Distributed Resource Allocation Over Dynamic Networks with Uncertainty

TL;DR

This paper develops a distributed Lagrangian algorithm for resource allocation in large-scale dynamic networks with uncertainty, demonstrating convergence bounds and applying it to power system economic dispatch problems.

Contribution

It introduces a distributed subgradient-based method that handles unknown and time-varying resources without central coordination, with proven convergence analysis.

Findings

Convergence rate bounds depend on network size and topology.

Effective in power system economic dispatch simulations.

Applicable to large-scale, dynamic, uncertain network environments.

Abstract

Motivated by broad applications in various fields of engineering, we study a network resource allocation problem where the goal is to optimally allocate a fixed quantity of resources over a network of nodes. We consider large scale networks with complex interconnection structures, thus any solution must be implemented in parallel and based only on local data resulting in a need for distributed algorithms. In this paper, we study a distributed Lagrangian method for such problems. By utilizing the so-called distributed subgradient methods to solve the dual problem, our approach eliminates the need for central coordination in updating the dual variables, which is often required in classic Lagrangian methods. Our focus is to understand the performance of this distributed algorithm when the number of resources is unknown and may be time-varying. In particular, we obtain an upper bound on the convergence rate of the algorithm to the optimal value, in expectation, as a function of the size and the topology of the underlying network. The effectiveness of the proposed method is demonstrated by its application to the economic dispatch problem in power systems, with simulations completed on the benchmark IEEE-14 and IEEE-118 bus test systems.