Re: pareto and exponential traffic sources

[Vern Paxson <vern@ee.lbl.gov>]

[I'm not on the mailing list, but Kevin forwarded your exchange with
 Subramaniam Vincent]

> The idea of warmup is to discard transient data collected during the
> start of the simulation.  The concept is not specific to any particular
> source models, and it can be applied to any simulation.  The length
> of the warmup period can be a function of the parameters of a simulation
> (including but not limited to source models).

I would add that for Pareto ON/OFF, there's an additional consideration.
What you ideally want is for each ON/OFF source to be in steady-state,
which means that at time T, when you start the simulation, they're either
in an ON or OFF state with the right probability, *and the amount of time
they're going to remain in that state* corresponds to the distribution you'd
expect to observe for an ON/OFF process started at time -infinity and
happily alternating between ON and OFF ever since.

The problem is, if you crunch the math for a Pareto distribution with parameter
alpha as to the distribution of how much time should be remaining in this
circumstance, you get a Pareto distribution with paramater alpha-1 [*].
So if you're doing the usual of 1 < alpha < 2, in order to have infinite
variance but finite mean, then the distribution you get for the steady
state snapshot has 0 < alpha < 1, or infinite mean; and in this regime,
it's not clear that you have a meaningful steady-state.

I'm not sure to what degree this is indeed a problem; nor, if it is,
how to fix it in a sound fashion.  I've cc'd Walter Willinger, in case
he has comments.

		Vern


[*] This assumes I didn't blow the math when I crunched this a while ago -
    not guaranteed!