Fast estimation of probabilities of soft deadline misses in layered software performance models

Quality of service requirements are normally given in terms of soft deadlines, such as "90% of responses should complete within one second". To estimate the probability of meeting the target delay, one must estimate the distribution of response time, or at least its tail. Exact analytic methods based on state-space analysis suffer from state explosion, and simulation, which is also feasible, is very time consuming. Rapid approximate estimation would be valuable, especially for those cases which do not demand great precision, and which require the exploration of many alternative models.This work adapts layered queueing analysis, which is highly scalable and provides variance estimates as well as mean values, to estimate soft deadline success rates. It evaluates the use of an approximate Gamma distribution fitted to the mean and variance, and its application to examples of software systems. The evaluation finds that, for a definable set of situations, the tail probabilities over 90% are estimated well within a margin of 1% accuracy, which is useful for practical purposes.