An Aggregation Technique for the Transient Analysis of Stiff Markov Chains
IEEE Transactions on Computers
Transient analysis of acyclic markov chains
Performance Evaluation
Performance and Reliability Analysis Using Directed Acyclic Graphs
IEEE Transactions on Software Engineering
Modelling with Generalized Stochastic Petri Nets
Modelling with Generalized Stochastic Petri Nets
A top-down Petri net-based approach for dynamic workflow modeling
BPM'03 Proceedings of the 2003 international conference on Business process management
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Workflows with transition execution times having exponential distributions are considered. The aim is to determine the overall execution time without looking into the reachability space and its analysis using Markov processes. We concentrate on the so called structural workflows, which are represented with Petri nets constructed by means of specific refinement rules. With each refinement rule (sequence, choice, parallelization, loop) we associate formulas which allow to compute the overall execution time distribution. The class of exponential distributions is too narrow to keep the result within itself. We analyze the so called exponential polynomials, generalizing exponential distributions. They are closed under SUM and MAX functions. This closure property combined with the knowledge of refinements history enables us to find the requested formulas.