Report on
Stochastic Equilibria of AIMD Communication Networks by F.Wirth, R.Stanojevic, R.Shorten and D.Leith
The paper analyses a random matrix model of communication networks, that employ additive increase multiplicative decrease congestion control. The results are of interest to the readers of SIMAX, but the paper seems to be too long. Perhaps Section 6 can be shortened. The relations between the paper and the references are not clear. It may be better to combine Comment 1 with earlier remarks on these relations. It will be helpful to clarify which papers use matrix synchronized / unsynchronized models. It is also important to clarify what are the differences between the paper and reference [25].
The following are some typos:
P1, L-14, cain
P2, L13, date
P2, L-9 i.e
P3, L5, source
P3, L-5, defines
P7, L-20, delete "that"
P7, L-16, for
P7, L-13, that
P7, L-4,-5, The assumption
P8, L-13, shows
P11, L-10, to
P13, end of L5, add "is what"
%report for Nabben, SIMAX
\documentclass[11pt]{article}
\begin{document}
\centerline {Report on the paper}
\centerline
{\bf Stochastic equilibria of AIMD communication networks}
\centerline {by F. Wirth, R. Stanojevic, R. Shorten and D. Leith}.
\bigskip
This report concerns only the mathematical part of this paper. The
reviewer understands that the more technical part is reviewed by an
expert in this field.
Mathematically this paper can be viewed as a very nice application of
the concept of paracontractivity. As such it is very interesting and
should be published. Here a list of remarks, most of them quite
superficial, which should be taken into
account in a revision.
\begin{itemize}
\item
on p.3 in (2.5) the inner index in the summation should not be i,
which is a global index.
\item
P.7 line 1: Which norm? On page 8 in Lemma 3.6 it is used for the
induced $l_1$-norm
\item
On p. 7 the last sentence of comment 3.2 is not clear.
\item
On p.8. Lemma 3.5 we have even $||A|| = 1$.
\item
P.8: In the proof of Lemma 3.6 better write $Ayy^T/n$ instead of
$1/nAyy^T$
\item
On p. 9 (3.3) the form of $M \in {\cal M}$ does not coincide with that
of $M$ on p.5, (2.14). They differ by a diagonal similarity using
$diag(\gamma_i)$. Please clarify.
\item
p.10 line 9 ..results..
\item
On p. 14 two lines before Theorem 5.1: ..$1^4$ .. is misleading.
\item reference [7] is incomplete, one author (Koltracht)
is missing.
\end{itemize}
\end{document}