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arXiv · 1202.3914

A formal proof of the optimal frame setting for Dynamic-Frame Aloha with known population size

Luca Barletta·Flaminio Borgonovo·Matteo Cesana
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Abstract

In Dynamic-Frame Aloha subsequent frame lengths must be optimally chosen to maximize throughput. When the initial population size ${\cal N}$ is known, numerical evaluations show that the maximum efficiency is achieved by setting the frame length equal to the backlog size at each subsequent frame; however, at best of our knowledge, a formal proof of this result is still missing, and is provided here. As byproduct, we also prove that the asymptotical efficiency in the optimal case is $e^{-1}$, provide upper and lower bounds for the length of the entire transmission period and show that its asymptotical behaviour is $\sim ne-\zeta \ln (n)$, with $\zeta=0.5/\ln(1-e^{-1})$.

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Luca Barletta, Flaminio Borgonovo, Matteo Cesana. 2012-02-17. A formal proof of the optimal frame setting for Dynamic-Frame Aloha with known population size. https://doi.org/10.1109/tit.2014.2354642

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