Delay Minimizing User Association in Cellular Networks via Hierarchically Well-Separated Trees

TL;DR

This paper proposes a novel approach using hierarchically well-separated trees to approximate delay-minimizing user association policies in cellular networks, balancing SINR and congestion considerations.

Contribution

It introduces a linearization technique for a non-convex delay minimization problem using HST embedding, enabling efficient approximation of optimal user associations.

Findings

Quadratic reformulation yields delay policies close to original optimization.

HST-based linearization provides constant distortion approximation.

Appropriate parameter tuning improves association delay performance.

Abstract

We study downlink delay minimization within the context of cellular user association policies that map mobile users to base stations. We note the delay minimum user association problem fits within a broader class of network utility maximization and can be posed as a non-convex quadratic program. This non-convexity motivates a split quadratic objective function that captures the original problem's inherent tradeoff: association with a station that provides the highest signal-to-interference-plus-noise ratio (SINR) vs. a station that is least congested. We find the split-term formulation is amenable to linearization by embedding the base stations in a hierarchically well-separated tree (HST), which offers a linear approximation with constant distortion. We provide a numerical comparison of several problem formulations and find that with appropriate optimization parameter selection, the quadratic reformulation produces association policies with sum delays that are close to that of the original network utility maximization. We also comment on the more difficult problem when idle base stations (those without associated users) are deactivated.