The aim of this talk is to analyze the performance
of a large number of long lived TCP controlled flows sharing many
routers, from the knowledge of the network parameters (capacity,
buffer size, topology) and of the characteristics of each TCP
flow (RTT, route etc.).
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 function of
the synchronization rate. It is shown that
the generalization of this dynamics to a network composed
of several routers can be described 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 us to emulate the interaction of
millions of flows on tens of thousands of routers.
This representation also leads to several results of mathematical
nature, including a general periodicity theorem for the
asymptotic behavior of the interacting flows and a new way of
assessing TCP's fairness, which is 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.
References:
Francois Baccelli & Dohy Hong
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