Benchmark Datasets for Stochastic Petri Net Learning

The existing Stochastic Petri Net (SPN) analysis methods are based on a series of steps, including generating the reachable graph, solving the state equation, etc. Unfortunately, these methods cannot perform performance analysis when the state equation has no unique solution. The end-to-end deep learning methods can build a mapping relationship from SPN to performance indicators, which avoids solving the state equation. However, there is a lack of benchmark datasets for SPN learning and training. This paper proposes an automatic generation method of SPN datasets, including SPN random generation, data labeling, data enhancement, and filtering. To relieve the local aggregation problem of random-based organization, a grid-based data organization method is proposed to ensure the diversity of the datasets. In the experimental section, the generated datasets are trained and tested on three types of neural networks. The results show that the generated benchmark datasets are useful, and the increase of dataset size will significantly improve the learning performance.

I. Introduction

Petri nets are able to model, simulate and analyze discrete event dynamic systems with concurrency, asynchrony, uncertainty, and randomness. A stochastic Petri Net (SPN) is an extension of the Petri Net [1]–[3], where the time delay of transition is a random variable. And it can be used for system modeling and performance analysis. Traditional SPN performance indicators (such as the average number of tokens and transition utilization ratio) are obtained by processes including generating the reachable graph, solving the state equation, etc. However, this method is not always practical since it relies on the premise that the state equation has a unique solution, i.e., the state transition matrix is full rank. It is a challenge to analyze system performance when the state equation has no unique solution.