Subject: [ippm] Jitter aggregation

From: Emmanuel Tychon <[email-masked]>
Date: 28 Aug 2002 16:38:33 +0200

Hello,

I have a quite rather simple question, but haven't found yet any answer
that convince me. Is there a way to calculate a global jitter based on
multiple measured jitter?

Let me show an example, with this network composed of 3 routers in line:

	[Ra] ----- [Rb] ----- [Rc]

I measure the jitter 'J_ab' and 'J_bc' respectively on the Ra->Rb and
Rb->Rc links. Now I want to calculate the corresponding jitter 'J_ac' on
the Ra->Rc path.

The big difference between jitter and other values is that jitter can be
positive (arrive later than expected), negative (arrive sooner than
expected) or null.

If Ra->Rb tends to give more positive jitter, and Rb->Rc give more
negative jitter, the total jitter is not a simple addition, but
something much more elaborated if ever there is something.

Thanks in advance,
Emmanuel Tychon

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From: Philip Chimento <[email-masked]>
Date: Wed, 28 Aug 2002 12:15:31 -0400

Emmanuel: 

It depends. If you are measuring IP packet delay variation (IPDV ~ "jitter")
and computing estimated means, then the estimates always add (in the limit), 
even if the random variables (i.e. the "jitter" at each stage) are dependent 
in complicated ways.

However, the distributions, because the "jitter" at successive stages is not 
independent, can't even be convolved in a simple way. Worse yet, if you are 
interested in a particular flow, it may "see" "jitter" that is much worse (or 
much better) than the average, depending on how the packet timing is distorted 
at the previous stage(s) and the nature of the delays at a given node. For 
example, in your case, if the delay introduced at Rb is cyclic and the
flow of interest happens to arrive in a pattern that say introduces close to 
(+-) maximum delay on every other packet of the flow, you will get an
arrival pattern at the endpoint that looks something like this: 

<------------ TIME 

 |----------|----------|----------|----------|----------|
            xx                    xx                    x

which will be pretty bad but also pretty far from the 
average probably. 

Hope this helps. 
Regards, Phil Chimento

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From: Mudhafar Hassan-Ali <[email-masked]>
Date: Wed, 28 Aug 2002 09:28:32 -0700

Emmanuel,

First, one needs to specify the method of jitter measurement (one point
delay vs. two point delay). Second, since the delay is a random variable,
hence jitter, and by accumulating (adding) the jitter injected by each
switch/router along the path, then, by probability law, the resulting jitter
is the convolution of the jitter distributions along the path (in your
example, J_abc= J_ab*J_bc, where * denotes the convolution operation).

Mudhafar

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From: Emmanuel Tychon <[email-masked]>
Date: 28 Aug 2002 18:46:55 +0200

Philip,

> even if the random variables (i.e. the "jitter" at each stage) are dependent 

So what you say is that, if I measure IP packet delay variation, the
estimated means can be blindly added? What changes is the distribution.

> at the previous stage(s) and the nature of the delays at a given node. 

This is what scares me. The main purpose of this measurement is to
assure that 95% of the packets are under a certain jitter - one of the
important parameter for a good voice-over-ip communication. So what we
need is the 95th percentile, and unless I do measure it end-to-end,
there is no way I can calculate it: it can only be measured.

In a typical network that classifies traffic, the jitter introduces at
each hop is pretty random and depends vastly on the traffic sent in
other classes as well as the queuing mechanism and other minor factors.

With all of this in mind, would you agree to say that calculations based
on IP inter-packet delay variation are risky operations that should be
avoided?

Thank you,
e.

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From: Mudhafar Hassan-Ali <[email-masked]>
Date: Wed, 28 Aug 2002 11:26:24 -0700

Emmanuel,

It is true that dependency (correlation) of the jitter distribution exists in
consecutive stages, making the total jitter distribution difficult to estimate.
However, in a heavy load case (that is when you need to be worrying about the
accuracy of the jitter any ways), this correlation loosens up leading to the use of
convolution to estimate the total distribution. The trick is to know the
distribution at each stage measured or estimated under a "typical load pattern".

Mudhafar

P.S. Since you are talking about voice over packet, you may want to look at:
1. KEES VAN DER WAL, MICHEL MANDJES, AND HARRIE BASTIAANSEN, "Delay Performance
Analysis of the New Internet Services with Guaranteed QoS" PROCEEDINGS OF THE IEEE,
VOL. 85, NO. 12, DECEMBER 1997.
2. ITU-T I.741, "Interworking and interconnection between ATM and switched telephone
networks for the transmission of speech, voiceband data and audio signals" June
1999.

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From: Jambi Ganbar <[email-masked]>
Date: Wed, 28 Aug 2002 14:19:55 -0400 (EDT)

Emmanuel, see in line.

> there is no way I can calculate it: it can only be measured.

I think that this point was raised on
this group a few times.  The question
that you need to answer for yourself is
"why am I measuring?"  If you are trying
to measure a certain call quality for
VoIP then your end user perception is
the most important value and an
end-2-end test is perhaps what is
needed.

> other classes as well as the queuing mechanism and other minor factors.

Exactly why you need to test end-2-end
to account for all potential variables.

> on IP inter-packet delay variation are risky operations that should be

I would most definitely not agree with
the above statement.

Jambi
vBNS Engineering.

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From: Philip Chimento <[email-masked]>
Date: Fri, 30 Aug 2002 08:37:38 -0400

> estimated means can be blindly added? What changes is the distribution.

Yes. There is a theorem about the linearity of expectations. Estimates of the 
mean approach the real mean only in the limit of course. The quality of the 
result will depend on the quality of your estimates.

> there is no way I can calculate it: it can only be measured.

I haven't read the Van der Waal, Mandjes and Bastiaansen paper that Mudhafar 
referred to. However, I am not sure that the heavy load case is the only one 
that you need to worry about (the example that I gave you wasn't a heavy 
traffic case, only cyclical congestion).

It is difficult to calculate, it is not that there is no way. I don't know 
about the composition of percentiles in the case that the random variables are 
dependent. This requires some research to see whether there has been any work 
done on this. I expect that it is the same problem as distributions, but I 
don't know.

It may be that the most expedient approach is as was suggested by Jambi, which 
is to measure end-to-end. Both Advanced Networks and Services and RIPE in 
Europe have "active measurement" devices which can measure the one-way delay 
(and hence also the one-way-delay-variation) by sampling. You can check out the
RFCs and I-Ds on these measurements by going to the IPPM WG page at the IETF, 
and the details of the devices by looking at the Advanced or RIPE web sites.

> other classes as well as the queuing mechanism and other minor factors.

Right. This is a difficult problem. 

> on IP inter-packet delay variation are risky operations that should be

I wouldn't say this as a blanket statement. There are some calculations that 
are perfectly straightforward (as expectations are) and others that are very 
difficult and would probably require empirical distribution estimates at each 
hop and numerical integration (and lots of compute time). It just may be 
easier in this case to measure end-to-end.

Good luck. 
Regards, Phil Chimento