In this paper, we investigate the behaviour of P-time event graphs, a class of time Petri nets with non-deterministic timing of places. Our approach is based on combined linear descriptions in both (max,+) and (min,+) semirings, where lower bounds on the state vector are (max,+)-linear and upper bounds are (min,+)-linear. We present necessary and sufficient conditions for the existence of extremal (fastest and slowest) periodic trajectories that are derived from the new description. The results are illustrated by a realistic example of an electroplating process.

中文翻译：

---

分析（max，+）和（min，+）半环中的P时间事件图

在本文中，我们研究了P时间事件图的行为，P时间事件图是一类具有地点不确定时间的时间Petri网。我们的方法基于（max，+）和（min，+）半环中的组合线性描述，其中状态向量的下限是（max，+）-线性，上限是（min，+）-线性。我们为从新描述中得出的极端（最快和最慢）周期性轨迹的存在提供了充分必要的条件。通过电镀过程的实际示例说明了结果。