Known an a criterion that solves the trade-off between fairness and efficiency, proportional fairness is well-studied in cellular networks in the Qualcomm High Data Rate System. In multi-hop wireless networks, proportional fairness is solved by maximizing the logarithmic aggregate utility function. However, this approach can deal with instantaneous rates only where long term fairness is to be targeted. In this case, cumulative rates are more suitable. This paper proposes a framework for multi-hop wireless networks to guarantee fairness of cumulative data rates. The framework can be extended to other kinds of fairness such as max-min fairness, and to more complex networks, multi-channel multi-radio wireless networks.

This letter introduces a new fairness concept, namely proportional quasi-fairness and proves that the optimal end-to-end rate of a network utility maximization can be proportionally quasi-fair with a properly chosen network utility function for an arbitrary compact feasible set.

In most cases in wireless networks, a user has a two-way communication that consists of two sessions: uplink and downlink sessions, and its overall satisfaction to the communication depends on the quality of service of both sessions. However, in most previous approaches in wireless resource allocation, the satisfactions of a user for its uplink and downlink sessions are modeled separately and treated independently, which fails to accurately model user's overall satisfaction to its communication. Hence, in this paper we model user's overall satisfaction to its communication considering both its uplink and downlink sessions. To this end, we propose a novel concept for a utility function to model user's overall satisfaction to its communication, which is called a user-level utility function, considering user's satisfaction to uplink and downlink sessions jointly. To show the appropriateness of our approach, we apply our user-level utility functions to scheduling problems in TDMA wireless networks and show the performance improvement of our approach over the traditional approach that does not treat uplink and downlink sessions of a user jointly.

We use the network utility maximization (NUM) framework to create an efficient and fair medium access control (MAC) protocol for wireless networks. By adjusting the parameters in the utility objective functions of NUM problems, we control the tradeoff between efficiency and fairness of radio resource allocation through a rigorous and systematic design. In this paper, we propose a scheduling-based MAC protocol. Since it provides an upper-bound on the achievable performance, it establishes the optimality benchmarks for comparison with other algorithms in related work.