I come from the computer science field and I am trying to find out what the latency (time it takes to execute) of certain operations is. I have a pipeline of two steps and I want to know the distribution of the latency that was added by the second step. I executed the pipeline two times: One time I just executed the first step and got the latency of each data point that was processed. Then I executed the first and the second together and got the latency of each data point that was processed.

I would like to know how much latency was added by that second step (1st, 25th, 50th, 75th and 99th percentile). To do this, I would need to subtract the latency distribution of the first step from the latency distribution of 1-2-step to get the increase caused by the second step. How do I do this statistically correct?

I expect most parts will have a log-normal distribution but it might be combinations of different distributions since the latency distribution of some steps might be f.e. normally distributed instead of log-normal.

Executing the second step separately is not an option.

Thank you all in advance for helping me out! Merely a link to a research paper handling this kind of problems would also be very welcome.