@inbook{92a9363093c540ca98c3851aeaaa5d68,
title = "Communicating piecewise deterministic Markov processes",
abstract = "In this chapter we introduce the automata framework CPDP, which stands for Communicating Piecewise Deterministic Markov Processes. CPDP is developed for compositional modelling and analysis for a class of stochastic hybrid systems. We define a parallel composition operator, denoted as /P/A/, for CPDPs, which can be used to interconnect component-CPDPs, to form the composite system (which consists of all components, interacting with each other). We show that the result of composing CPDPs with /P/A/ is again a CPDP (i.e., the class of CPDPs is closed under /P/A/). Under certain conditions, the evolution of the state of a CPDP can be modelled as a stochastic process. We show that for these CPDPs, this stochastic process can always be modelled as a PDP (Piecewise Deterministic Markov Process) and we present an algorithm that finds the corresponding PDP of a CPDP. After that, we present an extended CPDP framework called value-passing CPDP. This framework provides richer interaction possibilities, where components can communicate information about their continuous states to each other. We give an Air Tra.c Management example, modelled as a value-passing CPDP and we show that according to the algorithm, this CPDP behavior can be modelled as a PDP. Finally, we define bisimulation relations for CPDPs. We prove that bisimilar CPDPs exhibit equal stochastic behavior. Bisimulation can be used as a state reduction technique by substituting a CPDP (or a CPDP component) by a bisimulation-equivalent CPDP (or CPDP component) with a smaller state space. This can be done because we know that such a substitution will not change the stochastic behavior.",
author = "Stefan Strubbe and {van der Schaft}, Arjan",
year = "2006",
doi = "10.1007/11587392_3",
language = "English",
isbn = "978-3-540-33466-8",
series = "Lecture Notes in Control and Information Sciences",
publisher = "Springer",
pages = "65--104",
editor = "Blom, {Henk A.P.} and John Lygeros",
booktitle = "Stochastic Hybrid Systems",
address = "Germany",
}