Stochastic Timed Discrete-Event Systems: Modular Modeling and Performance Evaluation Through Markovian Jumps

We are interested in a scalable, flexible, and modular methodology, for modeling and performance analysis of stochastic discrete-event systems (SDES). In this sense, we propose a modular approach for timing non-markovian SDES expressed as a parallel composition of modules that interacts with each other through events. We show how general distribution for event lifetimes can be implemented systematically by coupling timing modules to the system model. As a result, this coupling mechanism preserves modularity, leading to a compact markovian model expressed in terms of flexible modules. Therefore the methodology allows us to write the whole SDES model as a composition of the system model and the timing one, giving flexibility and scalability in modeling design, as we can modify the modules individually according to the designer's interests. In addition, from the whole markovian SDES model, we show how to perform the model analysis through the analytic approach, as well as through Monte Carlo computer simulation. As an application, we present a numerical example of computing the abandonment rate for a service network with general service time employing both analytical and computer-simulation models.