Subject: Self-similarity and smoothness

From: [email-masked] (Mark Garrett)
Date: Tue, 16 Aug 1994 14:51:42 -0400

>   (*Traffic can be smooth and self-similar at the same time, but that's
 >   another discussion.)
 > do you have a ptr 
 > to such a discussion?

Kim,

Well I can point to the discussion that will happen in 2 weeks at
Sigcomm.  Some of this will be in the sigcomm paper, but more of
the resource allocation stuff is in the parts of my thesis (Ch 4)
that didn't make it into the Sigcomm version.

Here's the basic idea:  In their Sigcomm paper last year, you will
remember that Leland et al claimed that multiple sources of S-S
traffic when multiplexed, remain S-S and to the same degree.  In
our* work with VBR video traffic, the same statement can be made.
However the measure of self-similarity is the Hurst parameter, which
measures the relative content of frequencies.  Smoothness has more
to do with the bandwidth requirements of the traffic.  So, if we
multiplex 100 VBR video sources together, the mean rate increases
by a factor of 100, but the peak rate becomes only slightly larger
than the aggregate mean.  So statistical multiplexing is effective
because the bandwidth that carries 100 sources is less than 100 times
the bandwidth that carries one source.  The 100-source aggregate still
has the same Hurst parameter, and the concomitant low frequency content,
relative to the high frequencies etc.  However, the time-varying rate
is contained in a very tight interval from just below mean to just
above mean.

The case of internet traffic will be more complex than for VBR video,
I'm afraid.  First, it starts out more bursty, in both peak-to-mean
ratio and Hurst parameter.  Second, since TCP and other sources
interact with the network traffic state, you can (and apparently do)
have synchronization effects.  This means you can't necessarily take
10 independent measured traces of internet traffic, add them together
and call it a realistic trace for a link with 10 times the bandwidth.
So such an experiment would not accurately estimate the statistical
multiplexing gain, or smoothing of the traffic.

(*Note that Leland et al and Garrett et al have a common member:
we both work with Walter Willinger, who has brought all of this math
associated with self-similarity into the network traffic control field.)

You can get the sigcomm paper from
	ftp://thumper.bellcore.com/pub/mwg/sigcomm94.ps
If you want the thesis, the only way is paper mail, send me a mailing
address if you want one.

-Mark

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