[e2e] Is a control theoretic approach sound?

Thu Jul 31 08:29:58 PDT 2003

It's nice to see the term "stable limit cycles"! I have seen some folks
wrongly referring to such behavior as "unstable", when in practice, a
finite system like TCP (with finite link capacity, finite buffers, ...)
can *never* be unstable!

This wrong classification as "unstable" sometimes comes from using
standard stability analysis techniques on a model linearized around a
certain operating point. The system going outside this range does *not*
mean that the system is unstable - rather it might be oscillating
between two different operating regimes (cf, non-linearity). We point to
some of these issues in "On the Efficiency and Fairness of Transmission
Control Loops: A Case for Exogenous Losses"
http://www.cs.bu.edu/techreports/pdf/2003-013-exogenous-loss-effect.pdf

Ibrahim

--
Ibrahim Matta, Associate Professor 
Dept. of Computer Science, 111 Cummington Street
Boston University, Boston, MA 02215, USA
Email: matta at cs.bu.edu, Tel: (617) 358-1062, Fax: (617) 353-6457
http://www.cs.bu.edu/fac/matta

> -----Original Message-----
> From: Gaurav Raina [mailto:G.Raina at statslab.cam.ac.uk]
> Sent: Thursday, July 31, 2003 8:01 AM
> To: Saverio Mascolo
> Cc: Shivkumar Kalyanaraman; end2end-interest at postel.org; John Wen;
Murat
> Arcak
> Subject: Re: [e2e] Is a control theoretic approach sound?
> 
> 
> 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
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > >
> >
> >
> 
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