G. Vinnicombe

CUED/F-INFENG/TR.398, December 2000

In [2] Johari and Tan consider an Internet type network
with distributed congestion control of the form proposed by Kelly
et al in [3], and determine a sufficient condition
for local stability of the network under the condition that all
round trip times are equal. They conjecture that the same condition
will also guarantee local stability when the round trip times are
disparate. The continuous time version of this conjecture is true.
(** ps **)
(** pdf **)

G. Vinnicombe

To appear IFAC'02

We derive decentralized and scalable stability conditions for
a fluid approximation of a class of Internet-like communications
networks operating a modified form of TCP-like congestion control.
The network consists of an arbitrary interconnection of sources and
links with heterogeneous propagation delays.
The model here allows for arbitrary concave utility functions and the
presence of dynamics at both the sources
and the links.
(** ps **)
(** pdf **)

G. Vinnicombe

Submitted for publication, Feb 2002

We derive decentralized and scalable robust stability conditions for
a fluid approximation of a class of Internet-like communications
networks operating a modified form of TCP-like congestion control.
The network consists of an arbitrary interconnection of sources and
links with heterogeneous propagation delays. Unlike previous results
of this kind, the model here allows for dynamics at both the sources
and the links.
(** ps **)
(** pdf **)

G. Vinnicombe

Seminar, April 2002

We consider a network to consist of a collection of modules and
protocols. The modules belong to parameterized classes of dynamical
systems and the protocols determine how the modules may be
interconnected. An important property of an interconnection is it
stability, and the robustness of this stability to perturbations. If
the modules are linear dynamical systems, then the stability and
robustness of any particular interconnection may be assessed using
the existing tools of robust control. In this talk, though, we shall
concentrate on results which can guarantee stability and robustness
for any interconnection which satisfies the protocols. I shall
present prototypes of such results which use tools from classical
control, such as the multivariable Nyquist criterion, and graph
theory.
These techniques will then be applied to the problem of congestion
control of the Internet, where the two classes of modules are the
routers and the end-systems and the protocols are the way they
communicate (e.g. routers signal congestion by dropping, or marking,
packets). The result is a simple modification to the control laws
currently used which both works well in small-scale simulations and is
provably scalable to arbitrary sized networks.
**Slides(pdf)**