Measurement Accuracy & ANOVA

I have some time latency data for some processing on a single
computer, and I wanted to use ANOVA to determine the effect of certain
factors on it.

Here`s the problem: The computer clock precision is very good (<<
1 ms), but the timestamps of each time measurement are reported only
to a resolution of 1 ms. The latencies are for individual messages,
and the processing time are as low as 10 ms. So, a message latency is
calculated from two very precise times. The variance of the time
latency is << 1 ms.

The result is that I have many data points with 0 variance (to a
resolution of 1 ms). So, it seems I have no variance to analyze.

Please advise as to my alternatives. Thanks, Alan
.