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Another Point Of View (Round 2)

  Bill Frezza wrote in a message to Mike Bilow:
  >As I think should be obvious to anyone who made it past high 
  >school math, the only real issue is whether the value of d is 
  >different for voice calls and data calls.
   BF> No, this is not correct. This false assumption is the root
   BF> of your error. The two probability density functions have
   BF> completely different forms. Poisson distributions have much
   BF> smaller standard deviations than Power Law distributions
   BF> even if the means are equal. (You can see this just by
   BF> looking at histograms of raw call data.) The "flatter"
   BF> nature of measured internet call holding-time distribution
   BF> functions includes many more long holding-time calls than
   BF> would be produced by an exponential distribution. Most
   BF> significantly, these longer holding-time calls have a
   BF> disproportionate impact on total call-minutes, which is one
   BF> of the two real load issues you correctly identified. The
   BF> second is the overall Quality of Service impact of having
   BF> large hunt groups tied up with 30+ CCS of traffic. 
  I have been trying to simplify this into what should be an essentially
  non-mathematical discussion.  I supplied my examples of balls in tubes earlier
  with the explicit intent of showing intuitively what the Poisson distribution
  is and what it looks like.
  I have no idea what you mean when you say such things as "longer holding-time
  calls have a disproportionate impact on total call-minutes," and this is what
  both Fred Goldstein and I have been zeroing in on with regard to your claims. 
  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.  That's
  true in the most extreme cases of nailed up circuits, as Fred points out, but I
  don't see any justification for it in anything other than extreme cases.
  Fred has gone further and directly said that he thinks the appropriate model
  for both cases is still Poisson; while I think Fred is right, I'll let him
  discuss that aspect of it since he has more experience in testing such issues
  in the real world than I do.  The controversy hinges on verifying these models
  by experiment, not on paper.
   BF> I'll try to run down a current technical reference on the
   BF> PDFs if you're really interested in understanding this, it's
   BF> been a long time since my traffic modelling days back at
   BF> Bell Labs.
  I'm not asking for a curve fit.  What I am asking for is some sort of
  theoretical and empirical justification for the model.
  -- Mike
  Bilow Computer Science   | +1 401 944 3937 (voice) | Michael S. Bilow
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