Thinking ahead, before you have done the experiment: II some "Nice" packets ought to have shorter round-trip times and other "Ugly" packets ought to take much longer, then there is a big advantage in doing a paired test. So design the experiment to keep track of pairs.
If you have already done the experiment and happened to keep track of pairs: You might see if Protocol A scores are correlated with their respective Protocol B scores. If there is significant correlation, the advantage of doing a paired test may be considerable.
If you have data with no tracking of A/B pairs: Then you'll have to do a 2-sample test. Your chances of finding a significant difference is lower in this case.
Example: Consider vectors x1 (Protocol A) and x2 (Protocol B) of normal data, each with $n = 100# observations, and with pairing. They have the following sample summaries:
summary(x1); sd(x1)
Min. 1st Qu. Median Mean 3rd Qu. Max.
33.58 43.73 47.31 48.90 53.30 67.84
[1] 7.030837 # StDev
summary(x2); sd(x2)
Min. 1st Qu. Median Mean 3rd Qu. Max.
34.53 44.73 48.27 49.91 54.36 68.82
[1] 7.028975 # StDev
cor(x1, x2)
[1] 0.9998922 # Sample correlation
Then a paired t test has P-value 2.2e-16 (essentially 0), so there is a very clear difference between Protocols A and B (B has slightly, but significantly, longer times).
However, if paring is lost (order of observations within vectors is scrambled), then a paired test
is not possible. A Welch 2-sample t test has
P-value 0.3137, which provides no hint of
significance.
Note: Whether t tests can be used depends on having data that are nearly normal. But there are ways to do both paired tests and tests with two (independent) samples for non-normal data.