Re: Another Point Of View (Round 2)

["Fred R. Goldstein" <fgoldstein@bbn.com>]

  At 10:05 AM 12/2/96 -0500, Bill Frezza wrote:
  >At 10:35 PM +0000 12/1/96, Mike Bilow wrote:
  >>In effect, you are trying to assert that 20 calls each lasting one minute will
  >>present less demand on the system than one call lasting 20 minutes.
  >
  >No, that's not at all what I am saying. I am saying that a Power Law
  >distribution of mean holding time 20 minutes produces more long
  >holding-time calls (and, hence, a larger total call load) than a Possion
  >distribution of mean holding time of 20 minutes. It also produces a LOT
  >more traffic load than a Possion distribution with a mean holding time of 3
  >minutes, which is what the network was designed for.
  
  Not true!  The problem is clear when you analyze the words:  "mean holding
  time" is a "mean", regardless of the distribution.  The *total* is the mean
  times the number of calls.  Power Law vs. Poissonian with the same mean
  and the same number of calls will result in a differnt *distrubution* of
  calls, but the total number of minutes is still mean * quantity.  Power
  Law might have more long calls, for instance, but the mean is still the
  mean, by identity.
  
  Also, the assertion that it produces more load than a mean of 3 minutes
  is not true when the quantities are corrected for (i.e., 200 hours at 3
  minutes a call is more calls than 200 hours at 20 minutes).  There *may* be
  a small
  perturbation in the blocking probability, such that a 2% (or other) blocking
  factor might occur at a slightly lower average utilization.  So with the
  Poisson table, 200 trunks at P.02 carries 172 Erlangs, or 86% use; with
  some other distribution, 200 trunks at P.02 might carry 168 or 177 or 
  whatever.  This gets into lots of details about the *real* distribution and
  the appropriate math to handle it.
  
  But I doubt it ever goes more than, say, 10% lower than Poisson, so the
  cost of usage is not more than 11% higher.  This just isn't Earth-shattering.
  
  >The empircal conclusion that Internet data calls approximate a Power Law
  >distribution was made by Atai and Gordon. I believe you can order the paper
  >from Bellcore (document number OOC 1013, call 1-800-521-CORE.)
  
  I think I saw the document somewhere on line once.  I can't find it via
  AltaVista tho, so it may not be on the web.  In any case it looked a little
  fishy, like an experiment designed around a desired outcome.  Maybe it was
  taking traffic just below the knee of the blocking curve and jerking it
  over.  Given 160 Erlangs of poissonian traffic and 188 channels, you're just
  below P.02.  A mere 7% rise (to 171 Erlangs) brings you to around P.10,
  roughly quintupling blocking.  Certainly Bellcore is not neutral on this
  stuff anyway.
  
  >Meanwhile, let me see if I can track down an authoritative mathematical
  >reference on the Power Law PDF. The problem with these technical arguments
  >is that by the time we are done, there are going to be all of 3 people that
  >understand what we are talking about, and all of these probably work for
  >the phone company (the "bad" guys). Meanwhile, everyone else will go back
  >to either religious arguments or conspiracy theory.
  
  Probably true.
  ___
  Fred R. Goldstein      fgoldstein@bbn.com  
  BBN Corp.              Cambridge MA  USA    +1 617 873 3850