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}