Hi Shikharesh, Hi Azzedine, Thanks very much for the excellent reviews of the Performance Evalution submission "Variable Heavy Tails in Internet Traffic" by Hernandez-Campos, Samorodnitsky, Smith and I. In addition to the very detailed and careful attention to detail, we also appreciate the philosophical issues that the reviewers have raised. Many of the points made were right no target, and we have just implemented sutiable changes. Points that seem to need additional discussion are: Referee 1: Overuse of quotation marks: The point is very well taken, and the analysis very clear. We have tried hard to address this problem, in particular following these recommendations. Page 6: Yes, this is on target. We have added more discussion in the Size Distribution Analysis section. Referee 2: Major Comments: 1. There are different personal opinions on this type of organization, with probably something to be said for all sides of the issue. But as there seems to be some strong feelings on the matter at this point, we have instituted these changes. The potential for confusion between sizes and durations was a previously muriky issue that we have worked hard to clarify. 2. We prefer distributions that arise from "naturally occuring phenomena". The Gaussian is the best known of these (the natural distribution associated with summing and averaging), and other well known ones include the Poisson, the log-normal, and various types of mixture distributions. In our view, a big plus of all of the distributions we use is that they are also of this type. We are aware of earlier work where distributions are constructed in this piecewise way, but view this as a serious disadvantage, because we don't know of physical processes which give rise to such distributions. For us this outweighs the fact one may on occasion get slightly better fits from such distributions. We note further that many of these early papers were fitting data before the Double Pareto log normal distribution was defined. But now that the distribution is known and understood, it seems to make sense to use it as a natural model when the data have this special form, instead of these unnatural piecewise things. Such approaches were sensible to use when that was all that could be done. But with the advent of the double Pareto log normal distribution, that is no longer the case. We recognize that this choice is personal, and understand that people with other personal criteria will make other choices. We contemplated adding discussion on this point to the paper, but decided against it on the grounds that this point is already well treated in Gong, et al. Also we do not view it as appropriate to say negative things about the work of Barford, Arlitt and others because what they did was quite sensible in view of what was known at the time. 3. This discussion gets into "statistical style" issues. One way of dichotomizing statistical methods is into it/{exploratory} and it/{confirmatory} analyses. Most good quality data analyses involve both types, first working in exploratory mode to understand what is happening, and then working in confirmatory mode to be sure the ideas are correct. In this paper we have worked mostly in exploratory mode. The simulated envelope in the Q-Q plot is something of a hybrid, in that makes confirmatory suggestions while working really in exploratory mode. One could indeed push this further, in a more precise statistical way, by properly modelling the variation in these curves. But we are skeptical that this will be worth the effort, and instead believe that for our exploratory purposes, the present approach is adequate (and our statistical energies are better devoted to other issues). Another reason for not pursuing confirmatory analysis here is that with millions of data points, it makes much less sense to use say classical goodness of fit methods. This is because with such large data sets there is a huge amount of power in the data which is expected to result in the rejection of most any distribution (caused by very small scale departures from the given distribution). About Figure 4 and the "common wobbles for all 21", the idea was that if the wobbles were random phenomena, then one would expect them to appear in different locations for different realizations. We added a sentence to clarify this point in the paper. About applying the simulated envelope analysis to all of the 21 time blocks: sure we did this, and as noted in Section 2.1 of our original submission, we found very similar results (as expected from Figure 4). We also referred to an earlier paper which gave a web link. To make the point more clear, we now state explicitly in the test that Hernández-Campos, et al, (2003) is a web site. 4. Yes, we were vague on this point. We've added some discussion at the end of the Variable Tail Index Section. The location of the "start of the tail" is well known in the world of extreme value theory to be a very slippery issue. We are unaware of any reasonable automatic way of doing this, and in fact after understanding the "variable tail" lessons that this paper is about, it seems that we have provided new understanding as to why this problem can be so challenging. 5. This returns to the exploratory vs confirmatory statistical goals discussed in point 3 above. The concern about "arbitraryness" and "may lead to biases" seems a little ironic, because the point of our adding envelopes of simulated curves (which I believe nobody has previously done in this literature) is precisely to address these issues. But there is a clear message here that we need to give better guidelines about how to do this properly, so we have done so in the section on Pareto Tail Fitting. We have not chosen to compute the ks statistic, because we don't think it is very interpretable, as noted in point 3 above (recall the point about nothing fitting precisely for such large data sets). 6, One could always look at more and more data sets, and their are generally good reasons such as those raised for doing so. But one also needs to stop and publish at some point, and it seems OK to us to stop at this point. For this paper we already expanded beyond those that we had done done for the MASCOTS and Allerton proceedings. 7. Regular variation is a standard concept in the branch of probability called extreme value theory. Thanks for pointing out that we should include a reference. 8. We have discussed this point right at the very end. Referee 3: 1. Yes, there are many ways to organize a paper, and there does not seem to be an overall notioin of best, probably because of differing personal preferences. We prefer the organization that we used, and would like to call this an issue on which "two good authors may differ". 2. Good point, we have worked hard on this. Best, Steve