G.8271.2: pktSelected2WayTE Step Size
Introduction
G.8260 describes the pktSelected2WayTE metric for estimating the time error of a PTP packet stream that has been transmitted through a network exhibiting significant queuing delays (PDV, or packet delay variation). It selects a percentage of packets in a given window size, and averages them together to form a single value for that window.
G.8271.2 uses the metric to define the network limit in both APTS and PTS network configurations. It defines the window size as 200s, but doesn’t define a stepping size. For example, should the next window contain all new data, or should it partially overlap with the current window? This study presents eight example data sets, and analyses the difference made by using different stepping sizes. Of these data sets:
 Examples 1 and 2 were collected in a lab environment, using real switches and routers but at least part of the PDV was created by a packet impairment tool
 Examples 3, 4 and 5 were collected from a live operator network
 Examples 6, 7 and 8 were collected from a different operator’s live network
The Appendices present the raw data from the study for reference.
Effect of Step Size
The following chart (Figure 1) shows the variation of the peaktopeak value of the pktSelected2WayTE function reported using different step sizes. The function is calculated according to G.8271.2 using a window size of 200s and a percentile of 0.25%. The vertical axis is the difference in the reported peaktopeak value in nanoseconds, relative to the value for a 1s step size. Eight example data sets are shown, with the step sizes of 10s, 25s, 50s, 100s, and 200s.
Figure 1: Variation in peaktopeak values with step size
The second chart (Figure 2) shows the difference in the measurement of both the maximum and minimum peaks of the pktSelected2WayTE function:
Figure 2: Variation in max/min values with step size
Clearly, the step size has a big influence on the actual peaktopeak value reported. Stepping the window rather than sliding it effectively subsamples the pktSelected2WayTE function. The position of any peak in the function relative to the stepping point is critical, as shown in Figure 3 below.
Figure 3: Position of step size with respect to peak value
In this example, the peak coincides with the 1s, 10s, 25s and 50s step increments. However, using 100s and 200s step sizes, the peak is missed, resulting in about a 300ns difference in reported value.
In some cases, changing the step size can change which peak in the data set is being reported. This is shown in the following example (Figure 4). The purple trace was obtained using a 1s step size, while the orange trace was obtained using 200s. It can be seen that the 200s step size identifies an entirely different peak in the data.
Figure 4: Change of reported peak with step size 
Which step size to use?
If step size has such a large effect on the outcome, why not use a sliding window (i.e. a step size of 1 sample)? There are several reasons not to use a very small step size:
 Smaller step sizes will increase the peaktopeak measurement, making it harder to meet the network limits
 The end clock will have a lowpass filter that is likely to have a very low bandwidth, meaning that any peaks or troughs in the floor will tend to be smoothed. Therefore the peaktopeak value obtained from a very small step size may not resemble the actual effect of floor variation on the clock output.
 The compute power needed is much higher for small step sizes. There is a 200fold increase in compute power required for a step size of 1s compared to that of 200s. This should not be an issue for the clocks themselves because the pktSelected2WayTE metric is not a definition of the algorithm a clock must use, but it is an issue for the test equipment which may need to compute the metric in real time.
The chart below (Figure 5) shows both the mean error and the maximum error introduced by each step size, for both peaks and troughs. The grey and orange bars are the mean values across all examples for both peaks and troughs respectively. It can be seen that the mean value increases significantly from 25s to 50s.
The blue and yellow bars show the largest observed error in peaks and troughs respectively. Looking at the 25s step size, with the exception of one data set (example 8), the peak error is less than 5ns, while for troughs, the largest error is less than 18ns. Moving up to 50s step size, the peak error doubles to almost 100ns, while the error in the lowest trough triples to over 60ns.
Figure 5: Mean and peak errors with respect to step size
Conclusions
Step sizes larger than 25s make a considerable difference in the maximum and minimum values of the pktSelected2WayTE function, and hence to the peaktopeak value.
While G.8273.4 has not specified the clock bandwidth, it is commonly expected to be in the 1 to 5mHz range. A 5mHz clock has a time constant of about 32s. The stepping size of the metric should be smaller than the time constant of the clock, but not too much smaller otherwise the peak will be unrepresentative of the clock’s ability to handle floor variations.
Calnex therefore propose that a 25s step size is a good compromise between the required accuracy of the measurement, the compute power required to calculate the metric, and the actual effect on the end clock.
Appendix 1: Raw data sets
Example 1 (raw PDV data)
Example 1 (step size variation)
Example 2 (raw PDV data)
Example 2 (step size variation)
Example 3 (raw PDV data)
Example 3 (step size variation)
Example 4 (raw PDV data)
Example 4 (step size variation)
Example 5 (raw PDV data)
Example 5 (step size variation)
Example 6 (raw PDV data)
Example 6 (step size variation)
Example 7 (raw PDV data)
Example 7 (step size variation)
Example 8 (raw PDV data)
Example 8 (step size variation)
Appendix 2: Peak value data
The following table gives the peak values (maximum and minimum) for each example at the different step sizes. The “error” columns are the difference between the recorded value, and that recorded for a 1s step size.
Data set  Step size  Peaktopeak  PP Error  Maximum  Error in max peak  Minimum  Error in min peak 

Example 1  1s  1181  0  802  0  379  0 
10s  1181  0  802  0  379  0  
25s  1176  5  802  0  374  5  
50s  1171  10  802  0  369  10  
100s  1159  22  802  0  357  22  
200s  1159  22  802  0  357  22  
Example 2  1s  17900  0  10545  0  7354  0 
10s  17897  3  10543  2  7353  1  
25s  17893  7  10543  2  7349  5  
50s  17885  15  10543  2  7341  13  
100s  17587  313  10245  300  7341  13  
200s  17587  313  10245  300  7341  13  
Example 3  1s  2190  0  8857  0  11047  0 
10s  2187  3  8857  0  11044  3  
25s  2181  9  8857  0  11038  9  
50s  2041  149  8952  95  10993  54  
100s  2020  170  8972  115  10993  54  
200s  1930  260  8990  133  10920  127  
Example 4  1s  1464  0  184861  0  186325  0 
10s  1460  4  184865  4  186325  0  
25s  1464  0  184861  0  186325  0  
50s  1331  133  184932  71  186263  62  
100s  1323  141  184940  79  186263  62  
200s  1280  184  184983  122  186263  62  
Example 5  1s  1464  0  184861  0  186325  0 
10s  1460  4  184865  4  186325  0  
25s  1464  0  184861  0  186325  0  
50s  1331  133  184932  71  186263  62  
100s  1323  141  184940  79  186263  62  
200s  1280  184  184983  122  186263  62  
Example 6  1s  137  0  184  0  47  0 
10s  132  5  182  2  50  3  
25s  132  5  182  2  50  3  
50s  132  5  182  2  50  3  
100s  132  5  182  2  50  3  
200s  127  10  177  7  50  3  
Example 7  1s  662  0  732  0  70  0 
10s  650  12  727  5  77  7  
25s  640  22  727  5  87  17  
50s  638  24  727  5  89  19  
100s  603  59  704  28  101  31  
200s  589  73  701  31  112  42  
Example 8  1s  821  0  905  0  84  0 
10s  789  32  874  31  85  1  
25s  757  64  859  46  102  18  
50s  748  73  851  54  103  19  
100s  739  82  842  63  103  19  
200s  678  143  842  63  164  80 
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