[Iccrg] Re: Appropriate rate given corruption

[Michael Welzl]

On Sun, 2007-08-26 at 16:16 -0700, Lachlan Andrew wrote:
> Greetings Michael,
> 
> Our previous discussion on the appropriate rate for congestion control
> in the presence of corruption got a bit stuck on details.    If you
> have the time, I'd like to try again, starting with some things I
> think we can agree on.

Okay - I think that's a good approach, thanks!


> Do you agree that
> 
> 1. TCP responds with a rate approximately   K/sqrt(p)  where  K  is a
> constant dependent on such things as RTT and packet size,  and  p  is
> the total loss probability

Yes.


> 2. On a path with multiple bottlenecks, with loss rates  p_i,  the
> total loss rate is slightly    less   than the sum of the p_i.   That
> is,  p = 1-product(1-p_i) < (sum p_i)

No.

First of all, the way I think about it, there is only one
bottleneck along a path per definition (so the p_i's will
all be close to zero except for one of them, which
represents the bottleneck).

Secondly, I don't understand why the total loss rate of
the path would be slightly less than the sum of the p_i
and not precisely that sum.


> 3. As a result, TCP gives slightly  higher  rate to multi-hop flows
> than a hypothetical scheme which gave a rate  K/sqrt(sum p_i) <=
> K/sqrt(p)

No because this is based on 2, which I disagree with.


> 4. (More of a stretch)  Consider a network only one link  l_0 which
> corrupts packets, which transmits fraction  r  of the packets it
> receives.  Then each received packet on a flow traversing  l_0
> creates as much additional congestion as a flow in a modified network
> such that
>   (a) there is no loss
>   (b) each link  l_i  upstream of  l_0  is replaced by "1/r" links,
> each with the same amount of congestion as  l_i  had in the original
> network.

Yes.

Cheers,
Michael