Equivalence between Proportional Fairness and Time-Based Fairness in Multi-Rate Wireless LANs

Max-Min fairness offered by IEEE 802.11 based MAC is not desirable in multi-rate WLAN since the throughput of the entire system is determined by the lowest transmission rate in use. Instead, proportional fairness is more desirable as it strikes good balance between the fairness and the efficiency. Achieving the proportional fairness in multi-rate WLAN with proper tuning of IEEE 802.11 MAC is a challenging task. Previous work in this area has conjectured that the proportional fairness is same as the time-based fairness. In this work, we prove the conjecture.