Proportional Fairness in Multi-channel Multi-rate Wireless Networks-Part I: The Case of Deterministic Channels

TL;DR

This paper establishes the theoretical foundations of proportional fairness in multi-channel wireless networks, introduces optimization algorithms, and demonstrates improved throughput and fairness in large-scale WiFi systems.

Contribution

It provides the first comprehensive theoretical analysis of proportional fairness in multi-channel networks and develops efficient algorithms for capacity allocation.

Findings

PF leads to equal airtime in single-channel scenarios

PF achieves higher throughput and fairness in large WiFi networks

Developed fast, parallelizable PF-optimization algorithms

Abstract

This is Part I of a two-part paper series that studies the use of the proportional fairness (PF) utility function as the basis for capacity allocation and scheduling in multi-channel multi-rate wireless networks. The contributions of Part I are threefold. (i) First, we lay down the theoretical foundation for PF. Specifically, we present the fundamental properties and physical/economic interpretation of PF. We show by general mathematical arguments that PF leads to equal airtime allocation to users for the single-channel case; and equal equivalent airtime allocation to users for the multi-channel case, where the equivalent airtime enjoyed by a user is a weighted sum of the airtimes enjoyed by the user on all channels, with the weight of a channel being the price or value of that channel. We also establish the Pareto efficiency of PF solutions. (ii) Second, we derive characteristics of PF solutions that are useful for the construction of PF-optimization algorithms. We present several PF-optimization algorithms, including a fast algorithm that is amenable to parallel implementation. (iii) Third, we study the use of PF utility for capacity allocation in large-scale WiFi networks consisting of many adjacent wireless LANs. We find that the PF solution simultaneously achieves higher system throughput, better fairness, and lower outage probability with respect to the default solution given by today's 802.11 commercial products. Part II of this paper series extends our investigation to the time-varying-channel case in which the data rates enjoyed by users over the channels vary dynamically over time