Understanding the Impact of Neighborhood Information on End-to-End Fairness in Multi-Hop Wireless Networks

Fair resource allocation for end-to-end flows is an important yet challenging problem in multi-hop wireless networks. Recent research on fair resource allocation mainly focuses on two directions: 1) theoretical methods for joint optimization of scheduling and rate allocation, which are inherently hard to implement; 2) heuristic rate allocation solutions, which are practical for implementation, but simplify the scope of resource sharing regions using different neighborhood models. One key question that remains unanswered is how well these heuristic neighborhood-aware rate allocation solutions approximate the fair point defined in the theoretical optimal resource allocation framework. To evaluate the impact of different neighborhood models on end-to-end fairness, we first establish a baseline fairness model (i.e., proportional fairness) using the price-based resource allocation framework. In this framework, price represents the cost of the resource usage incurred by unit flow. The rate of a flow is directly linked to its price, which is the aggregated price of the links it traverses. The link price is the sum of the prices of all the resource sharing regions which it belongs to. Obviously, when the resource sharing regions are approximated by different neighborhood models in the heuristic solutions, link prices will manifest as different values. To quantify the deviations of these heuristic neighborhood-aware solutions from the baseline proportional fairness model, we introduce a normalized fairness index model. Six different neighborhood models are evaluated. Our study makes two significant observations: 1) symmetric knowledge on the construction of a neighborhood is important in achieving fairness. Such a knowledge has not been considered in any of the existing neighborhood-aware rate allocation algorithms; 2) while 1-hop neighborhood information brings noticeable gain in fairness, the knowledge of 2-hop neighborhood information does not necessarily bring additional benefit.