Rate Performance Objectives of Multi-hop Wireless Networks
We consider the question of what performance metric to maximize when designing ad-hoc wireless network protocols such as routing or MAC. We focus on maximizing rates under battery lifetime and power constraints. Commonly used metrics are total capacity (in case of cellular networks) and transport capacity (in case of ad-hoc networks). However, it is known in traditional wired networking that maximizing total capacity conflicts with fairness, and this is why fairness oriented rate allocations, such as max-min fairness, are often used. We revisit this issue for wireless ad-hoc networks. Indeed, the mathematical model for wireless networks has a specificity that makes some of the findings different. On one hand, it has been reported in the literature on Ultra Wide Band that gross unfairness occurs when maximizing total capacity or transport capacity, and we confirm by a theoretical analysis that this is a fundamental shortcoming of such metrics in wireless ad-hoc networks, as it is for wired networks. In contrast, the story is different for max-min fairness. While it is perfectly viable for wired network, it is much less so in our setting. We show that, in the limit of long battery lifetime, the max-min allocation of rates always leads to strictly equal rates, regardless of MAC layer, network topology, choice of routes and power constraints. This is due to the ``solidarity" property of the set of feasible rates. This results in all flows receiving the rate of the worst flow, and leads to severe inefficiency. We show numerically that the problem persists when battery lifetime constraints are finite. This generalizes the observation reported in the literature that, in heterogeneous settings, 802.11 allocates the worst rate to all stations, and shows that this is inherent to any protocol that implements max-min fairness. Proportional fairness is an alternative to max-min fairness that approximates rate allocation performed by TCP in the Internet. We show by numerical simulations that proportional fairness of rates or transport rates is robust and achieves a good trade-off between efficiency and fairness, unlike total rate or maximum fairness. We thus recommend that metrics for the rate performance of mobile ad-hoc networking protocols be based on proportional fairness.