[e2e] Is a control theoretic approach sound?

[Cannara]

It depends entirely on what your output measures are and how inputs affect
them whether the system behaves linearly or not.  Queue management in real
routers is highly nonlinear.  TCP's behavior under noise loss is highly
nonlinear, etc.  So, as in accounting, it's what you account for that defines
a choice of model.

Alex

Saverio Mascolo wrote:
> 
> 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.
> > > > >