Subject: [ippm] concatenation of QoS parameters

From: Victor Reijs <[email-masked]>
Date: Thu, 14 Feb 2002 10:09:49 +0000

Hello all of you,

In IPPM, we are developing some great documents on definitions of
parameters. When using them, I see one issue (perhaps already covered
earlier in e-mail discussions), and I would like to hear your ideas
about this.
When measuring the parameters, I am sometimes not doing end-to-end
measurements, but more concatenating measurement results gotten from
several non overlapping domains. 
My question is now how is the concatenation done for all the defined
IPPM parameters. Perhaps some parameters have only validity between the
points measured?
I assume it is also dependent how fine grained you are looking (in micro
sec accuracy or milli second accuracy). So we have to keep that also in
mind. 
In my below ideas I am looking at millisec accuracy.

. OWD. I assume, I can just add figures in case of concatenation of
domains.
. IPDV. This is a difficult one. I would tend to say one can not just
added the figures. I once heard a convolution is needed here. What are
your ideas?
. IP Packet Loss. This is not a simple addition. Because a lost packet
in one domain can not be lost again in another domain, it can be
calculated mathematically (I think). I will give this a shot in the
coming time;-)
. IP Loss patterns. This is really a parameter that can not be used in
concatenation, in my opinion.
. IP packet reordering: I would say the same as loss patterns...

Would be great to hear your ideas on this (and possible solutions how to
concatenate).
The above was for the millisec range, perhaps other ideas are needed in
microsec range.

Thanks for your feedback.

All the best,

Victor
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From: Philip Chimento <[email-masked]>
Date: Thu, 14 Feb 2002 09:56:51 -0500

Hi Victor: 
It depends on what you want to do mathematically. The short answer is that 
means and rates add, with very few restrictions and almost nothing else does.
So, if you have the MEAN VALUES of OWD in two different domains, go ahead and 
add them (it doesn't even matter if the delays in the domains are somehow 
dependent on one another). The VARIANCES do NOT simply add if the random 
variables are dependent, you have to add in 2*covariance (measure of 
dependence), but if they are independent you can add them.

Distributions, on the other hand must be convolved (and you can think of 
histograms as distributions, for example). So, what does all this mean from a 
practical point of view ?

Go ahead and add AVERAGE OWD figures with a clear conscience. Oddly enough, (I 
believe) IPDV AVERAGEs can be added (even though they are dependent)[I would 
gladly hear from any statisticians out there if I am wrong about this]. The 
loss measures, on the other hand, I would simply add, because they are in fact 
measuring events on different probability spaces. What you have in successive 
domains are conditional average losses (or loss rates), where the losses are 
conditioned on the number of packets entering the domain (which is not 
necessarily the number of packets originally transmitted). Packet re-ordering 
is difficult, depending on how you define it; a domain may re-order packets to 
a permutation of the order in which it received them, but because of previous 
re-ordering, it may put some fraction of packets back into the original order 
as transmitted. If you define re-ordering conditional to the order received by 
a domain, I think that you can add the re-ordering rates. But what that means 
in terms of the original packet order, I am not sure.

If you want to go further than averages, however, you run into a lot of 
mathematical issues, and so combining histograms from different domains means 
that you have to look at numerical convolutions....

My 2 cents anyway. (What are fractions of a Euro ;-) ?

Regards, Phil 
-- 
Phil Chimento             Ericsson IPI
Phone: 240-314-3597	  7301 Calhoun Place
[email-masked]   Rockville, Md. 20855
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From: Steven Van den Berghe <[email-masked]>
Date: Thu, 14 Feb 2002 16:49:47 +0100

Hi Phil, Victor

i'm certainly not a statistician, so what i'm about to say might be 
completely wrong. If the loss in successive domains is on the average n,n',n" 
(probabilty of packets being dropped), couldn't i say that if i sent x 
packets, i can expect x * n * n' * n" being dropped (so multiply instead of 
add the loss rates)?

I agree on the delay part and must say i'm also afraid delay variations and 
re-ordering measurements are not very willing to be concatenated.

so far for my two cents (the expression remains the same if you talk about 
fractions of a euro:) )

Regards,
Steven

On Thursday 14 February 2002 15:56, Philip Chimento wrote:
> means and rates add, with very few restrictions and almost nothing else
> does. So, if you have the MEAN VALUES of OWD in two different domains, go
> ahead and add them (it doesn't even matter if the delays in the domains are
> somehow dependent on one another). The VARIANCES do NOT simply add if the
> random variables are dependent, you have to add in 2*covariance (measure of
> histograms as distributions, for example). So, what does all this mean from
> a practical point of view ?
>
> Go ahead and add AVERAGE OWD figures with a clear conscience. Oddly enough,
> (I believe) IPDV AVERAGEs can be added (even though they are dependent)[I
> would gladly hear from any statisticians out there if I am wrong about
> this]. The loss measures, on the other hand, I would simply add, because
> they are in fact measuring events on different probability spaces. What you
> have in successive domains are conditional average losses (or loss rates),
> where the losses are conditioned on the number of packets entering the
> domain (which is not necessarily the number of packets originally
> transmitted). Packet re-ordering is difficult, depending on how you define
> it; a domain may re-order packets to a permutation of the order in which it
> received them, but because of previous re-ordering, it may put some
> fraction of packets back into the original order as transmitted. If you
> define re-ordering conditional to the order received by a domain, I think
> that you can add the re-ordering rates. But what that means in terms of the
> original packet order, I am not sure.
>
> mathematical issues, and so combining histograms from different domains
> means that you have to look at numerical convolutions....
>

-- 
Steven Van den Berghe             
[email-masked]
Workgroup Broadband Communication Networks
Department Information Technology 
Ghent University - Belgium
Phone:  +32 (0)9 267 35 86 | Fax  :  +32 (0)9 267 35 99
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From: stanislav shalunov <[email-masked]>
Date: 14 Feb 2002 12:03:54 -0500

This is probably outside of scope of IPPM WG activities (and in the
realm of a statistics), but: Everything hinges on the assumption of
independent distribution of the delay variables for different domains.
On one hand, since the next domain doesn't explicitly know about
treatment in the previous one you could say that the independence
assumption should be true.  On the other hand, if there exist global
congestion oscillation phenomena (and why wouldn't they?) the
assumption would be incorrect.

Further, you do not specify your metrics.  Averages, for example,
would be much easier to analyze in this way than medians.

> . OWD. I assume, I can just add figures in case of concatenation of

Sum is correct for averages regardless of independence.

> added the figures. I once heard a convolution is needed here. What are

Sum is correct for variances provided that there is independence.

> . IP Packet Loss.

Loss probability, assuming independence, is, of course, 1-\Pi(1-p_i).
Accidentally, for small values of p_i the first order approximation of
this quantity happens to be \Sigma p_i.

> . IP Loss patterns.

No numeric parameter.

> . IP packet reordering:

No defined metric and no defined model.

> The above was for the millisec range, perhaps other ideas are needed
> in microsec range.

Scale doesn't matter.

-- 
Stanislav Shalunov		http://www.internet2.edu/~shalunov/

"You wake me up early in the morning to tell me I am right?  Please
wait until I am wrong."	-- John von Neumann, on being phoned at 10 a.m.
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From: Victor Reijs <[email-masked]>
Date: Mon, 18 Feb 2002 09:47:54 +0000

Hello Stanislav,

> would be much easier to analyze in this way than medians.

I would say: averages. I then avergae over two different time periods:
say over 10 micro sec (for micro sec range) and say over 1 msec (for
milli sec range).

All the best,

Victor

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From: Attila Pásztor <[email-masked]>
Date: Thu, 14 Feb 2002 17:27:45 +0100

Hi All,

in my understanding if independent losses are assumed, then one can expect
(1-n'), (1-n'') 'no-loss' rate, what gives:

x*(1-(1-n')*(1-n'')*..)

as the number of packets, one could expect to transmit successfully.

Regards,
Attila

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From: Matthew Roughan <[email-masked]>
Date: Thu, 14 Feb 2002 13:03:30 -0500

Hi,

addition of the loss probabilities is a reasonable approximation for low 
loss (assuming losses in different domains are independent).

If the loss probabilities in each domain are high then you run into 
obvious problems such as the sum being larger than 1.

The correct way to compute the loss (assuming independence) is
	p_{loss} = 1 - product_{i} (1 - p_{i})
where p_{i} is the probability of being lost in domain i. This computes 
1 - the probability that the packet is not lost in any of the domains.

The summation formula is the first order approximation.

The assumption of independence might not always hold. If the losses 
occurred because of an overload in traffic, then this could be 
correlated between domains (conceivably) and therefore cause correlated 
losses. Syncronization could also cause correlated losses. I don't 
personally think these will be a big issue, but one should be quite 
careful when considering general data.

Matt