In: IEICE Trans. on Fundamentals in Electronics, Communications and Computer Science, Vol. E79-A, No. 11, pages 1781-1790. 1996.
Abstract: A new class of stochastic Petri nets, called non-regenerative stochastic Petri nets (NRSPNs) is developed. It allows the firing time of its transitions to have arbitrary distribution. A bounded reachability graph that is equivalent to a generalization of the Markov renewal process in which some of the states may not constitute regeneration points, is automatically generated. Thus this model can represent and analyze behavior of a system whose states include some non-regeneration points. It is shown how to model a system by a NRSPN, and how to obtain numerical solutions for the NRSPN model. The probabilistic behavior of the modeled system can be clarified with the reliability measures such as the steady-state probability, the expected numbers of visits to each state per unit time, availability, unavailability and mean time between failures. Finally, to demonstrate the modeling ability and analysis power of the NRSPN model, an example of a fault-tolerant system is presented using a NRSPN and numerical results are given for specific distributions.
Keywords: Markov renewal processes, behavior modeling, fault tolerance, non-regenerative stochastic Petri nets, reliability analysis.