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<doi>R03-02-012-cd</doi>
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<article-title>Advanced Markov Modeling and Simulation for Safety Analysis of Autonomous Driving Functions up to SAE 5 for Development, Approval and Main Inspection</article-title>
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<author>Ivo H&#228;ring<sup>1,a</sup>, Yupak Satsrisakul<sup>1,2,b</sup>, J&#246;rg Finger<sup>1,c</sup>, Georg Vogelbacher<sup>1,d</sup>, Corinna K&#246;pke<sup>1,e</sup>, Fabian H&#246;flinger<sup>1,f</sup>, and Patrick Gelhausen<sup>3</sup>  </author>

<aff><sup>1</sup>Fraunhofer EMI, Freiburg, Germany. </aff>

<email><a href="mailto:haering@emi.fraunhofer.de"><sup>a</sup>haering@emi.fraunhofer.de</a></email>

<email><a href="mailto:finger@emi.fraunhofer.de"><sup>b</sup>finger@emi.fraunhofer.de</a></email>

<email><a href="mailto:vogelbacher@emi.fraunhofer.de"><sup>c</sup>vogelbacher@emi.fraunhofer.de</a></email>

<email><a href="mailto:koepke@emi.fraunhofer.de"><sup>d</sup>koepke@emi.fraunhofer.de</a></email>

<email><a href="mailto:hoeflinger@emi.fraunhofer.de"><sup>e</sup>hoeflinger@emi.fraunhofer.de</a></email>

<email><a href="mailto:Gelhausen@emi.fraunhofer.de  "><sup>f</sup>Gelhausen@emi.fraunhofer.de  </a></email>

<aff><sup>2</sup>Endress &#43; Hauser InfoServe GmbH&#43;Co. KG, Freiburg, Germany. </aff>

<email><a href="mailto:yupak.satsrisakul@endress.com  "><sup>b</sup>yupak.satsrisakul@endress.com  </a></email>

<aff><sup>3</sup>University of Hagen, Human-Computer Interaction, Faculty of Mathematics and Computer Science, Hagen, Germany. </aff>

<email><a href="mailto:gelhausen@fernuni-hagen.de ">gelhausen@fernuni-hagen.de </a></email>

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<title>ABSTRACT</title>
<p>The development, approval and recurring testing of driving assistance, partial and conditional automation (SAE levels 1 to 3) and, above all, high and full automation (4 to 5) requires an ever-increasing effort. At the same time, there is a lack of recognized sufficiently scalable general quantitative approaches in this area, in particular simulation methods including models, software and hardware up to vehicle-in-the-loop simulations, e.g. in the context of main inspection. In this context, the paper explores the potential of non-classical Markov modeling. First, it exemplifies how vehicles, drivers and other road users can be modeled for different driving scenarios using the Systems Modeling Language (SysML). Based on this model an abstract Markov diagram is presented. The two Markov simulation methods used operate on a discrete finite state space and allow for time-dependent state transitions. When compared to the matrix solver-based simulation, the Monte Carlo based simulation method is in principle extensible to state history-dependent as well as rule-based state transitions. Also, it allows to include subsystem simulation models. The extended Markov model allows to evaluate states with respect to functionality and safety, e.g. to determine whether it is sufficiently likely to reach fail operational states. It can also be used to determine dominant critical transitions and insufficient system resolution. In addition, numerous standardized safety and reliability measures are accessible. It will be shown how such a reference model can be quantified using simple failure models, as well as how it could be fed with further transition and failure models at different levels of abstraction using simulations as well as software tests data up to field test data. Finally, the paper hints at the potential of such an extended Markov modeling, especially with respect to an understandable and efficient safety verification in different product life cycle phases including after-sales.</p><p>  <italic>Keywords: </italic>Non-classical Markov model, Autonomous driving function, Safety and security assessment and simulation, Model-based system engineering, Monte Carlo simulation. </p>
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