[Paper Review] Flow-level performance of random wireless networks

Richard Combes, Eitan Altman|arXiv (Cornell University)|Jul 28, 2013

Advanced MIMO Systems Optimization35 references3 citations

TL;DR

This paper studies flow-level performance in random wireless networks with Poisson-distributed base stations (BSs), modeling each BS as a queue whose load depends on user distribution and inter-cell interference. It derives exact Laplace transforms for load distributions on the line and moment formulas on the plane, showing that in dense networks, interference becomes normally distributed and load can be well-approximated by a gamma distribution with known mean and variance.

ABSTRACT

We study the flow-level performance of random wireless networks. The locations of base stations (BSs) follow a Poisson point process. The number and positions of active users are dynamic. We associate a queue to each BS. The performance and stability of a BS depend on its load. In some cases, the full distribution of the load can be derived. Otherwise we derive formulas for the first and second moments. Networks on the line and on the plane are considered. Our model is generic enough to include features of recent wireless networks such as 4G (LTE) networks. In dense networks, we show that the inter-cell interference power becomes normally distributed, simplifying many computations. Numerical experiments demonstrate that in cases of practical interest, the loads distribution can be well approximated by a gamma distribution with known mean and variance.

Motivation & Objective

• To model and analyze the flow-level performance of wireless networks with randomly located base stations (BSs) using stochastic geometry and queuing theory.
• To understand how dynamic user behavior—such as random user entry, mobility, and shared resource access—affects BS load and network stability.
• To derive analytical expressions for the first and second moments of BS load, and in some cases the full distribution via Laplace transforms.
• To evaluate the impact of frequency reuse strategies (hard and soft) on average load and network performance in Poisson-dense networks.
• To assess the accuracy of approximating the load distribution by a gamma distribution with known mean and variance in practical scenarios.

Proposed method

• Models BS locations as a homogeneous Poisson point process (PPP), representing real-world irregular deployment.
• Associates each BS with a queue, where the load is defined as the integral of a function over the Voronoi cell, depending on distance and interference.
• Uses stochastic geometry to model interference as Poisson shot-noise, enabling derivation of interference distribution moments.
• Applies Laplace and Fourier transforms to derive the full distribution of load in one-dimensional networks.
• For two-dimensional networks, derives closed-form expressions for the first and second moments of the load using integral transforms.
• Employs numerical experiments to validate that the load distribution is well-approximated by a gamma distribution with known mean and variance.

Experimental results

Research questions

• RQ1 How does the distribution of BS load behave in random wireless networks with Poisson-distributed base stations?
• RQ2 What are the first and second moments of the load in two-dimensional networks, and when can the full distribution be derived?
• RQ3 How does inter-cell interference affect the load distribution, and under what conditions does it become normally distributed?
• RQ4 How accurate is the gamma distribution approximation for the load in practical network scenarios?
• RQ5 How do different frequency reuse strategies (hard vs. soft) impact the average load and overall network performance?

Key findings

• In one-dimensional networks, the full distribution of the load can be derived in closed form using Laplace transforms.
• In two-dimensional networks, the first and second moments of the load are derived using integral transforms and stochastic geometry.
• In dense networks, the inter-cell interference power becomes approximately normally distributed, simplifying performance analysis.
• Numerical results show that the load distribution is well-approximated by a gamma distribution with known mean and variance, especially when the path-loss exponent is small.
• Soft frequency reuse with a power reduction of −20 dB provides up to twice the network capacity compared to reuse factor 1, significantly outperforming hard reuse.
• The average load decreases with increasing BS density due to reduced cell size, despite increased interference, indicating that reduced congestion dominates the performance trend.