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)