The urgent need for industrial efficient solutions allowing to reduce the environmental footprint of modern manmade systems is nowadays acknowledged by all and becomes a central issue. This reality is all the more true for cyber-physical systems where the integrations of computation, networking, and physical processes are intensively realized. These intelligent systems which combine several computing resources interacting with the physical environment using sensors and actuators are known to be energy-intensive. So, the management of the energy becomes one of the major concerns driven by the increasing number of connected systems.This paper addresses the challenge of estimating least-cost firing sequences within P-Time Labeled Petri Net systems, incorporating both energy considerations and temporal constraints into the modeling framework. By extending the existing models with a dynamic programming algorithm, the proposed method calculates optimal sequences that minimize energy consumption for a given set of actions over time. An industrial example is presented to illustrate the practical application of the approach, demonstrating the potential for significant energy savings and efficiency improvements in industrial systems.

Energy considerations become a critical issue for modern man-made systems and the need for efficient ecoresponsible solutions ensuring energy savings is crucial. This paper develops an energy aware method allowing to optimize the energy consumption of data centers systems thanks to the introduction of Inhibitor P-Time Petri nets (IP-TPN) and Deep Reinforcement Learning techniques. Indeed, thanks to a schedulability analysis method and being given an energy cost function, the global energy consumed for a particular behavior of the system considered can be computed. Furthermore, Petri nets are a good framework for deep reinforcement learning, on the one hand because the cost function we introduce in this paper will naturally train an agent to minimize the total cost according to random inputs, and on the other hand because the observation space containing the tokens as well as their age in the square is high dimensional, which makes traditional algorithms less efficient than deep reinforcement learning.