Analyzing Web Server Performance Models with the Probabilistic Model Checker PRISM

We report our experience with formulating and analyzing in the probabilistic model checker PRISM various closely related web server performance models that were previously described in literature in terms of classical queuing theory. By our work various ambiguities and deficiencies (also errors) are revealed; in particular, the PRISM models which combine state machines descriptions with performance characteristics show that the original descriptions used slightly differed assumptions for their analysis. Furthermore, while the queuing models are typically based on infinite queues, the state spaces of the PRISM models have to be finite for an automated analysis. While this forces us to explicitly deal with buffer overflows, it also gives us the possibility to investigate appropriate buffer sizes for concrete implementations of the models. Although also one of the previously reported models used a finite queue in some place, our investigations reveal that the size of that queue is actually not critical, while another (previously not constrained) one is. Based on these observations, we argue that nowadays performance modeling should make use of (at least be accompanied by) state machine descriptions such as those used by PRISM. On the one hand, this helps to more accurately describe the systems whose performance are to be modeled (by making hidden assumptions explicit) and give more useful information for the concrete implementation of these models (appropriate buffer sizes). On the other hand, since probabilistic model checkers such as PRISM are furthermore able to analyze such models automatically, analytical models can be validated by corresponding experiments which helps to increase the trust into the adequacy of these models and their real-world interpretation.