Piecewise Deteministic Markov Processes represented by Dynamically Coloured Petri Nets
M.H.C. Everdij, H.A.P. Blom · 1999
Piecewise Deterministic Markov Processes (PDPs) are known as the largest class of Markov processes virtually describing all continuous-time processes not involving difftisions. In general the state space of a PDP is of hybrid type, i.e. a tensor product of a discrete set and a continuousvalued space. Since Stochastic Petri Nets have proven to be extremely useful in developing continuous-time Markov Chain models for complex practical discrete-valued processes, there is a clear need for a type of Petri Nets that can play a similar role for developing PDP models for complex practical problems. To fulfil this need, the paper defines a new type of Petri Net, named Dynamically Coloured Petri Net (DCPN), and proves that there exist into-mappings between PDPs and DCPNs.