Efficient approximation of response time densities and quantiles in stochastic models

Response time densities and quantiles are important performance and quality of service metrics, but their analytical derivation is, in general, very expensive. This paper presents a technique for determining approximate response time densities in Markov and semi-Markov stochastic models that requires two orders of magnitude less computation than exact Laplace transform-based techniques. The method computes the first four moments of the desired response time and then makes use of Generalised Lambda Distributions to obtain an approximation of the corresponding density. Numerical results show good agreement over a range of response time curves, particularly for those that are unimodal.