Compositional safe approximation of response time probability density function of complex workflows

We evaluate a stochastic upper bound on the response time Probability Density Function (PDF) of complex workflows through an efficient and accurate compositional approach. Workflows consist activities having generally distributed durations with bounded supports, composed sequence, choice/merge, balanced/unbalanced split/join operators, possibly breaking structure well-formed nesting. are specified using formalism defined in terms Stochastic Time Petri Nets (STPNs), that permits decomposition into hierarchy subworkflows positively correlated times, guaranteeing stochastically larger end-to-end PDF is obtained when intermediate results approximated by PDFs dependencies simplified replicating appearing multiple subworkflows. In particular, combining shifted truncated Exponential positive or negative rates. Experiments performed sets manually randomly generated models increasing complexity, illustrating under which conditions different heuristics work well accuracy showing proposed approach outperforms simulation same execution time.