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The Best of Both Worlds: Analytically-Guided Simulation of HPnGs for Optimal Reachability

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Performance Evaluation Methodologies and Tools (VALUETOOLS 2023)

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Abstract

Efficient reachability analysis, as well as statistical model checking have been proposed for the evaluation of Hybrid Petri nets with general transitions (HPnG). Both have different (dis-)advantages. The performance of statistical simulation suffers in large models and the number of required simulation runs to achieve a relatively small confidence interval increases considerably. The approach introduced for analytical reachability analysis of HPnGs however, becomes infeasible for a large number of random variables. To overcome these limitations, this paper applies statistical simulation for optimal reachability defined as until property in Stochastic Time Logic to a pre-computed symbolic state-space representation of HPnGs, i.e., the Parametric Location Tree (PLT), which has previously been used for model checking HPnGs. A case study on a water tank model shows the feasiblity of the approach and illustrates its advantages w.r.t. the original simulation and analysis approaches.

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Notes

  1. 1.

    https://zivgitlab.uni-muenster.de/ag-sks/tools/hpnmg/-/tree/simulation.

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Authors and Affiliations

  1. Westfälische Wilhelms-Universität, 48149, Münster, Germany

    Mathis Niehage & Anne Remke

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  1. Mathis Niehage
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  2. Anne Remke
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Correspondence to Mathis Niehage .

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Editors and Affiliations

  1. University of Cambridge, Cambridge, UK

    Evangelia Kalyvianaki

  2. University of Southern California, Los Angeles, CA, USA

    Marco Paolieri

A Visual Representation of the Tank Model

A Visual Representation of the Tank Model

Fig. 2.
figure 2

Tank system modeled as HPnG as in [32]. The continuous place \(P_{\text {tank}}^c\) models the fluid level of the tank. The two valves are modeled by the continuous transitions \(T^C_{\text {valve}\_1}\) and \(T^C_{\text {valve}\_2}\), which are enabled while a token is in \(P^d_{1\_\text {on}}\) respectively \(P^d_{2\_\text {on}}\). The nondeterministic choice is modeled by the conflict of the immediate transitions \(T^I_{\text {start}\_1}\) and \(T^I_{\text {start}\_2}\) if a token is in \(P^d_{\text {choice}}\).

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Fig. 3.
figure 3

Tank system modeled as singular automaton with random clocks [40]. The fluid level of the tank is modeled by the variable x. The nondeterministic choice is highlighted. The active time for the two valves is given by the clocks \(c_1\) and \(c_2\). Additionally the random blocking times for the valves are modeled by the random clocks \(r_1\) and \(r_2\).

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Niehage, M., Remke, A. (2024). The Best of Both Worlds: Analytically-Guided Simulation of HPnGs for Optimal Reachability. In: Kalyvianaki, E., Paolieri, M. (eds) Performance Evaluation Methodologies and Tools. VALUETOOLS 2023. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 539. Springer, Cham. https://doi.org/10.1007/978-3-031-48885-6_5

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