Modelling and Efficient Solution of Multiple-Phased Systems

Multiple-Phased Systems (MPS) are systems whose behaviour can be split in a set of successive periods, called phases, and the system behaviour typically depends on the current phase. Previous work has modelled MPS as Deterministic Stochastic Petri Nets (DSPN) composed of two parts: a Phase net (PhN) that describes the progress of the phases and a System Net (SN) that describes the system behaviour, typically influenced by the current phase. By imposing certain restrictions on the net, the authors were able to devise an ad-hoc technique, implemented in the tool DEEM, that reduces the computation of the mission performances to a sequence of transient solutions of Markov chains. In this paper we define X-PPN, an extension of the PPN formalism that allows the modeller more freedom in the structure and in the stochastic distribution of the phases (from deterministic to general) and in the definition of the dependencies among the system and the phase net. X-PPN are solved using the solvers of the GreatSPN tool for Markov Regenerative Processes (MRgP). The GreatSPN solution can solve X-PPN with millions of state and, when the net is actually only a PPN, the computational cost in time reduces to that of the ad-hoc technique of PPN.