Fractals Associated with TCP Bandwidth Sharing:

The following fractals were obtained using the TCP/IP flow interaction model introduced in RR-4437 (see below). This model features a collection of TCP controlled flows of different classes that share a set of links. There are as many classes as there are routes through this set of links. These fractals describe the bandwidth sharing operated by TCP; each of them plots the instantaneous throughput obtained by one TCP class in function of that obtained by another class, when varying one of the shared link speeds. In some of the fractals, the variations of speed are represented by different colors.

3 links, 3 classes:

tcp-fairness-33-1.pdf, zoom of tcp-fairness-33-1.pdf, tcp-fairness-33-2.pdf.

3 links, 6 classes:

tcp-fairness-36-1.pdf, tcp-fairness-36-2.pdf, tcp-fairness-36-3.pdf, zoom of tcp-fairness-36-3.pdf.

4 links, 6 classes:

tcp-fairness-46-1.pdf, tcp-fairness-46-2.pdf.

5 links, 10 classes:

tcp-fairness-5.10-1.pdf, tcp-fairness-5.10-2.pdf, tcp-fairness-5.10-3.pdf, tcp-fairness-5.10-4.pdf, zoom1 tcp-fairness-5.10-4.pdf, zoom2 tcp-fairness-5.10-4.pdf, zoom3 tcp-fairness-5.10-4.pdf.

---

References

Baccelli, F. and Hong, D. (2002) "Interaction of TCP Flows as Billiards"
Technical Report, April 2002, RR-4437 (.ps.gz), RR-4437 (.pdf), INRIA Rocquencourt.

-> [TCP modeling, networks] The multi-AIMD model is the network extension of the model introduced in RR 4155 (see below). The associated dynamical system can be seen as iterates of piecewise affine random maps or geometrically as a billiards in a polyhedron.

Chaintreau, A. and De Vleeschauwer, D. (2002) "Closed Form Formula for Long-Lived TCP Connections Throughput"
Performance, 2002.

Hong, D. and Lebedev, D. (2001) "Many TCP User Asymptotic Analysis of the AIMD Model"
Technical Report, July 2001, RR-4229 (.ps.gz), RR-4229 (.pdf), INRIA Rocquencourt.

-> [TCP modeling, Single router] This paper studies the asymptotic model of the AIMD model (RR-4155) when the number of TCP sessions N goes to infinity.

Baccelli, F. and Hong, D. (2001-2002) "AIMD, Fairness and Fractal Scaling of TCP Traffic"
RR-4155 INRIA Rocquencourt and Infocom, June 2002, lastversion (.ps.gz). lastversion (.pdf).

-> [TCP modeling, Single router] This paper gives a representation of N TCP connections sharing a single link in terms of iterates of random affine maps.

Baccelli, F., Hong, D. (2001) "The AIMD Model for TCP Sessions Sharing a Common Router"
Proc. of 39th Annual Allerton Conf. on Communication, Control and Computing, October 2001, Allerton Park. lastversion.ps.gz.

-> A survey of RR-4155 and RR-4229 with some improvements.

---

TREC Research Group

Computer Science Department, ENS

---