[Tmrg] convergence time

[Hideyuki Shimonishi]

Hi Lachlan, David, Cesar, and all,

The meeting will begin soon. Unfortunately, I could not manage to attend 
the meeting...

Yeah, I agree to the idea that we should look at the aggregate rate, and 
its convergence, in different level of congestion in realistic environment. 
But I think we also need to look at fairness of each flow, or distribution 
of per-flow throughput, as well. Even if the aggregate rate converges, I do 
not think this means the convergence of each flow.

However, looking at the behavior of individual flows in a realistic 
environment can be difficult, so I think it might be a good idea to look at 
the distribution of per-flow average throughput. What I mean is the following:
1) Obtain per-flow throughput distributions with a variety of RTTs, hop 
counts, load levels, and so on. In this case, all flows are long-lived.
2) Obtain per-flow throughput distributions with the very same environment, 
but flows are mix of short-lived and long-lived.
3) Compare the difference of these distributions, or its COV.
I guess 1) could be a measure for fairness, and firendliness also if we mix 
different kinds of flows, and 3) could be a measure for convergence. If a 
protocol has good cenvergence, the difference should be smaller.
Also, it might be good to see the distribution with only small files or 
large files. The former reflects slow-start behavior of a protocols, and 
the latter reflects congestion avoidance behavior.

That is why I proposed our tool (literature [7]) and published it at UCLA 
website. We can do the above testing easier with the tool.

Does this sound more realistic measure of convergence, in addition to the 
ones you have proposed ?
I am not sure Cesar will cover this point, but I guess this would be one of 
the important points we should cover.

Thanks,

HIDEyuki Shimonishi


At 07/10/31 09:18 -0800, Lachlan Andrew wrote:
>Greetings David,
>
>On 28/10/2007, Xiaoliang (David) Wei <weixl at caltech.edu> wrote:
> >     Another option, to eliminate the dependency to stability and
> > timescale, is that we don't study the convergence of current rate.
> > Instead, we study the convergence of the aggregate average rate. That is,
> > if the instanenous rate of a flow at time t is x(t), we define the
> > aggregate average rate of the flow at time t to be
> > X(t) = 1/t * sum u=0->t x(u).
> > ("sum" can be "integrate" if the time is continous).
>
>Good idea.
>
> > Then we study the convergence of the curve X(t) to the "final value".
> > This process might be easier as:
> > 1. X(t) is easier to measure because we can just look at the amount we
> > have transfered from time 0 to time t;
> > 2. X(t) converges even x(t) has a limit-cycle oscillation, so it is less
> > sensitive to stability
> > 3. If x(t) converges fast, X(t) converges fast too. We can still compare
> > the convergence with X(t)
> > 4. X(t) does have meaning in user-experience. It measures how long the
> > users have to participate in the network to get to the desired rate.
>
>They're all good points.
>
>The main drawback is that  X(t)  converges (much) more slowly, since
>it always gives some weight to the early rates.  If we want to observe
>the impact of each of several newly arriving flows, we need to space
>them out further if we use  X(t)  than we do if we use  x(t), or else
>the transients will interact.
>
>The time required to find the "final" value could already be quite
>long, especially in the case of Reno, which takes hours to reach
>equilibrium on large BDP paths.
>
>What do others think?
>
>Cheers,
>Lachlan
>
>--
>Lachlan Andrew  Dept of Computer Science, Caltech
>1200 E California Blvd, Mail Code 256-80, Pasadena CA 91125, USA
>Ph: +1 (626) 395-8820    Fax: +1 (626) 568-3603
>http://netlab.caltech.edu/~lachlan
>_______________________________________________
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Hideyuki Shimonishi, Ph.D
         Assistant Manager
         R&D Unit / System Platforms Research Laboratories, NEC Corporation
         h-shimonishi at cd.jp.nec.com
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