Towards a Calculus for Wireless Networks

TL;DR

This paper develops a mathematical framework for analyzing wireless network performance by exploring the capacity process, deriving bounds, and considering dependence structures, with implications for delay and backlog analysis.

Contribution

It introduces a calculus for wireless networks by establishing capacity process properties, bounds, and stochastic orders, addressing the impact of self-interference and extending stochastic network calculus.

Findings

Instantaneous and cumulative capacities are light-tailed for typical fading channels.

Cumulative capacity and delay can be upper-bounded by exponential distributions.

Results are provided for different dependence structures and self-interference effects.

Abstract

This paper presents a set of new results directly exploring the special characteristics of the wireless channel capacity process. An appealing finding is that, for typical fading channels, their instantaneous capacity and cumulative capacity are both light-tailed. A direct implication of this finding is that the cumulative capacity and subsequently the delay and backlog performance can be upper-bounded by some exponential distributions, which is often assumed but not justified in the wireless network performance analysis literature. In addition, various bounds are derived for distributions of the cumulative capacity and the delay-constrained capacity, considering three representative dependence structures in the capacity process, namely comonotonicity, independence, and Markovian. To help gain insights in the performance of a wireless channel whose capacity process may be too complex or detailed information is lacking, stochastic orders are introduced to the capacity process, based on which, results to compare the delay and delay-constrained capacity performance are obtained. Moreover, the impact of self-interference in communication, which is an open problem in stochastic network calculus (SNC), is investigated and original results are derived. The obtained results in this paper complement the SNC literature, easing its application to wireless networks and its extension towards a calculus for wireless networks.