Joint Bandwidth Allocation and Path Selection in WANs with Path Cardinality Constraints

TL;DR

This paper introduces a novel ADMM-based method for joint bandwidth allocation and path selection in WANs with path cardinality constraints, addressing a complex non-convex multi-objective optimization problem.

Contribution

It proposes a simple, implementable algorithm for a challenging non-convex problem, providing convergence guarantees and outperforming existing relaxation-based methods.

Findings

The algorithm effectively finds stationary points in the non-convex problem.

Numerical results show superior performance over baseline methods.

The approach handles multiple objectives like fairness and utilization efficiently.

Abstract

In this paper, we study a joint bandwidth allocation and path selection problem via solving a multi-objective minimization problem under the path cardinality constraints, namely MOPC. Our problem formulation captures various types of objectives including the proportional fairness, the total completion time, as well as the worst-case link utilization ratio. Such an optimization problem is very challenging since it is highly non-convex. Almost all existing works deal with such a problem using relaxation techniques to transform it to be a convex optimization problem. However, we provide a novel solution framework based on the classic alternating direction method of multipliers (ADMM) approach for solving this problem. Our proposed algorithm is simple and easy to be implemented. Each step of our algorithm consists of either finding the maximal root of a single-cubic equation which is guaranteed to have at least one positive solution or solving a one-dimensional convex subproblem in a fixed interval. Under some mild assumptions, we prove that any limiting point of the generated sequence under our proposed algorithm is a stationary point. Extensive numerical simulations are performed to demonstrate the advantages of our algorithm compared with various baselines.