[e2e] Is a control theoretic approach sound?

[Shivkumar Kalyanaraman]

Saverio,

we seem to be hair-splitting the word "non-linear"... which means
different things to different people.

The point is not to model TCP -- but to understand the dynamic properties
of a larger class of de-centralized control systems.

you are a controls person, but just for the sake of the broader audience,
here is a clarification of terms being used more commonly nowadays...:

TCP has already been modeled in kelly/low's "non-linear" but "static"
opimization framework. Non-linear here refers to the shape of the
objective function (sum of concave utility functions) and the inequality contraints
on the problem. The value of this framework (arguably a
"control-theoretic viewpoint") has been for a cleaner "flow-level"
"steady-state" understanding of TCP behavior that generalizes to a
broader class of schemes. This is clearly one of the modeling victories in
the last 5-6 years.

Practically, a lot of interesting AQM work as resulted from this
viewpoint (eg: REM from Low, and AVQ from srikant et
al). We can use this framework also to design edge-based methods to handle
non-cooperative/misbehaving flows.

Beyond "static" optimizations which describe steady state or converged
flow-level throughputs and fairness, we are interested in "dynamics":
stability, robustness and performance characteristics. This could be
thought of as "dynamic" optimization, an area deeply studied in control
theory, but considered hard in a non-linear and decentralized context like
in the case of internet congestion control.

Here there is control-theoretic talk of "local-stability",
"global-stability" "time-delay robustness" etc. The analysis techniques
can be done in a linearized framework (with a limited and somewhat ad-hoc
toolkit) or a non-linear framework (that admits a broader and systematic
set of tools).

In my prior note, I meant non-linear in this sense of toolkits that
aid in the analysis of dynamics at the flow-level. Understanding and
modeling dynamic decentralized control in elegant frameworks is the
next control-theoretic frontier (to step up from static optimization
frameworks) and the Wen/Arcak framework is an important step in that
direction.

So, i think it makes sense to study these frameworks to take the
congestion control robustness and dynamics discussion above the level of
handwaving "packet-level" dynamics to rigorous flow-level models. The
contributions of control-theoretic folks to networks in this area is
invaluable.

best
-Shiv

On Thu, 31 Jul 2003, Saverio Mascolo wrote:

> Hi,
>
> why do you think that TCP is a nonlinear system?
>
> By quoting V. Jacobson cornerstone paper :
>
> "Network is, to a a very good approximation, a linear system. That is, it is
> composed of elements that behave like linear operator-integrators, delays,
> gain stages, etc"
> - Van Jacobson, "Congestion Avoidance and Control," in Proceedings of ACM
> Sigcomm'88.
>
> I think that modeling the TCP as a nonlinear system not only introduces not
> useful complexity but it is  wrong!
>
> Saverio Mascolo
>
>
>
> ----- Original Message -----
> From: "Shivkumar Kalyanaraman" <shivkuma at ecse.rpi.edu>
> To: <end2end-interest at postel.org>
> Cc: "John Wen" <wen at ecse.rpi.edu>; "Murat Arcak" <arcak at ecse.rpi.edu>
> Sent: Thursday, July 31, 2003 2:49 AM
> Subject: Re: [e2e] Is a control theoretic approach sound?
>
>
> >
> > The issue of considering delay robustness and several other
> > properties directly in a non-linear dynamic control theoretic framework
> > has been proposed by my control-theory colleagues John Wen and Murat Arcak
> > in their INFOCOM 2003 paper -- this framework is a superset of Kelly and
> > Low static optimization frameworks and linearized stability analyses.
> > Since my colleagues do not read this mailing list, please cc your
> > responses directly to them too.
> >
> > It is becoming clear that basic dynamics and steady state behavior of
> > congestion control schemes are best understood at the "flow"
> > level in optimization frameworks; and "fine-tuning" of schemes can be done
> > at the "packet" level (eg: estimation robustness issues,
> > increase/decrease: AIMD etc, slow start, interaction with timeout/rtt
> > estimation etc). This "packet-level" dynamic behavior can be validated by
> > ns-2 simulations or implementation trials.
> >
> > This is the essence of the approach of Kelly and Low frameworks and the
> > other generalized frameworks...
> >
> > -Shiv
> > ===
> > Shivkumar Kalyanaraman
> > Associate Professor, Dept of ECSE, Rensselaer Polytechnic Institute (RPI)
> > 110, 8th Street, Room JEC 6003, Troy NY 12180-3590
> > Ph: 518 276 8979   Fax: 518 276 4403
> > WWW: http://www.ecse.rpi.edu/Homepages/shivkuma
> >
> > A goal is a dream with a deadline -C. Knight
> >
> >
> > On Thu, 31 Jul 2003, Panos GEVROS wrote:
> >
> > >
> > > ----- Original Message -----
> > > From: "Yunhong Gu" <ygu1 at cs.uic.edu>
> > > Subject: Re: [e2e] Is a control theoretic approach sound?
> > >
> > > > Well, I think to decide how "aggressive" the AI will be is not that
> > > > *simple* a problem :) It is not the more aggressive the better (even
> if
> > > > the per flow throughput is the only objective), right?
> > >
> > > agreed but only if you want to address the problem in its full
> generality
> > > ... if it is restricted to those areas of the (capacity,traffic) space
> where
> > > the packet loss is in [0...7-8%] range (and AIMD is indeed relevant)
> since
> > > out of this range timeouts start becoming the norm) then it is
> > > *fairly*straightforward* to decide on AIMD parameters which provide
> specific
> > > outcomes (wrt individual connection perfromance -within limits
> obviously-
> > > and wrt capacity utilisation).
> > >
> > > > > ..in their case they know pretty much that the links they are using
> are
> > > in the
> > > > > gigabit range and there are not many others using these links at the
> > > same time.
> > > > >
> > > >
> > > > But what if there are loss, especially continuous loss during the bulk
> > > > data transfer? No matter how large the cwnd is initially, it can
> decrease
> > > > to 1 during the transfer, then the problem arise again.
> > >
> > > drastic measures (timeout, exponential backoff etc) will always need to
> be
> > > in place -
> > > I 'm saying that (at least in the first attempt)  it pays being
> optimistic
> > > (this is the idea underlying slow start anyway..)-  and in certain
> > > environments indeed more optimistic than the standard prescribes since
> there
> > > is a-priori knowledge of the network path characteristics and even
> traffic
> > > conditions - which is the case when considering OCxx links connecting
> > > particle physics laboratories.
> > > this approach seems to me a lot simpler and (most likely) equally
> effective
> > > compared to elaborate control schemes which try to do better while
> trying
> > > hard to remain "friendly" at the same time.
> > >
> > > Panos
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> >
>