Tomography measurement in a laboratory network
2004 10 12
Description of the measurement
The goal of the measurement was to resolve the internal time delay
distributions from end-to-end packet-pair data. In the measurement 500
packet-pairs were sent from the source node to both of the receivers.
During the measurement the clocks of all the
source and the receiver nodes were synchronized by GPS, and the sending
and capturing of the probe packets were accomplished by DAG cards. To be able
to test the validity of the resolved delay distributions the probe
traffic was also monitored by a GPS synchronized DAG card at the
branching node. We use the following
notations:
- Yi means the measured end-to-end delay,
- Xj stands for the delay contributions of the individual links.
The end-to-end delays are related to the link delays by Y1=X1+X2, Y2=X1+X3.
The figure on the left indicates a part of the obtained end-to-end delay time-series.
The red and green curves stand respectively for the delays Y1 and
Y2.
To achieve the desired goal we implemented the network tomography tool described in detail in our technical report. In short the tool quantized the measured end-to-end delays into uniform sized bins, and uses a maximum-likelihood estimation based approach to specify the probabilities of the delay to fall into a given bin on a given link. Below we show the comparison between the real and the estimated link delay distributions, and the associated average delays.
| X1 | X2 | X3 | |
|---|---|---|---|
 |
 |
 |
|
| Measured | 0.1 ms | 0.38 ms | 0.016 ms |
| Estimated | 0.086 ms | 0.39 ms | 0.036 ms |
Above the tomography tool used 40 bins each of size 0.05 ms. It is apparent looking at the values in the table, that the error between the real and the estimated average delays are within the minimal theoretical limit of 1 bin size.