From van@lbl-csam.arpa  Tue Feb 16 18:51:24 1988
Posted-Date: Tue, 16 Feb 88 18:50:36 PST
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To: ddc@lcs.mit.edu
Cc: end2end-interest@venera.isi.edu
Subject: Re: [atheybey@PTT.LCS.MIT.EDU: Sequence number PS file.] 
In-Reply-To: Your message of Tue, 16 Feb 88 15:51:42 EST.
Date: Tue, 16 Feb 88 18:50:36 PST
From: Van Jacobson <van@lbl-csam.arpa>
Status: R

That's fascinating data, Dave.  It even looks familiar.  But
why is the retransmit timer so bad?  It looks like rto is at
best ~ 10 times rtt and occasionally 20 or 30 times rtt.  Are
you simulating the bugs in the 4.2 srtt algorithm as well as
the broken retransmit policy?

 - Van

From van@lbl-csam.arpa  Tue Feb 16 20:28:48 1988
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To: Jon Crowcroft <jon@cs.ucl.ac.uk>
Cc: end2end-interest@venera.isi.edu
Subject: Re: Randomising events 
In-Reply-To: Your message of Mon, 15 Feb 88 12:42:31 GMT.
Date: Tue, 16 Feb 88 20:28:01 PST
From: Van Jacobson <van@lbl-csam.arpa>
Status: R

I don't know of any network-related references (I'd be real
interested if you come up with any) but this is a well
studied problem in biology and chemistry.  In chemistry
the problem comes up in determining the cluster size and
growth rate for coagulation in colloidal solutions (one
sees increasing organisation in space rather than the
organisation in time you see with routed or rwhod, but the
underlying math is the same) and in determining the rate
coefficients for diffusion controlled reactions.

Around the turn of the century, Smoluchowski did some very
elegant analysis of this problem and derived its basic equations
(the main one is a special case of the Fokker-Planck equation
now called the Smoluchowski equation).  One result concerned the
growth rate of "clumps":  If you start with some random, uniform
distribution of particles (or packets) with density c0 at time
zero, the concentration of clumps of size k at time t, c(k,t),
evolves like
			      k-1
		      (c0 g t)
	c(k,t) = c0 -----------
				k+1
		    (1 + c0 g t)

where 'g' is a constant fixed by the properties and geometry
of the system but independent of the distribution or number
of 'particles'.  (I think this same result shows up in statistics
and operations research when you study the distribution of a
brownian motion subject to absorbing barriers.)

I've fit the above to a simulation of a large number of Decnet
routers sharing one ethernet and the agreement was pretty good.
If some funding comes through, I hope to have a post-doc this
summer look at some real data, finish the simulations and
publish the results.

  - Van

ps: I don't know of any good references (you might check with a
    chemist, statistician or OR person) but, if you like math,
    I found some good stuff in "Introduction to the Physics of
    Complex Systems" by Serra, Andretta, Zanarini & Compiani,
    Pergamon Press, 1986, ISBN 0-08-032628-5.