On phased delay stochastic Petri nets: definition and an application

We present a novel stochastic Petri net formalism where both discrete and continuous phase-type firing delays can appear simultaneously in the same model. By capturing non-Markovian behavior in discrete or continuous time, as appropriate, the formalism affords higher modeling fidelity. Alone, discrete or continuous phase-type Petri nets have simple underlying Markov chains, but mixing the two complicates matters. We show that, in a mixed model where discrete-time transitions are synchronized, the underlying process is semi-regenerative and we can employ Markov renewal theory to formulate stationary or time-dependent solutions. Also noteworthy are the computational trade-offs between the so-called embedded and subordinate Markov chains, which we employ to improve the overall solution efficiency. We present a preliminary stationary solution method that shows promise in terms of time and space efficiency and demonstrate it on an aeronautical data link system application.