A computational complexity-aware model for performance analysis of software servers

Queueing models are routinely used to analyze the performance of software systems. However, contrary to common assumptions, the time that a software server takes to complete jobs may depend on the total number of active sessions in the server. We present a queueing model that explicitly takes into account the time, taken by algorithms in the server, that varies with the user population. The model analytically predicts the response time and the "saturation number" of such systems. We validate our model with simulation and further demonstrate its usefulness by suggesting a heuristic technique to "discover" the complexity of algorithms in server software, solely from response time measurement. We applied the discovery technique to a Web-server testbed, and found that we can identify the asymptotic behavior of processing time as a function of the user population with a fair amount of accuracy. The results show that this promises to be one of the many "black-box analysis" techniques, often found necessary in the real world.