Piecewise deterministic Markov processes represented by dynamically coloured Petri nets

Abstract

Piecewise deterministic Markov processes (PDPs) are known as the largest class of Markov processes virtually describing all continuous-time processes not involving diffusions. For PDPs, a substantial amount of powerful analysis and control results are available. As such, PDPs are attractive for use in modelling complex distributed systems. However, the specification of an appropriate PDP model for complex distributed systems that exist in practice is far from trivial. This difficulty already applies for the specification of a continuous-time Markov chain (CTMC). For a compositional specification of a CTMC model, Petri Nets have proven to be extremely useful. In order to realise a similar situation for PDP, this paper develops a novel type of Petri Net, named dynamically coloured Petri Net (DCPN), and proves that there exist into-mappings between PDPs and DCPNs.† †Part of this research has been performed within the project HYBRIDGE of the European Commission, contract number IST-2001-32460