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Performance Evaluation
Volume 64, Issue 6, July 2007, Pages 507-523
 
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doi:10.1016/j.peva.2006.07.001    
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Copyright © 2006 Elsevier Ltd All rights reserved.

Versatile stochastic models for networks with asymmetric TCP sources

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Nicky D. van Foreesta, Boudewijn R. Haverkorta, Corresponding Author Contact Information, E-mail The Corresponding Author, Michel R.H. Mandjesb, a, 1 and Werner R.W. Scheinhardta, b

aFaculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

bCenter for Mathematics and Computer Science (CWI), P.O. Box 94079, 1090 GB, Amsterdam, The Netherlands


Received 15 March 2006. 
Available online 27 September 2006.

Abstract

In this paper we use stochastic Petri nets (SPNs) to study the interaction of multiple TCP sources that share one or two buffers. No analytical nor numerical results have been presented for such cases yet. We use SPNs in an unconventional way: the tokens in the SPN do not represent the packets being sent in the network, but merely model fractions of buffer occupancy and the congestion window sizes. In this way, we use the SPNs to obtain a discretisation of a fluid model for TCP dynamics. Thus, we pair the modelling flexibility of SPNs with the modelling efficiency of fluid models. In doing so, our approach also avoids the (numerical) solution of partial differential equations; instead, just the steady-state solution of a (large) continuous-time Markov chain is required.

We first consider two TCP sources sharing a single buffer and evaluate the consequences of two popular assumptions for the loss process in terms of fairness and link utilization. The results obtained with this model are in agreement with existing analytic models. A comparison with (more costly) simulations in ns2 shows that the real loss process is somewhere in between the two loss models.

Secondly, we consider a network consisting of three sources and two buffers and study how the sources share the capacity of the links. This leads to an interesting conjecture on fairness in large TCP networks.

Keywords: TCP; Fluid-flow model; Stochastic Petri nets; Fairness analysis

Article Outline

1. Introduction and related work
2. Background: A fluid model for TCP
3. An SPN-based TCP fluid model
3.1. Discretising source and buffer model
3.2. Two sources and one buffer with proportional loss
3.2.1. The subnets S1, S2 and B
3.2.2. From initial state to congestion (congestion avoidance)
3.2.3. The proportional loss model
3.2.4. Removing the congestion (multiplicative-decrease)
3.3. Performance measures
3.4. The synchronous loss model
3.5. Computational complexity
4. A comparison with analytic models and ns2
4.1. Traffic scenarios
4.2. Performance results
5. An extended model: Three TCP sources sharing two buffers
5.1. Scenario and model
5.2. Performance measures
5.3. Performance results
6. Summary and conclusions
Acknowledgements
References
Vitae










Corresponding Author Contact InformationCorresponding author.
1 Current position at Korteweg-de Vries Instituut, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands.

Performance Evaluation
Volume 64, Issue 6, July 2007, Pages 507-523
 
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