Timed weighted marked graphs are a subclass of timed Petri nets that have wide applications in the control and performance analysis of flexible manufacturing systems. Due to the existence of multiplicities ( i.e., weights ) on edges, the performance analysis and resource optimization of such graphs represent a challenging problem. In this paper, we develop an approach to transform a timed weighted marked graph whose initial marking is not given, into an equivalent parametric timed marked graph where the edges have unitary weights. In order to explore an optimal resource allocation policy for a system, an analytical method is developed for the resource optimization of timed weighted marked graphs by studying an equivalent net. Finally, we apply the proposed method to a flexible manufacturing system and compare the results with a previous heuristic approach. Simulation analysis shows that the developed approach is superior to the heuristic approach.

中文翻译：

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定时加权标记图的参数转换：在最佳资源分配中的应用

定时加权标记图是定时Petri网的子类，其在柔性制造系统的控制和性能分析中具有广泛的应用。由于边缘上存在多重性（即权重），因此此类图的性能分析和资源优化是一个具有挑战性的问题。在本文中，我们开发了一种方法，可以将未给出初始标记的定时加权标记图转换为等效参数定时标记图，其中边具有单位权重。为了探索系统的最优资源分配策略，通过研究等效网络，开发了一种用于时间加权标记图资源优化的分析方法。最后，我们将建议的方法应用于柔性制造系统，并将结果与​​以前的启发式方法进行比较。仿真分析表明，该方法优于启发式方法。