[e2e] Is a control theoretic approach sound?

[John T. Wen]

The link capacity constraint is a nonlinear function.  The queue dynamics at
zero queue length is also nonlinear.   I don't think you can come up with a
linear controller to address these issues.   Furthermore, fairness is
addressed through optimization, and unless the optimization index is
quadratic, the resulting controller would also be nonlinear.
John

----- Original Message -----
From: "Saverio Mascolo" <mascolo at poliba.it>
To: "Shivkumar Kalyanaraman" <shivkuma at ecse.rpi.edu>
Cc: <end2end-interest at postel.org>; "John Wen" <wen at ecse.rpi.edu>; "Murat
Arcak" <arcak at ecse.rpi.edu>
Sent: Friday, August 01, 2003 6:17 AM
Subject: Re: [e2e] Is a control theoretic approach sound?


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