WLC38-2: Proportional Fairness in Multi-channel Multi-rate Wireless Networks

This paper 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. Examples of applications include (i) access point (AP) association and transmission scheduling in large-scale IEEE 802.11 networks; and (ii) subcarrier assignment and transmission scheduling in orthogonal frequency division multiplexing (OFDM) cellular networks. The contributions of this paper are twofold. First, we study the fundamental properties and physical/economic interpretation of PF. We show by general mathematical arguments that PF leads to equal airtime allocation to individual users for the single-channel case; and equal equivalent airtime allocation to individual 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. In addition, we establish the Pareto efficiency of PF solutions and derive characteristics of PF solutions that are useful for the construction of PF algorithms. Second, we generate numerical results for application (i) above. We find that the PF solution simultaneously achieves higher system throughput, better fairness, and lower outage probability with respect to the default AP-association and medium access control (MAC) protocol adopted in today´s 802.11 commercial products.