one-step update when the desired distribution is Gaussian. We introduce a "civility model" for negotiations between the agents to allow for flexibility in local preferences and maintaining robustness against local disturbances. We demonstrate the effectiveness of the proposed method by considering the application of demand-response in smart grids through the problem of power allocation in a group of building thermal loads.