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| HAL : hal-00338640, version 3 |
| arXiv : 0811.2180 |
| DOI : 10.1016/j.spa.2010.03.019 |
| Fiche détaillée |  Récupérer au format |
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| Stochastic Processes and their Applications 120, 8 (2010) 1518-1534 |
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| Versions disponibles : | v1 (13-11-2008) | v2 (26-02-2009) | v3 (16-12-2009) |
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| On the long time behavior of the TCP window size process |
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Djalil Chafai 1Florent Malrieu 2 |
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| (08/04/2010) |
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| The TCP window size process appears in the modeling of the famous Transmission Control Protocol used for data transmission over the Internet. This continuous time Markov process takes its values in $[0,\infty)$, is ergodic and irreversible. It belongs to the Additive Increase Multiplicative Decrease class of processes. The sample paths are piecewise linear deterministic and the whole randomness of the dynamics comes from the jump mechanism. Several aspects of this process have already been investigated in the literature. In the present paper, we mainly get quantitative estimates for the convergence to equilibrium, in terms of the $W_1$ Wasserstein coupling distance, for the process and also for its embedded chain. |
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| 1 : | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA) |
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Université Paris Est Marne-la-Vallée – Université Paris XII - Paris Est Créteil Val-de-Marne – CNRS : UMR8050 – Fédération de Recherche Bézout |
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| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II |
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| 3 : | Laboratoire de Mathématiques (LM-Besançon) |
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CNRS : UMR6623 – Université de Franche-Comté |
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| 4 : | DIONYSOS (INRIA - IRISA) |
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INRIA – Université de Rennes 1 |
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| Processus stochastiques |
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| Domaine | : | Mathématiques/Probabilités Informatique/Réseaux et télécommunications |
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| Network Protocols – Queuing Theory – Additive Increase Multiplicative Decrease Processes (AIMD) – Piecewise Deterministic Markov Processes (PDMP) – Exponential Ergodicity – Coupling |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00338640, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00338640 | |
| oai:hal.archives-ouvertes.fr:hal-00338640 | |
| Contributeur : Djalil Chafai | |
| Soumis le : Mardi 15 Décembre 2009, 22:14:19 | |
| Dernière modification le : Samedi 6 Novembre 2010, 00:48:15 | |
