Solving Dynamic Reliability Problems by means of Ordinary and Fluid Stochastic Petri Nets

A benchmark on dynamic reliability taken from Marseguerra & Zio (1996) is considered; though the behaviour of this system is dynamic and is described by continuous variables, we show that the system is suitable to an analytical solution, instead of simulation. The system consists of a tank containing some liquid whose level is monitored by a controller acting on two pumps and one valve, in order to avoid the liquid dry out or overflow. The reliability evaluation of the system is obtained by resorting to Generalized Stochastic Petri Nets (GSPN) and Fluid Stochastic Petri Nets (FSPN). FSPNs are hybrid models and differ from GSPNs by the presence of both fluid places (modelling continuous variables) and discrete places (containing a discrete number of tokens). GSPNs are used for the analytical solution of the benchmark, while the simulation on the FSPNs, is run with the aim of validating the analytical results.