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Re: Another Point Of View (Round 2)
At 1:57 PM -0500 12/2/96, Fred R. Goldstein wrote:
>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.
Hmm. Yes, you have to be right on this point. I'm clearly not thinking
straight. Sorry about that, I must be a bit rusty <g>.
>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).
Huh? What do you mean "when the quantities are corrected for?" 100
Poisson-distributed voice calls of mean holding times of three minutes will
produce substantially less load than 100 Power Law-distributed data calls
of mean holding times of 20 minutes. (3/20ths of the load, to be exact)
What are you correcting for here?
>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 only way to know for sure is to calculate the blocking probability
tables for Power Law PDFs. This is beyond my math capabilities. Even if it
is only a 10% reduction in capacity, and I suspect your're right since once
the number of trunks gets large enough these load tables get almost linear,
the *main* issue remains the fact that the system is having to cope with a
growing number of longer holding time calls. The rest may be second order.
And on a point raised in another post, yes I see the biggest short term
threat as being nailed-up calls, a practice likely to become even more
prevalent as increasing numbers of individuals and small businesses try to
host web sites on their home PCs. Nailed-up circuit-switched circuits are
truly anti-social (even more than calling for taxpayer supported subsidies
for the info have-nots <g>.) The biggest long term threat is that we never
get facilities based competition and have to live with a regulated monopoly
and all of this unproductive lobbying forever because folks like the CPT
create an economic environment inhospitable to potential competitors by
setting mandated rates too low (which will also have the side effect of
slowing down the rollout of ISDN even further).