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A mean-field analysis of short lived interacting TCP flows

Published: 01 June 2004 Publication History

Abstract

In this paper, we consider a set of HTTP flows using TCP over a common drop-tail link to download files. After each download, a flow waits for a random think time before requesting the download of another file, whose size is also random. When a flow is active its throughput is increasing with time according to the additive increase rule, but if it suffers losses created when the total transmission rate of the flows exceeds the link rate, its transmission rate is decreased. The throughput obtained by a flow, and the consecutive time to download one file are then given as the consequence of the interaction of all the flows through their total transmission rate and the link's behavior.We study the mean-field model obtained by letting the number of flows go to infinity. This mean-field limit may have two stable regimes : one without congestion in the link, in which the density of transmission rate can be explicitly described, the other one with periodic congestion epochs, where the inter-congestion time can be characterized as the solution of a fixed point equation, that we compute numerically, leading to a density of transmission rate given by as the solution of a Fredholm equation. It is shown that for certain values of the parameters (more precisely when the link capacity per user is not significantly larger than the load per user), each of these two stable regimes can be reached depending on the initial condition. This phenomenon can be seen as an analogue of turbulence in fluid dynamics: for some initial conditions, the transfers progress in a fluid and interaction-less way; for others, the connections interact and slow down because of the resulting fluctuations, which in turn perpetuates interaction forever, in spite of the fact that the load per user is less than the capacity per user. We prove that this phenomenon is present in the Tahoe case and both the numerical method that we develop and simulations suggest that it is present in the Reno case too. It translates into a bi-stability phenomenon for the finite population model within this range of parameters.

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    cover image ACM Conferences
    SIGMETRICS '04/Performance '04: Proceedings of the joint international conference on Measurement and modeling of computer systems
    June 2004
    450 pages
    ISBN:1581138733
    DOI:10.1145/1005686
    • cover image ACM SIGMETRICS Performance Evaluation Review
      ACM SIGMETRICS Performance Evaluation Review  Volume 32, Issue 1
      June 2004
      432 pages
      ISSN:0163-5999
      DOI:10.1145/1012888
      Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Published: 01 June 2004

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    Author Tags

    1. HTTP connections
    2. mean-field model

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    SIGMETRICS04
    SIGMETRICS04: SIGMETRICS 2004 / PERFORMANCE 2004
    June 10 - 14, 2004
    NY, New York, USA

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    • (2016)Asymptotic Behavior of a Generalized TCP Congestion Avoidance AlgorithmJournal of Applied Probability10.1239/jap/118971753344:03(618-635)Online publication date: 14-Jul-2016
    • (2014)Physics-inspired methods for networking and communicationsIEEE Communications Magazine10.1109/MCOM.2014.695715552:11(144-151)Online publication date: Nov-2014
    • (2009)Deriving a closed-form expression for worm-scanning strategiesInternational Journal of Security and Networks10.1504/IJSN.2009.0273394:3(135-144)Online publication date: 1-Jul-2009
    • (2008)Transient behavior of processes in the tcp paradigmProbability in the Engineering and Informational Sciences10.1017/S026996480800025922:3(431-471)Online publication date: 1-Jul-2008
    • (2008)A stochastic model for the throughput of non-persistent TCP flowsPerformance Evaluation10.1016/j.peva.2007.12.00665:6-7(512-530)Online publication date: 1-Jun-2008
    • (2007)The effects of fairness in buffer sizingProceedings of the 6th international IFIP-TC6 conference on Ad Hoc and sensor networks, wireless networks, next generation internet10.5555/1772322.1772415(867-878)Online publication date: 14-May-2007
    • (2007)Beyond fluid modelsComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2006.04.01351:1(114-133)Online publication date: 17-Jan-2007
    • (2007)The Effects of Fairness in Buffer SizingNETWORKING 2007. Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet10.1007/978-3-540-72606-7_74(867-878)Online publication date: 2007
    • (2006)A stochastic model for the throughput of non-persistent TCP flowsProceedings of the 1st international conference on Performance evaluation methodolgies and tools10.1145/1190095.1190169(58-es)Online publication date: 11-Oct-2006
    • (2005)A square root formula for the rate of non-persistent TCP flowsNext Generation Internet Networks, 200510.1109/NGI.2005.1431673(247-254)Online publication date: 2005
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