[e2e] Is a control theoretic approach sound? (fwd)

Thu Jul 31 09:50:03 PDT 2003

Vishal,

Sorry - wrong connotation. Once linearized, the methods are not 
ad-hoc. 

I meant that to get broader non-linear analysis results in more 
than single-bottleneck time-delay cases, there are difficulties in 
constructing Razumikhin-type Lyapunov functions and Krakovskii-type 
infinite-dimensional Lyapunov functionals. The search for these functions 
and functionals has been somewhat ad-hoc... my colleague Murat Arcak could 
perhaps add more insight on this issue...

best
-Shiv

> Shiv,
>      I am curious why you refer to "linearized
> framework" having "ad-hoc toolkits". What exactly is
> "ad-hoc" about them?
> 
> -Vishal
> --- Shivkumar Kalyanaraman <shivkuma at ecse.rpi.edu>
> wrote:
> > 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).
> > 
> === message truncated ===
> 
> 
> =====
> http://www.cs.columbia.edu/~misra/
> 
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-- 
-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