Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space

TL;DR

This paper proposes a system theoretic approach to accurately determine wireless network capacity in finite time and space, accounting for queueing and spatial correlations, providing practical insights beyond traditional asymptotic models.

Contribution

It introduces a novel system theoretic methodology for finite regime capacity analysis that includes queueing behavior and spatial correlations, offering rigorous closed-form results.

Findings

Provides closed-form capacity results in finite regimes.

Accounts for queueing and spatial correlations in networks.

Enables practical computation of optimal routing strategies.

Abstract

In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends itself to conservative numerical results in finite regimes. To properly account for queueing behavior beyond a simple calculus based on average rates, we advocate a system theoretic methodology for the capacity problem in finite time and space regimes. This methodology also accounts for spatial correlations arising in networks with CSMA/CA scheduling and it delivers rigorous closed-form capacity results in terms of probability distributions. Unlike numerous existing asymptotic results, subject to anecdotal practical concerns, our transient one can be used in practical settings: for example, to compute the time scales at which multi-hop routing is more advantageous than single-hop routing.