[e2e] theory behind staistical multiplexing

[Jon Crowcroft]

I agree about this, but its the
statistics of the sources that make stat muxing make sense - 

depends on timescales, but at least 2 characteristics are
the session arrivals and the packet arrivals within session
(this is sort of circular definition, since if there was no stat muxing gain,
then we might not talk about packets at all - i guess as a computer scientist though
one might talk about the symbols of an alphabet - very old networks used
byte/character/octet as the unit of the net -  - newer systems use packets which correspond
to convenient size units for computers (disk block size, page size, 
delta in a change to screen, or multimedia sample size) Â

so
if you have a set of CBR flows that are relatively long lived
(e.g. a lot of TV and radio stations, or a lot of voice/video calls with legacy CODECs) 
then the stat mux "gain" is typically small to zero

but
if you have a set of VBR flows that may also be short lived
then you have periods of silence during which resources on a path
between  one source and destination can be shared by another source and/or destination

so thats to do with the temporal characteristics of the sessions.
now you can also think about spatial characteristcs of traffic overal (i.e. the 
overal sparsity or denseity of the source/destination set at any time)

you could have very short lived CBR flows too (then it depends on the
spatial layout of the sources and destinations, and the economics of 
link versus switches, what sort of concentration you get in your net
therefore what the stat muxing gain on the loinger haul links is)

I dont know a single reference that discusses this - the best stuff is probably
in books on network design - the problem with these is that most are donkey's years old, so dont have in stuff
about modern flow characteristics (e.g. TCP source model, like Padhye or other, and RTP/VOIP source models)
nor about the traffic matrix (e.g. the stuff in various papers out of sprint and at&t research in last few years..)
or about the network topology (which is not _designed_ per se: in the Internet today, once one gets past a single
AS, since the way the inter-domain topology has evolved is an economic/natural process, and therefore the way the
trafficmatrix and the topology interact, and the way the source model and aggregation/stat muxing work on
inter-domain paths is an altogether not fully understood thing, no not at all....

I guess I like Keshav's book on an Engineering approach to networking, as capturing some of this stuff about as
well as you can, but that is getting on a bit - I dont know of an accessible book (there's walrand and other folks,
but they are for math folk really...)

In missive <41C4B71B.8080605 at aero.org>, Steven Berson typed:

 >>I think of the law of large numbers as being the basis for statistical 
 >>multiplexing.  Any good probability book (e.g. Feller, Ross) will have 
 >>good coverage of the law of large numbers.
 >>
 >>The law of large numbers is far more general than specific queueing models.
 >>
 >>Steve
 >>
 >>Alok wrote:
 >>
 >>>Hi,
 >>>
 >>>What would be a good reference to the mathematical work behind "stastical
 >>>multiplexing".
 >>>
 >>>For example, does it assume a model M/G/1, M/M/infinity etc?
 >>>
 >>>-thanks
 >>>Alok
 >>>
 >>>
 >>>  
 >>>
 >>

 cheers

   jon