[e2e] queue averaging introduces delay

[Steven Low]

Hi Ramki

Ramakrishna Gummadi wrote:
> 
> Hi
>         We have been thinking about the same for sometime now---a PI
> controller has a transfer function of the form (K_p+K_i/s), while the
> averaging part of a queue has the form: K/(K+s). It seems to me like the
> queue averaging component can subsume (is more general than) the integral
> part (assuming a suitable gain factor is used when the averaging component
> is used).

It does not.  Averaging is just a lowpass and adds a phase lag (and
gain).   PI (or REM) adds an integrater, to clear buffer, which adds
90degree lag and compensates this by a phase lead.  In other words,
the justification for accepting the cost of 90degree lag introduced
by the integrator is to clear buffer (or match it to target) in 
equilibrium.  Alternatively, one can clear the buffer, not by integral
action, but by "virtual buffer"; this is the approach of Kelly and
Srikant, and a recent algorithm of Paganini, Doyle and Low.  It is 
however not entirely clear what purpose queue averaging serves in 
this context.

Note that queue dynamics is not an integrater, as Hollot, Misra, Towsley
and Gong's infocom paper points out, but has a more complicated dynamics
(which turns out to be critical in determining the stability of
TCP/RED).

One can look at the local stability of the feedback loop of TCP/AQM, and 
think of different AQMs as different ways to stabilize the high gain
and a lowpass action of TCP.   It then suggests that there is limitation
on what AQMs can achieve in stabilizing TCP.   This is already apparent
from extensive TCP/RED simulations in the literature (e.g., 
Hollot-Misra-Towsley-Gong's paper) in the literature that show that we 
can choose RED parameters to have either sluggish response and large
equilibrium queue (in order to have a stable operation), or an unstable
and wildly oscillatory operation.   

We have a *draft* that touches upon all these if anyone is interested.

Steven

-- 
__________________________________________________________________
Steven Low, Assoc Prof of CS & EE 
slow at caltech.edu			netlab.caltech.edu
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