[e2e] Queue size of routers

[Damon Wischik]

> The results of the exercise were that routers in the network with
> the same output buffer configurations, including those on long-delay
> international circuits, produced indistinguishable loss/load curves
> and that all 4 configurations of routers matched M/M/1/K queuing
> predictions my not-so-idiotic co-workers used with almost uncanny
> accuracy
> ...
> Note that the network in question was one of the largest backbones in
> existence at the time, and even though the data was crude it was still
> data obtained at a scale of aggregation inaccessable to contemporaneous
> researchers who might have been interested.  I really wanted to publish this
> data in particular since the measurements seemed to flatly contradict the
> expectations of the effect of scale expressed by some of the people who
> were finding long-tailed distributions all over at much smaller levels
> of aggregation

There is recent paper:
  "A Poisson limit for buffer overflow probabilities"
  Jin Cao and Kavita Ramanan, IEEE Infocom 2002
  http://www.ieee-infocom.org/2002/papers/655.pdf
which may be interesting. From the abstract:

> We consider n independent identical traffic sources modelled as point
> processes, which are fed into a link with speed proportional to n. Under
> fairly general assumptions on the input processes we show that the
> steady state probability of the buffer content exceeding a threshold b >
> 0 tends to the corresponding probability assuming Poisson input
> processes. We verify the assumptions for a large class of long-range
> dependent sources commonly used to model data traffic.

Damon Wischik.