Rate Performance Objectives of Multi-hop Wireless Networks

We consider the question of what performance metric to maximize when designing adhoc 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 the case of cellular networks) and transport capacity (in the case of adhoc 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 review this issue for wireless ad-hoc networks. Indeed, the mathematical model for wireless networks has a specificity that makes some of the findings different. 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. The story is different for max-min fairness. Although it is perfectly viable for a 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 the MAC layer, network topology, choice of routes and power constraints. This is due to the ``solidarity