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Since the timestamps of measurements for one MA to a target are not synchronized with another MA to the same target, they are sampling the network at different times. Thus we decided not to use the residuals in the RTTs between one pair and another. Typically the difference in the time of a measurement from say pinger.slac.stanford.edu to sitka.triumf.ca versus pinger-raspberry.slac.stanford.edu to sitka.triumf.ca averages at 8 mins (see spreadsheet).
To find the probability of the distributions overlapping we can use a nomogram of mean differences versus error ratios given in Overlapping Normal Distributions. John M. Linacre for normal distributions. However this does not cover the range we are interested in.
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However the ping distributions are decidedly non-normal (see for example the figure below) have wide outliers, and are heavy tailed on the upper side (see https://www.slac.stanford.edu/comp/net/wan-mon/ping-hi-stat.html). This leads to large standard deviations (one to two order of magnitude greater than the IQR) in the RTT values. As can be seen from the table this results in low values of the Z-test and a false probability of no significant statistical difference. Using the IQRs of the frequency distributions instead generally leads to much higher values of the Z-test and hence a higher probability that the distributions of RTTs between two pairs of hosts are significantly different. Comparing the frequency distributions it is seen that there is indeed a marked offset in the RTT values of the peak frequencies and a resultant difference in the cumulative RTT distributions, Using the non-parametric Kolomogorov Smirnoff test (KS test) also indicated significant differences in the distributions.
The RTT measurements made from pinger.SLAC and pinger-raspberry.SLAC to TRIUMF and CERN average around 23ms and 151ms respectively. Despite this large difference in average RTTs', comparing the average RTTs from pinger.SLAC with those from pinger-raspberry.SLAC yields a difference of only ~0.35ms for both TRIUMF and CERN.
Looking at the traceroutes, using Matt's traceroute to measure the RTT to each hop, indicates that this difference starts at the first hop and persists for later hops. See spreadsheet (MTR tab). We therefore made ping measurements from each SLAC MA to its to its loopback network interface. The measurements were made at the same times to facilitate comparisons. They indicate that the pinger-raspberry.SLAC is ~0.13ms lslower in responding than the pinger.SLAC MA. Thus approximately 1/3rd of the difference in average RTS tro TRIUMF measured by the two SLAC MAs is due to the MA platform itself.
IPDV
PingER's main metric for measuring jitter is the IPDV. A typical IPD distribution is shown below.
IPD distributions are centered on 0ms and have very wide tails. The one in the figure is cut off below the 2 percentile and above the 98% percentile. The number of outliers not shown is given in the figure, as are the maximum and minimum values of IPD. The distribution is thus seen to have very positive and negative tails. Also as illustrated in the figure a typical IPD distribution has a very sharp peak. To derive the IPDV we take the IQR of the IPD dsitribution. The values for the IPDV for the various measurements are shown in the followjng table; The errors(S) in the IPD are taken from the IQR for the hourly PingER IPDVs observed for the same period. It is seen that the Z-Test in this indicates a value of < 2.0. Assuming the Z-Test is relevant for the non-normal IPD distributions if one uses the IQRs instead of the standard deviation, a value of < 2 for the Z-test statistics indicates the two samples are the same (see http://homework.uoregon.edu/pub/class/es202/ztest.html.
Powerpoint of figures.
Kolmogorov-Smirnov Test
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