***Title: Almost-sure large deviations and application to TCP traffic Joint work with Julien Barral (LAGA, Université Paris 13, Villetaneuse, France), Paulo Gonçalves and Pascale Vicat-Blanc Primet (INRIA Rhônes-Alpes/ENS Lyon, Lyon, France) ***Abstract: Most of today's Internet traffic is carried using the TCP transport protocol. Yet, most of the numerous models that have been proposed in the last decade to understand the performance achieved by one or several long TCP connections are limited to the prediction of a mean throughput value. In this talk, we expose a new model, based on an original large-deviations theorem, which allows predicting the deviations of the throughput around its mean. We first present an almost-sure large-deviations theorem for stationary mixing processes. This theorem expresses the "ergodic transfer" of classical large-deviations properties of the process to almost-every realizations. It allows estimating the proportion of time, within a single realization averaged at a given (large) scale, where the process deviates from its almost-sure mean behavior. Applying this theorem to a Markov chain modeling the TCP congestion-window evolution, we then show that it permits in practice to quantify and to statistically bound the variations of the throughput within a long flow. The Markov-chain model can take into account various network conditions. We discuss in particular the classical case of Bernoulli losses, as well as more realistic cases from experiments and real Internet traces. ***References (see http://perso.ens-lyon.fr/patrick.loiseau/publications.html): [1] Julien Barral and Patrick Loiseau. Large deviations for the local fluctuations of random walks and new insights into the ``randomness'' of Pi. preprint, submitted, arXiv:1004.3713, April 2010. [2] Patrick Loiseau, Paulo Gonçalves, Julien Barral, and Pascale Vicat-Blanc Primet. Modeling TCP throughput: an elaborated large-deviations-based model and its empirical validation. In IFIP Performance, Namur, Belgium, November 2010. ***Speaker's bio: Patrick Loiseau received a degree of Professeur-Agrégé de Sciences-Physiques (2005), a M.S. degree of physics (2006), and a Ph.D. degree of computer science (2009) from Ecole Normale Supérieure de Lyon (France). He also received a M.S. degree of mathematics (2010) from Université Pierre et Marie Curie (Paris 6) and Ecole Polytechnique (France). After his PhD, he spent 10 months as a post-doctoral fellow at INRIA Paris-Rocquencourt (France) and one month as a visiting researcher at the University of Waterloo (ON, Canada). He is currently working as a post-doctoral scholar at UC Santa Cruz (CA, USA). His main research interests are in probability and stochastic modeling of communication networks; and in game theoretic modeling of network economics problems. He has also worked on statistical estimation in the context of network measurement, and on analysis and modeling of the heart-rate variability.
