[e2e] Is a control theoretic approach sound?

[Gaurav Raina]

The analysis in:

Dynamics of TCP/RED and a Scalable Control
S. H. Low, F. Paganini, J. Wang, S. Adlakha, J. C. Doyle
Proceedings 2002 IEEE Infocom, New York, June 2002.

Showed very carefully (using ns) how as delays increase, stable limit
cycles are formed which increase in amplitude as the delay increases.
With delays we get an infinite-dimensional system, which
will not produce limit cycles if it has a linear structure.

Linear (delayed) systems will either have fixed points as attractors or
unbounded trajectories - So it is a boon that TCP has a non-linear 
component to it.

Gaurav 


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

--------------------------------------------
Academia: Academia was a public garden near
Athens where Plato lectured his pupils. The
school became known as the Academy and the 
teachers and pupils as academics.

tel: +44 (0)1223 519 166
web: http://www.statslab.cam.ac.uk/~gr224
--------------------------------------------