HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation

Interaction of TCP Flows as Billiards

François Baccelli 1 Dohy Hong 1
1 TREC - Theory of networks and communications
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt
Abstract : The aim of this paper is to analyze the performance of a large number of long lived TCP controlled flows sharing many routers (or links), from the knowledge of the network parameters (capacity, buffer size, topology) and of the characteristics of each TCP flow (RTT, route etc.) in the presence of synchronization. This work is based on the AIMD model which describes the joint evolution of the window sizes of all flows in the congestion avoidance phase over a single bottleneck router, in terms of iterates of random affine maps. It is shown that the generalization of this dynamics to a network composed of several routers can be described in terms of iterate of random piecewise affine maps, or geometrically as a billiards in the Euclidean space with as many dimensions as the number of flow classes and as many reflection facets as there are routers. This can first be used as a simulation tool allowing one to emulate the interaction of millions of flows on tens of thousands of routers. This representation also leads to results of mathematical nature: this class of billiards exhibits both periodic and non-periodic asymptotic oscillations (to be interpreted as network level fluctuations for traffic aggregates), the characteristics of which are extremely sensitive to the parameters of the network; the consequences on TCP's fairness are exemplified on a few typical cases of small dimension. Finally, we also show that aggregated traffic generated by this billiards representation exhibits the same short time scale statistical properties as those observed on real traces.
Document type :
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download

Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Tuesday, May 23, 2006 - 7:55:11 PM
Last modification on : Thursday, March 17, 2022 - 10:08:32 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:37:11 PM


  • HAL Id : inria-00072151, version 1



François Baccelli, Dohy Hong. Interaction of TCP Flows as Billiards. [Research Report] RR-4437, INRIA. 2002. ⟨inria-00072151⟩



Record views


Files downloads