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[ih] FC vs CC Re: [e2e] Fwd: Re: Once again buffer bloat and CC. Re: A Cute Story. Or: How to talk completely at cross purposes. Re: When was Go Back N adopted by TCP

I suggest starting with Erlang. Since he died in 1929, you are certainly
looking for papers that are mainly to be found on paper ;-).

According to Wikipedia his first significant paper was published in 1909.
Of course it was about circuit switching.


On 26/08/2014 07:44, Jack Haverty wrote:
> On 08/25/2014 10:09 AM, Detlef Bosau wrote:
>> Am 23.08.2014 um 05:34 schrieb Jack Haverty:
>>> It's been a looonnggg time, but I still remember studying a lot of
>>> mathematics about 50 years ago - queueing theory, graph theory, etc. 
>>> Used to be able to do it too.
>>> My recollection is that terms such as "flow control" and "congestion
>>> control" were used in mathematics, well before they were used in
>>> computer networks. 
>> Hm. I read quite a lot of mathematical models used for computer networks.
>> However, I never happened to see, how flow control and congestion
>> control were modelled. The models were made that abstract, that
>> congestion control and flow control vanished.
>> I really appreciate concrete pointers here.
>> Detlef
> Detlef,
> I suggest you research the literature of the "Operations Research"
> branch of mathematics.   That is where pure mathematics concepts of
> queueing theory et al. were applied to real-world problems.
> I did a quick google search of ("queueing theory" "flow control") and
> found this example of a mathematical paper discussing queues and "flow
> control" in computer networks:
> http://www.jstor.org/discover/10.2307/2582975?uid=2&uid=4&sid=21104558206567
> Here's another one, about flow control in "supply chain networks" in the
> manufacturing environment:
> http://www.isr.umd.edu/~baras/publications/papers/2012/Ion_Asane_MTNS2012.html
> What we might call "packet loss" they might call "supply chain disruption".
> I suspect most of the material you may find online will be about the use
> of mathematics in computer networks.  Unfortunately, most earlier work,
> before we had the Internet, is probably not available online - it may
> only be in university libraries.  So that's where you may be able to
> find papers on flow control in pre-computer environments like railroads.
> Also, the basic mathematical concept which we networking people call
> "flow control" might have been described using different terminology in,
> for example, the old railroad or other business examples.
> I suggest researching Bell Laboratories work from before 1970.   They
> did a lot of theoretical work modelling the telephone network, and in
> particular the issues of managing many simultaneous voice calls.  The
> problem of designing the telephone network to minimize the probability
> of busy signals is about the management of multiple simultaneous flows
> and controlling congestion on circuits in the interior of the network.  
> But they may have used different terminology.
> My recollection is also that, as you said, the mathematical models were
> so abstract that they were not very useful in the real world of computer
> networks.  Mathematics could be used to model hypothetical cases, and
> was useful to see how things might behave in theory.   The real-world
> was sufficiently chaotic and unpredictable that it was difficult to
> model with sufficient accuracy.   That's why the Internet was built by a
> continuing series of experiments and refinements.
> At one point, someone published a mathematical paper that proved that
> the ARPANET would lock up and all traffic flows would stop.   This cause
> some great concerns among the users of the ARPANET who were depending on
> it.  Our analysts at BBN examined that paper in great detail and
> concluded that it was mathematically correct -- but one of the
> assumptions made in the model was that every packet switch computer was
> started at the same moment in time, and all those computers ran at
> exactly the same speed so instructions in all machines were executed in
> total synchrony.   We advised the users that, if such a situation could
> be created, the ARPANET would crash, but that the likelihood of that
> situation of perfect synchrony was so tiny that there was no reason to
> worry.  It was a mathematically interesting theoretical problem, but not
> a real-world concern.
> I can't recall when I first encountered the terms "flow control" or
> "congestion control" in computer networks, or seeing any formal
> definitions of those terms. 
> My personal view is that "flow control" refers to the management of a
> single flow of information between two end-points.  It could be a TCP
> connection, or a telephone call, or a stream of railroad cars between a
> factory and warehouse.   There are mechanisms in the endpoints, as well
> as in the interior, to manage that flow.
> Conversely, "congestion control" refers to the management of a set of
> many flows as they compete for resources.   If there are too many flows
> going through a bottleneck, congestion happens and may result in broken
> flows or "busy signals".
> These two phenomena interact in complex ways, so it was common in the
> early Internet work to discuss them both when working on any particular
> problem.   For example, the TCP algorithms in host computers would
> interact with the routing algorithms in switching components, the
> error-control algorithms on individual circuits, the load-levelling
> schemes of server farms, and almost anything else you can imagine that's
> involved in regulating the flows through the Internet.
> IMHO, the Internet is way more complex than we know how to model.  It's
> probably at the same level of complexity as other hard problems -
> weather, astronomy, etc.
> We didn't model it.  We just built it.
> Hope this helps,
> /Jack Haverty