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.

Integration of optical paths and packets in a switch is a key technique to support ultra-high-speed traffic in the future Internet. However, the question of how to efficiently allocate wavelengths for optical paths and optical packets has not been solved yet due to the lack of a systematic model to evaluate the performance of the integrated switch. In this paper, we model the operation of the integrated switch as a system of two queuing models: M/M/x/x for optical paths and M/M/1/LPS for optical packets. From the model, we find an optimal policy to dynamically allocate wavelength resources in an integrated switch. Simulation results demonstrate that our mechanism achieves better performance than other methods.