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 ...
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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 additiveincrease 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 also be present in the Reno case. It tran
The general aim of this paper is to analyze the throughput of a HTTP flow. For this, we introduce a simplified model of such a flow which consists of a succession of idle and download periods. The file downloads are s...
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The general aim of this paper is to analyze the throughput of a HTTP flow. For this, we introduce a simplified model of such a flow which consists of a succession of idle and download periods. The file downloads are subject to a fixed packet loss probability. The same TCP connection is possibly used for the download of a random number of files, for which the effect of the slow start is taken into account. For this stochastic model, we derive a closed form formula for the stationary throughput obtained by a flow. We also derive closed form expressions for the mean time to transfer a file and for the distribution of the throughput. Several laws of file sizes and idle times are considered including heavy tailed distributions. We also briefly discuss how the formulas can be applied to predict bandwidth sharing among competing HTTP flows. (C) 2008 Elsevier B.V. All rights reserved.
We propose a natural and simple model for the joint throughput evolution of a set of TCP sessions sharing a common tail drop bottleneck router, via products of random matrices. This model allows one to predict the flu...
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ISBN:
(纸本)0780374762
We propose a natural and simple model for the joint throughput evolution of a set of TCP sessions sharing a common tail drop bottleneck router, via products of random matrices. This model allows one to predict the fluctuations of the throughput of each session, as a function of the synchronization rate in the bottleneck router;several other and more refined properties of the protocol are analyzed such as the instantaneous imbalance between sessions, the autocorrelation function or the performance degradation due to synchronization of losses. When aggregating traffic obtained from this model, one obtains, for certain ranges of the parameters, short time scale statistical properties that are consistent with a fractal scaling similar to what was identified on real traces using wavelets.
In this survey paper, we review recent results on a class of partial differential equations associated with the dynamics of TCP. We show how to use the closed form solutions obtained for them via Mellin transforms in ...
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ISBN:
(纸本)1424403499
In this survey paper, we review recent results on a class of partial differential equations associated with the dynamics of TCP. We show how to use the closed form solutions obtained for them via Mellin transforms in order to optimize the parameters of a variety of communications channels when TCP is used.
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