Hybrid systems are systems with mixed discrete-continuous behavior, typical examples being continuously
evolving physical systems controlled by discrete controllers. If such systems also posses some stochastic
behavior, then we talk about stochastic hybrid systems. In this talk we focus on the question how to model
a group of such systems, which evolve concurrently.
Different modeling formalisms offer different views on concurrent stochastic hybrid systems. On the one hand,
(discrete) Petri nets, which model concurrency in a deeply inherent way, have been extended with continuous
and stochastic components. On the other hand, finite automata has been extended with continuous evolution
to hybrid automata, and different approaches have been proposed to integrate also stochastic
components to hybrid automata.
In the first part of this talk, we will have a closer look on the modeling of hybrid systems within these formalisms,
and discuss an open problem, which sounds simple, but it seems to be hard to solve.
In a second part, we will turn our attention to adding stochasticity to these modeling formalisms. We will discuss
and relate existing approaches, make an attempt to find motivations for different design choices,
and conclude with some general observations.