Geodesic
Analysis of an algorithm catching elephants on the Internet
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008).

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The paper deals with the problem of catching the elephants in the Internet traffic. The aim is to investigate an algorithm proposed by Azzana based on a multistage Bloom filter, with a refreshment mechanism (called $\textit{shift}$ in the present paper), able to treat on-line a huge amount of flows with high traffic variations. An analysis of a simplified model estimates the number of false positives. Limit theorems for the Markov chain that describes the algorithm for large filters are rigorously obtained. The asymptotic behavior of the stochastic model is here deterministic. The limit has a nice formulation in terms of a $M/G/1/C$ queue, which is analytically tractable and which allows to tune the algorithm optimally. 
@article{DMTCS_2008_special_254_a18,
     author = {Chabchoub, Yousra and Fricker, Christine and Meunier, Fr\'ed\'eric and Tibi, Danielle},
     title = {Analysis of an algorithm catching elephants on the {Internet}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science},
     year = {2008},
     doi = {10.46298/dmtcs.3572},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3572/}
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Chabchoub, Yousra; Fricker, Christine; Meunier, Frédéric; Tibi, Danielle. Analysis of an algorithm catching elephants on the Internet. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008). doi : 10.46298/dmtcs.3572. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3572/

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