Optimizing the Medium Access Control in Multi-hop Wireless Networks
  We study the problem of geometric optimization of medium access control in multi-hop wireless network. We discuss the optimal placements of simultaneous transmitters in the network and our general framework allows us to evaluate the performance gains of highly managed medium access control schemes that would be required to implement these placements. In a wireless network consisting of randomly distributed nodes, our performance metrics are the optimum transmission range that achieves the most optimal tradeoff between the progress of packets in desired directions towards their respective destinations and the total number of transmissions required to transport packets to their destinations. We evaluate ALOHA based scheme where simultaneous transmitters are dispatched according to a uniform Poisson distribution and compare it with various grid pattern based schemes where simultaneous transmitters are positioned in specific regular patterns. Our results show that optimizing the medium access control in multi-hop network should take into account the parameters like signal-to-interference ratio threshold and attenuation coefficient. For instance, at typical values of signal-to-interference ratio threshold and attenuation coefficient, the most optimal scheme is based on triangular grid pattern and, under no fading channel model, the most optimal transmission range and network capacity are higher than the optimum transmission range and capacity achievable with ALOHA based scheme by factors of two and three respectively. Later on, we also identify the optimal medium access control schemes when signal-to-interference ratio threshold and attenuation coefficient approach the extreme values and discuss how fading impacts the performance of all schemes we evaluate in this article. 
Salman Malik, Philippe Jacquet, Cedric Adjih
cs.IT cs.NI math.IT