Petri Nets Generating Markov Reward Models for Performance/Reliability Analysis of Degradable Systems

This paper discusses how the formalism of Stochastic Petri Nets (SPN), with generally distributed transition times, can be used to generate Stochastic Reward Models (SRM) for the unified analysis of the performance and reliability of complex systems. In a SRM the working capacity (or performance level) of the system is modeled by attaching to each state of the process a real variable called the reward rate. The integral of the reward rate over a finite horizon provides the total amount of work accumulated by the system in a given time. An interesting and related figure of merit is the probability that an assigned task will be completed in a given time. We will refer to this problem as the completion time problem. The pictorial representation of the completion time problem at the Petri Net level is investigated. Two examples illustrate the application of the introduced modeling technique in simple cases.

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