[e2e] [Fwd: RED-->ECN]

[Alhussein Abouzeid]

On Thu, 1 Feb 2001, Fred Baker wrote:

> At 08:40 AM 2/1/01 -0500, Michael B Greenwald wrote:
> >If the input rate is less than the
> >output rate, then (independent of variations in inter-arrival time) the
> >queue length is 0 -- always empty.  For an arbitrarily low *average* input
> >rate, and a long enough interval, and an unbounded queue, I can construct
> >an arrival schedule that will cause an arbitrarily high *average* queue
> >length.
> 
> who told you that?
> 
> I think you'll find that with any distribution, mean queue depth is not a 
> binary flip-flop between zero and infinity. With poisson distributions 
> (M/M/1) and a ratio if input rate to output rate of p and mean service 
> interval m, Kleinrock tells me that the average time in queue (which is to 
> say mean queue depth including the packet itself)
> 
>               p/m
>          W = -----
>              1 - p
> 
> and in the general case
> 
>               average remaining service time
>          W = --------------------------------
>                          1 - p
> 
> That's far from a step function.
> 

Fred,

I agree with your result (that the queue fluctuations are not step
from 0 to infinity) but not with the approach. Kleinroch did tell you
the above equations, but also said that they are only valid for p<1. If
p=1, the system is critically (un)stable and for p>1, the average queue
occupancy grows without bound (until buffer overflow).

Thus, the key issue here is that we are dealing with a closed queueing
system where the input rate is a function of the output rate, and hence I
prefer Vishal's reasoning (please refer to his earlier e-mail).

Regards,

Alhussein.