In: IEEE Trans. on Reliability, Vol. 44, No. 3, pages 428-440. 1995.
Abstract: This paper describes a methodology to construct dependability models using generalized stochastic Petri nets (GSPN) and stochastic reward nets (SRN). Algorithms are provided to convert a fault tree (a commonly used combinatorial model type) model into equivalent GSPN and SRN models. In a fault-tree model, various kinds of distributions can be assigned to components such as defective failure-time distribution, non-defective failure-time distribution, or a failure probability. The paper describes subnet constructions for each of these different cases, and shows how to incorporate repair in these models. We consider the cases: 1) Each component has an independent repair facility. 2) Several components share a repair facility; such repair dependency cannot be modeled by combinatorial model types such as fault trees. We illustrate how such dependencies and various scheduling disciplines (for the repair queue) such as first-come first-served (FCFS), processor-sharing, preemptive priority with resume, and non-preemptive priority repair, can be modeled by GSPN and SRN. If the operational dependence of a system on its components is specified by means of a fault-tree and a repair dependence is described in some (other) form, then our methodology provides an automatic way to generate GSPN and SRN models of system dependability. The subnet constructions allow us to compare SRN with GSPN as dependability model types. For the dependability models of repairable systems, the complexity (number of places and transitions) of GSPN models is appreciably higher than the complexity of equivalent SRN models. The state-space of the underlying continuous-time Markov chain (CTMC) remains the same, however. Thus SRN reduce the complexity of model specification at the net level, but the complexity of model solution remains the same. Since SRN include all the features of GSPN, the additional features of SRN such as reward rates, variable cardinality arcs, halting condition, and timed transition priorities, greatly simplify model construction and specification.
Keywords: Markov models, combinatorial model type, dependability analysis, fault tree, stochastic Petri nets, stochastic activity networks, stochastic reward model.