This work is concerned with the computation of problematic configurations and problematic choice-join pairs in timed continuous Petri nets under the infinite server semantics; those net structural objects explain possible bad/counter-intuitive behaviors of systems, such as non-monotonicities and discontinuities of the equilibrium throughput. The calculation of problematic configurations is a computationally complex task since their number grows exponentially with the input cardinality of join transitions. In order to alleviate this inconvenience, four type of reduction rules preserving the set of problematic configurations are addressed. Reduction rules are weighted versions of the macroplace, macrotransition, and fusion of transitions rules, the elimination of implicit places rule is also provided. Reduced nets are useful to better understand the net substructures leading to unexpected behaviors in the equilibrium throughput. They help to highlight that the structural objects named problematic choice-join pairs , defined in this work, are the actual responsible of these counter-intuitive throughput behaviors. The great advantage over the set of problematic configurations is that the set of problematic choice-join pairs grows polynomially in the size of the net.

中文翻译：

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Mono-T-Semiflow 网络上的问题配置和选择连接对：对行为结构特性的表征

这项工作涉及在无限服务器语义下计算定时连续 Petri 网中的有问题的配置和有问题的选择连接对；这些净结构对象解释了系统可能的不良/反直觉行为，例如均衡吞吐量的非单调性和不连续性。有问题的配置的计算是一项计算复杂的任务，因为它们的数量随着连接转换的输入基数呈指数增长。为了减轻这种不便，解决了保留一组有问题的配置的四种类型的减少规则。归约规则是宏位置、宏转换和转换规则融合的加权版本，还提供了消除隐式位置规则。减少的网络有助于更好地理解导致平衡吞吐量中意外行为的网络子结构。它们有助于强调在这项工作中定义的名为有问题的选择连接对的结构对象是这些违反直觉的吞吐量行为的实际责任人。相对于有问题的配置集的巨大优势在于，有问题的选择连接对集在网络的大小上呈多项式增长。