Subtyping for Hierarchical, Reconfigurable Petri Nets

分析参数化Petri网的家空间与不变量

Home Spaces and Invariants to Analyze Parameterized Petri Nets

本文比较了Petri网及衍生网中的家空间与不变量概念，提出了基于半流逐步细化家空间的分析方法，并应用于电信行业的参数化示例，提升了分析效率并推动自动化分析。

Unbounded product-form Petri nets

Computing steady-state distributions in infinite-state stochastic systems is in general a very dificult task. Product-form Petri nets are those Petri nets for which the steady-state distribution can be described as a natural product corresponding, up to a normalising constant, to an exponentiation of the markings. However, even though some classes of nets are known to have a product-form distribution, computing the normalising constant can be hard. The class of (closed) Π3-nets has been proposed in an earlier work, for which it is shown that one can compute the steady-state distribution effici…

Synthesis and Analysis of Product-form Petri Nets

For a large Markovian model, a "product form" is an explicit description of the steady-state behaviour which is otherwise generally untractable. Being first introduced in queueing networks, it has been adapted to Markovian Petri nets. Here we address three relevant issues for product-form Petri nets which were left fully or partially open: (1) we provide a sound and complete set of rules for the synthesis; (2) we characterise the exact complexity of classical problems like reachability; (3) we introduce a new subclass for which the normalising constant (a crucial value for product-form express…

Toward uniform random generation in 1-safe Petri nets

We study the notion of uniform measure on the space of infinite executions of a 1-safe Petri net. Here, executions of 1-safe Petri nets are understood up to commutation of concurrent transitions, which introduces a challenge compared to usual transition systems. We obtain that the random generation of infinite executions reduces to the simulation of a finite state Markov chain. Algorithmic issues are discussed.

Deficiency Zero Petri Nets and Product Form

Consider a Markovian Petri net with race policy. The marking process has a "product form" stationary distribution if the probability of viewing a given marking can be decomposed as the product over places of terms depending only on the local marking. First we observe that the Deficiency Zero Theorem of Feinberg, developped for chemical reaction networks, provides a structural and simple sufficient condition for the existence of a product form. In view of this, we study the classical subclass of free-choice nets. Roughly, we show that the only such Petri nets having a product form are the state…

选择Petri网中的持久可交换性

Persistent Permutability in Choice Petri Nets

研究了选择Petri网中的持久可交换性，证明了某些类别的Petri网中持久可交换性可推导出整体持久性。