Papers:  J.-C. Bolot, End-to-End Packet Delay and Loss Behavior in the Internet.
                V. Paxson, End-to-End Routing Behavior in the Internet

Lecture date: 10/5/99

Prof. John Byers

Scribe: Igor Stubailo

Setup, data analysis strategy.

What's so important about characterization?

Rather than to do measurements it's better to model a situation.  This paper is one of the first important papers on measurements.  And numbers given there shows quite interesting results.  Authors made their own assumption based only on their measurements.

The main setup is the following:

In each experiment the source sends UDP probes  from  A  to  B at regular intervals.

If we denote by s_n  the time at which packet  n  is sent by the source,  by  r_n  the time at which it is received by the source  and  rtt_n  the packet round trip delay then  the interval between the send times of two successive packets is:   d = s_n+1 - s_n  for all n.  Where  d is fluctuating between traces.  Also RTT:    rtt (n) = r_n - s_n   and  rtt = 0  if a packet is lost.

What did they get from that setup?  The following graph shows a time series plot of measured round trip delays as a function of  n:

Analysis of packet delay.

To simplify analysis and to understand the structure of the phase plot on Fig.2  it is convenient to introduce a simple model which captures the essential features of our experiments.
 
 

where D is a constant (propagation) delay to model the fixed component of the round trip delay of the probe packets. Then if  w_n  is waiting time and  p/m is transmission time, we are getting the following expression:

Crucial assumptions: their is only one bottleneck  (very simplification), but a lot of people find that model as a quite reasonable.  Though this technique is not applicable to a system with multiple bottlenecks.

We can plot rtt in the following way:

From this plot :   rtt -> min  when D-> min.

So, we have light load and heavy load.

Light load:    w_n+1 = w_n + e_n ,    where e_n  is a random process with mean 0 and low variance.

Heavy load: what happens if two consecutive probes are injected?
 

As we see, in case of heavy load  packets   n+2, n+3 ...  will cause a probe compression.
And what with waiting times?
     w_n+1 = w_n + B/m  - it's true when n sees no queue;  B/m  is the delay associated with transmitting
a packet of size B bit.   Also: n sees an empty queue,  w_n = 0 ;   n+1 sees only  Br,  B/m = w_n .
The other consequence:
    n+2,  n+3,  n+4  are going to be compressed  and   w_n+1 = w_n + P/m - d , where P/m is a delay at n+1.

When d is small, we observe a probe compression phenomenon and waiting time is decreasing.
When d is large, we observe that the points in the phase plane (Fig. 5) are scattered around the line  rtt_n+1 = rtt_n .

What of those parameters can be actually calculated?
We know  P, d  => can compute  m , so the bottleneck  B/w.

A few words about Fig.8:
 

Let's say  (w_n+1 - w_n + d) = Q ,
 
    if  Q = 20  then  d = 20,  w_n+1 - w_n = 20,  we experience no load;
    if  Q = 0    then we have probe compression, the d  is removed from the queues;
    if  Q = 40  then there is a particular frequent packet size by what you can estimate the
        value of  B (approx. 600 bytes).
The distances between picks are fixed and arrival of packets between probes is exponential
distribution.

Fig.9 shows the distribution of   w_n+1 - w_n + d    for    d = 100 ms.  The correlation goes down
dramatically.  If  d  is small  then you have too many probes and they can affect the traffic.

Conclusion:

In the paper authors have shown that UDP echo tool is useful to analyze the end-to-end characteristics
of the Internet over different time scales.