# Loss-based proportional fairness in multihop wireless networks

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## Abstract

Proportional fairness is a widely accepted form of allocating transmission resources in communication systems. For wired networks, the combination of a simple probabilistic packet marking strategy together with a scheduling algorithm aware of two packet classes can meet a given proportional vector of *n* loss probabilities, to an arbitrary degree of approximation, as long as the packet loss gap between the two basic classes is sufficiently large. In contrast, for wireless networks, proportional fairness is a challenging problem because of random channel variations and contention for transmitting. In this paper, we show that under the physical model, i.e., when receivers regard collisions and interference as noise, the same packet marking strategy at the network layer can also yield proportional differentiation and nearly optimal throughput. Thus, random access or interference due to incoherent transmissions do not impair the feasibility of engineering a prescribed end-to-end loss-based proportional fairness vector. We consider explicitly multihop transmission and the cases of Markovian traffic with a two-priority scheduler, as well as orthogonal modulation with power splitting. In both cases, it is shown that sharp differentiation in loss probabilities at the link layer is achievable without the need to coordinate locally the transmission of frames or packets among neighboring nodes. Given this, a novel distributed procedure to adapt the marking probabilities so as to attain exact fairness is also developed. Numerical experiments are used to validate the design.

### Keywords

Proportional fairness Quality of service Packet marking Loss proportional service Two class queues## Notes

### Acknowledgments

This work was supported by the Ministerio Ciencia e Innovación, under Grant TEC2009-12135, and is also partially funded by the EU under the FEDER program.

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