In this study, we propose a model called LFSPN , which serves as an extension of stochastic Petri nets dedicated to the multi-agent systems paradigm. The main objective is to specify, verify, validate, and evaluate the flow of materials within an automated production chain. We illustrate the practicality of our model by engaging in a systematic process of modeling and simulating a production chain involving material flow. To evaluate the performance, we employ a mobile learning agent, which has distinct characteristics, namely mobility and learning. The distinctive characteristics of the learning agent are manifested in two key behaviors: mobility and learning. Notably, the learning agent is equipped with a flexible learning algorithm that integrates stochastic elements based on transitions. We validate the effectiveness of our model by performing a comparative analysis with similar existing works. The advantages of our LFSPN model are twofold. Firstly, it offers a representation with two levels of abstraction: a graph representing the classic components of an SPN, and an additional layer encompassing the learning and migration aspects inherent to a mobile learning agent. Secondly, our model stands out for its flexibility and simulation simplicity.