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arXiv 1706.02641cs.LO
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流体随机Petri网的行为等价

Behavioural equivalences for fluid stochastic Petri nets

Igor V. Tarasyuk, Peter Buchholz

摘要:

我们提出流体等价比较和减少标记流体随机Petri网(LFSPNs)的行为,同时保持其离散和连续的属性。我们定义了一个线性时间关系的流体跟踪等价和它的分支时间对应,流体互模拟等价。这两种流体关系考虑到LFSPNs行为的基本特征:功能活动,随机定时和流体流动。我们考虑了连续标记对离散标记没有影响,离散部分是连续时间随机Petri网的LFSPN。LFSPN的离散部分的基础随机模型是连续时间马尔可夫链(CTMCs)。LFSPN的连续部分的性能分析是通过相关的随机流体模型(SFM)完成的。我们表明,流体迹等价保持平均潜在的流体变化量的过渡序列的每一个特定的长度。我们证明了流体互模拟等价性保留了聚集的概率函数:底层CTMC的静态概率质量,以及相关SFM的静态流体缓冲区空概率,流体密度和分布。因此,等价保证了一些离散和连续的性能指标的身份。流体互模拟等价,然后使用简化的定性和定量分析的LFSPN通过离散可达图和底层CTMC。为了描述与SFM相关的商,定义了概率函数的导数。基于Hennessy-Milner逻辑HML,我们用两种新的流体模态逻辑$HML_{flt}$和$HML_{flb}$刻画了逻辑上的流体迹和互模拟等价.以公文处理系统为例,通过流体互模拟等价性验证了行为分析方法。

英文摘要:

We propose fluid equivalences to compare and reduce behaviour of labeled fluid stochastic Petri nets (LFSPNs) while preserving their discrete and continuous properties. We define a linear-time relation of fluid trace equivalence and its branching-time counterpart, fluid bisimulation equivalence. Both fluid relations take into account the essential features of the LFSPNs behaviour: functional activity, stochastic timing and fluid flow. We consider the LFSPNs whose continuous markings have no influence to the discrete ones and whose discrete part is continuous time stochastic Petri nets. The underlying stochastic model for the discrete part of the LFSPNs is continuous time Markov chains (CTMCs). The performance analysis of the continuous part of LFSPNs is accomplished via the associated stochastic fluid models (SFMs). We show that fluid trace equivalence preserves average potential fluid change volume for the transition sequences of every certain length. We prove that fluid bisimulation equivalence preserves the aggregated probability functions: stationary probability mass for the underlying CTMC, as well as stationary fluid buffer empty probability, fluid density and distribution for the associated SFM. Hence, the equivalence guarantees identity of a number of discrete and continuous performance measures. Fluid bisimulation equivalence is then used to simplify the qualitative and quantitative analysis of LFSPNs via quotienting the discrete reachability graph and underlying CTMC. To describe the quotient associated SFM, the quotients of the probability functions are defined. We characterize logically fluid trace and bisimulation equivalences with two novel fluid modal logics $HML_{flt}$ and $HML_{flb}$, based on the Hennessy-Milner Logic HML. The application example of a document preparation system demonstrates the behavioural analysis via quotienting by fluid bisimulation equivalence.

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