Comparing is not easy!

I am kind of stuck with a kind of silly problem. The problem is pretty simple but for some reason I couldn’t to see any way. I got to compare two systems with respect to their response time. These are data stream management system like STREAM, Aurora. Actually the problem may lies in more primitive level. The first question is what is response time for such systems? So far my definition is, “Time needed to give the output after receiving input”. It sounds okay but I am not happy with it :( They do not work such a straight forward manner. First the time could not be clock time, then what it is? If the time is measured in terms of some other metrics then how could I differentiate between queuing time and processing time? Finally, the big question what does the result mean then? Actually tons of other questions are around there even if I forget the nasty platform issue.

Basically what I am looking for is a mathematical foundation of doing these kind of things. My point is whatever I choose it should have an underlying mathematics in it. Other than that it is pointless. I could find thousands of ideas but hard to find the mathematical foundation for them. Well, let me simplify the problem a little bit, how could you define the efficiency for a water refinery plant with multiple refinery units while multiple units share the same set of resources. Actually how to measure something? How to compare two things? Comparing is not easy at all, still we do that very often.