Institut für Informatik Lehrstuhl 7 up
Kai-Steffen Hielscher 04/06/02

Stability of undisciplined local clocks

We conducted measurements of time differences of the undisciplined local clocks of two nodes of the cluster and the beginning of a second as transmitted by GPS using the PPS API and a Meinberg GPS 167 PCI GPS receiver. The measurement process took over five days and generated a trace file with 453336 observations (one observation per second) on each node. The time difference of the local clocks (ntpserver-slave10) is plotted for comparison with one-way UDP packet delays.

The following figure shows how the time offsets of the clocks evolved.
PPS Offset
The following figures show the Allan Variance, modified Allan Variance and Time Variance of the undisciplined internal clocks of two of our PCs in the cluster.
Please note that all figures are log-log plots of the variances against the averaging interval (τ) in seconds. The plots do not reflect the variances of the quarz oscillators of the computers since the frequency of the kernel clock is corrected using an optimized value for tickadj.
Allan Variance
Modified Allan Variance
Time Variance

Why did we do those measurements?
When looking at packet traces generated with disciplined local clocks it is not easy to decide if variances in delay times are caused by the system or the measurement process (i.e. the clock synchronization). The well-known separation of variance technique is not applicable here since the datasets are correlated and the variances estimated with this method are even negative in our example.

References
  • David W. Allan: Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators, IEEE Transcations on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. UFFC-34, No. 6, November 1987
  • Judah Levine: Introduction to Time and Frequency Metrology, Review of Scientific Instruments, Vol. 70, No. 6, June 1999
  • Stefano Bregni: Fast Algorithms for TVAR and MTIE Computation in Characterization of Network Synchronization Performance, in Advances in Signal Processing and Computer Technologies, Editors: G. Antoniou, N. Mastorakis, O. Panfilov. WSES Press, 2001.

Contact
We can offer diploma theses for students interested in this field of application. A basic knowledge of the mathematics of estimation and some electrical engineering might be useful.
Please contact Kai-Steffen Hielscher