Hi Thomas, Thanks for your comments. But the hypotheses of Theorem 1 and Corollary 1 are different. The 0-1 law is only used in proving Corollary 1 where the independence required by the 0-1 law is stated in the corresponding hypothesis.
Cheers, Guang-Liang and Victor ----- Original Message ----- From: "Thomas C. Schmidt" <[email protected]> To: "Professor V.O.K. Li" <[email protected]> Cc: <[email protected]>; "Dr. Guang-Liang Li" <[email protected]> Sent: Wednesday, January 16, 2013 7:23 PM Subject: Re: [Tccc] Technical Report: Reconsidering Network Traffic Modeling > Hi Guang-Liang Li and Victor O. K. Li, > > I only had a very brief zip over your paper with the following impression: > You're struggling with Kolmogorov's Zero-One law, which requires > independence of the random variables under consideration. It seems you're > violating this requirement (see e.g. Feller for the details). > > In network measurement/traffic modeling, it is of course not a new insight > that measurable quantities are *not* independent and thus network traffic > differs significantly from, e.g., Poisson processes (see the famous paper > by Walter Willinger et al.). > > Cheers, > > Thomas > > On 16.01.2013 10:58, Professor V.O.K. Li wrote: >> Dear Colleagues, >> Many research questions in networking are described by probability >> theory formulated with measure theory. Recently we find that >> measure-theoretic probability appears to be inconsistent. The >> inconsistency >> has caused undesirable consequences in applications including >> network traffic modeling. Our findings are presented in a technical >> report. >> >> The title and abstract are as follows. >> Reconsidering Network Traffic Modeling >> We question current techniques ofnetwork traffic modeling. >> Measure-theoretic probability is the foundation of current traffic >> models. However, >> due to a fundamental flaw of measure-theoretic probability, >> current traffic models cannotproperly characterize the growth trend >> of network traffic. By demonstrating theinconsistency of >> measure-theoretic probability implied >> by unbounded random variables, we justify theabove claim with a rigorous >> analysis, and discuss >> the implications of our analysis to traffic modeling and some other >> related >> issues, such as performance evaluation of traffic control. >> >> >> The technical report is available at >> http://www.eee.hku.hk/research/doc/tr/TR2012006_Reconsidering_Network_Traffic_Modeling.pdf >> >> Your comments will be very much appreciated. >> >> Best regards, >> Guang-Liang Li and Victor O. K. Li >> _______________________________________________ >> IEEE Communications Society Tech. Committee on Computer Communications >> (TCCC) - for discussions on computer networking and communication. >> [email protected] >> https://lists.cs.columbia.edu/cucslists/listinfo/tccc >> > _______________________________________________ IEEE Communications Society Tech. Committee on Computer Communications (TCCC) - for discussions on computer networking and communication. [email protected] https://lists.cs.columbia.edu/cucslists/listinfo/tccc
