# Joint User Association and Resource Allocation in Heterogeneous Cellular Networks: Comparison of Two Modeling Approaches

## TL;DR

This paper compares queueing and snapshot modeling approaches for joint user association and resource allocation in heterogeneous cellular networks, highlighting similarities and differences in their insights and robustness.

## Contribution

It introduces a queueing model-based approach for joint UA and RA optimization and compares it with traditional snapshot models, revealing insights into their respective robustness.

## Key findings

- RA trends are similar across models, validating the approaches.
- User association trends differ, indicating model sensitivity.
- Numerical techniques effectively solve non-convex optimization problems.

## Abstract

The performance of different combinations of user association (UA) and resource allocation (RA) in heterogeneous cellular networks has been extensively studied using a classic modeling approach based on system snapshots. There have been also many studies focusing on the dynamics of the system using queueing models. These modeling approaches are rarely compared with each other though they each bring different insights to the design problem. In this paper, we consider a queueing model-based approach to study the interplay of UA and RA, and compare the results to those obtained using snapshot models. Specifically, we formulate three different joint UA and RA optimization problems corresponding to the following three performance metrics: the maximum achievable arrival rate, the average system delay, and the maximum per-user delay. These problems are non-convex integer programs. We have therefore developed numerical techniques to compute either their exact solutions or tight lower bounds. We obtain results for different combinations of RA and UA schemes, and compare the trends with those obtained via the snapshot approach. The trends on RA are very similar, which we take as a cross-validation of the two modeling approaches for this kind of problem. The trends on user association are somewhat different which indicates a lack of robustness of the results and the need for a careful validation of UA models.