In: Journal of Systems and Software, Vol. 46, No. 1, pages 41-58. 1999.
Abstract: Time Petri nets (TPNs) is a powerful technique for studying the specification, verification, and temporal behavior of real-time distributed systems. For evaluating the performance of these systems, this paper extends the TPNs by distributing probability density functions (pdfs) with uniform distributions over the time intervals associated with the transitions of the net. These pdfs are used to determine the state transition probabilities of branching from the current state to the possible next states. Thus the reachability graph obtained from the extended TPN can be interpreted as a Markov process. This extended TPN is called a real net or R-net. To improve the modeling capability of R-nets, its structure is allowed to contain multiple tokens, multiple arcs, inhibitor arcs, and two types of transitions: real-time transitions and zero-time transitions. The R-net methodology is illustrated through a simple example. In view of the important application for which R-net is used, a performance model for a fault-tolerant real-time multiprocessor (FRMP) system is developed and analyzed. The FRMP system is used as the central computer in air traffic control applications.
Keywords: Markov processes, R-nets, fault-tolerant systems, multiprocessor systems, performance analysis, real-time systems, time Petri nets.