[e2e] Is a control theoretic approach sound?

[Saverio Mascolo]

Shiv,

we all agree with VJ that a network is to a very good approximation a linear
system. Linear system means that it can be modeled by linear differential
equations (and the superposition principle holds).
The only way to get a non linear system from a linear one is to use a
nonlinear controller.
So the question is: why should we use a nonlinear controller?

Saverio

----- Original Message -----
From: "Shivkumar Kalyanaraman" <shivkuma at ecse.rpi.edu>
To: "Saverio Mascolo" <mascolo at poliba.it>
Cc: <end2end-interest at postel.org>; "John Wen" <wen at ecse.rpi.edu>; "Murat
Arcak" <arcak at ecse.rpi.edu>
Sent: Thursday, July 31, 2003 2:53 PM
Subject: Re: [e2e] Is a control theoretic approach sound?


> 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
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > >
> >
>