[Iccrg] Appropriate rate given corruption

[Lachlan Andrew]

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.

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

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)

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)

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.


If you disagree with any, let's discuss that before continuing.

Cheers,
Lachlan

-- 
Lachlan Andrew  Dept of Computer Science, Caltech
1200 E California Blvd, Mail Code 256-80, Pasadena CA 91125, USA
Phone: +1 (626) 395-8820    Fax: +1 (626) 568-3603